But immediately prior to the telescopic era, the most accurate mapping to date of the celestial sphere had been carried out by the Danish astronomer Tycho Brahe. After Tycho's death, his assistant Johannes Kepler analysed his astronomical data to come up with the famous laws of planetary motion.
Kepler worked at the forefront of the mathematics of the time, using recently published tables of logarithms, including logarithms of trigonometric functions (without which he admitted that he would have given up his work as too laborious), and having to develop elements of differential calculus himself. He also, incidentally, had to fight off numerous challenges from Tycho's relatives who wanted to assert rights over the data Kepler was using.
Recently I got into a conversation with some people about the accuracy of Tycho's data, the type and quality of his instruments, and the level of mathematical skill and intuition needed by Kepler. We wondered if today's average educated person could reproduce what he did. We suspected that they could not -- even with the mathematical advances since Kepler's time.
As a lesson in humility, yesterday I was reminded that I have difficulty understanding even the apparent motion of the most conspicuous celestial object -- the Sun. I was out for an early morning stroll on Dun Laoghaire pier, and I snapped this picture of sunrise:
That dark blob on the horizon just left of the Sun is "The Muglins" -- a rock which poses a navigational hazard, and you can just about see the silhouette of its pointed warning beacon. To the right of the Sun, the first tiny artificial protuberance you see is the cylindrical Martello tower on Dalkey Island, built in 1804 at the start of the Napoleonic Wars as a lookout for a possible French invasion. The east edge of the island is visible in this view, but the tower is peeking up from behind the promontory at the end of Scotsman's Bay in Sandycove.
Those landmarks, combined with my known position half way along the east pier, allowed me to get a compass bearing on the position of sunrise. With the winter solstice only a fortnight away I was interested in how much further the sun has to travel to its most southerly point of sunrise. I found the bearing was in excellent agreement with the expected value: 128°, as measured clockwise from north:
Looking up timeanddate.com, I see that the most southerly sunrise will be at 130°, before the sun moves north again, rising due east at the vernal equinox, and at its most northerly point of 47° on the summer solstice.
But hang on! 130° is 40° south of east, while 47° is 43° north of east. The variation in the position of sunrise is caused by the fixed tilt of the earth's axis in space, and it must be tilted toward the sun on one side of its orbit by exactly the same amount as it is tilted away on the other. What gives?
Try checking the position of the sunrise at the solstices for your latitude ... I wonder if you see the same asymmetry.
251 comments:
1 – 200 of 251 Newer› Newest»A puzzle this early in the morning? Aaaaargh!
Is the discrepancy normal?
Sounds kind of like we're wobbling.
Beautiful sunrise pic. I might have to learn how to upload pics to my computer. My camera is digital, but my phone is rather...er...cheap, as I've been informed again and again by various people. So it doesn't make it easy to upload, although I've managed to send pics to people.
I managed to bake off four part batches of cookies yesterday, and am going to finish the other two today. Plus I forgot the candy I always do. I'll have to run over to the grocery store for ingredients. And each year I vow to cut back. *sigh*
"Is the discrepancy normal?"
When I set out to write the post, I had no idea. The reason for it came to me while I was writing it. I still haven't checked if I'm right but it's a fair old hunch. Will leave you to chew on it a bit more ;-)
P.S. No, it's not a wobble as such. The earth's axis does wobble, but as one wobble takes 26,000 years, it can't be the cause of our asymetric sunrise. (The wobble is the result of gyroscopic precession caused by the moon's gravity pulling on the earth's equatorial bulge. That's a fancy way of saying it's pretty much the same reason you wobble when you take your hands off the handlebars on a bike -- your lateral balancing motions cause the front wheel to precess left and right).
"What gives?"
The earth happens to be not precisely spherical. Or you're not allowing for the fact that magnetic north is not true north. Or the sun doesn't set dead east at your location when you think it should (not allowing for a parallax effect). Pick one; pick more than one maybe.
"The earth happens to be not precisely spherical. Or you're not allowing for the fact that magnetic north is not true north. Or the sun doesn't set dead east at your location when you think it should."
Nope, none of the above. (The first and third are true, but are not the cause of the effect).
Okay, I checked. I used Minneapolis as they didn't have my town listed. But it's close enough.
Minneapolis is at 45 (dang it, cheap keyboard, I don't have a degree sign) degrees. At the winter solstice in December the sun is at 123 degrees. At the summer solstice in June the sun is at 55 degrees. The difference in winter is 33 degrees from east( 90 degrees) and and the difference in summer is 35 degrees from east. The variation being 2 degrees. Whereas the variation was 3 degrees at your location. We are further north than you are.
You know, this might be easier if I had a visual. Hmmm...maybe if I look at the blog background for a while.
Soooo I'm thinking that the closer you get to the equator the greater the variance. Something to do with the Earth being spherical and how the sun hits the surface.
*sigh*
Okay, my brain is overloading, I'm going to go read the paper and see who has killed whom today.
"The variation being 2 degrees."
Ok, so it's not specific to Ireland. It's a bit less extreme at your latitude, but then so are day length variations in general.
"We are further north than you are."
Ahem. No, you're 8° further south. In spite of you getting all that snow and us getting none, we're considerably closer to the north pole :-)
"Soooo I'm thinking that the closer you get to the equator the greater the variance."
Other way round, in fact.
It seems that Petes is taking his numbers off of the website entirely. No measurments of his own to screw up. So… It's a parallax effect. (They'd not have missed using true north and are probably not interested in geography, so they won't have adjusted for geography; that leaves the parallax effect.) That's why Petes deleted that part when copied my quote and then said I was wrong. He had to delete that part to keep his word game going. (0° longitude 0° latitude is point at sea level on the equator in the eastern Atlantic. The variance is the result measuring the angle at a distance from that 0,0 point.)
Ahem. No, you're 8° further south.
Huh! Yes, you're right. I was mixing up your dial with the degree measurements.
That makes it doubly unfair that we get more snow then.
We've got the equivalent of more than 12,000 Niagara Falls of warm water circulating up from the Gulf of Mexico, where it starts out at up to 80 F. It means our average winter temperature is more than 20 F warmer than it has any right to be for our latitude.
Basically, we're robbing all your heat, thank you very much :) :) :)
"That's why Petes deleted that part when copied my quote and then said I was wrong. He had to delete that part to keep his word game going."
LOL. I deleted it to cut down on extraneous noise. Should've known it would spark Jesuitical howls. :)
"So… It's a parallax effect (They'd not have missed using true north and are probably not interested in geography, so they won't have adjusted for geography; that leaves the parallax effect.) ... 0° longitude 0° latitude is point at sea level on the equator in the eastern Atlantic. The variance is the result measuring the angle at a distance from that 0,0 point."
LOL some more. So you reckon they "adjusted for geography" to calculate the time of sunrise -- otherwise my 6°W longitude would throw the time off by 25 minutes or so, and Lynnette's would be wrong by over six hours. But didn't bother adjusting when calculating the angle of sunrise? Wouldn't that mean they show the same angle for every location? But they don't. Mine and Lynnette's are different. If you try a city near the equator like Nairobi, it's very different.
Quite apart from all that, it wouldn't explain an asymmetry between the angles in mid-summer and mid-winter.
"Wouldn't that mean they show the same angle for every location?"
No.
Since you haven't pounced on it yet (means you hadn't noticed the rough editing) The variance is, technically, a function of the distance from the nearest point of the equator, the 0° latitude at sea level.
"The variance is, technically, a function of the distance from the nearest point of the equator, the 0° latitude at sea level."
Well yes, we know that. Lynnette just measured it for Minneapolis and it's less than for Dublin. I'd already checked it for various latitudes (as I hinted in the last sentence of the post). So the question is not whether it's a function latitude -- it's why it's a function of latitude.
Latitude at sea level to be precise. And the answer is parallax. Still!
Lynnette,
The Republicans haven't given up on Benghazi yet. See this week's Weekly Standard. They won't give up on unless Hillary decides not to run for president. (If she wins they'll never let it go--it'll become another entrenched Republican fairie tale history.)
"And the answer is parallax. Still!"
You've got a decidedly odd idea of what parallax is. (Not that you having odd ideas is unprecedented). We're looking to explain a discrepancy in the behaviour of the sun as viewed from a single location on different dates.
"You've got a decidedly odd idea of what parallax is."
Trust me, you don't want to do this one either. Wait for one ya got a chance at winning.
Trust me. Yer talkin' through yer anus -- it's nothing to do with parallax. I'd have happily given you the real explanation. Now we're just gonna have to watch you make a fool of yourself. Except, knowin' yer M.O., I'm gonna predict right now that you just keep mutterin' "because parallax" til the cows come home, and never elaborate on what you mean. Fact is, you don't mean anything, you just found a fancy word to misapply.
"I'd have happily given you the real explanation."
But now ya can't. Boxed yourself out.
Oh no, don't worry: I can. And will. I'll just wait about a week to give you a chance to explain yourself. You won't, of course. And you won't explain why you won't. But the rest of us will know, and that's good enough for me.
Post Script to Lynnette,
I mentioned that the sun didn't sit dead east when he thought it should. (Sun Dec 07, 10:30:00 am) If you check the web site he gave ya for the spring equinox (21 March 2014) you'll find they compute it comes up about one and a half degrees north of due east for his latitude.
He's given himself a full week to figure out how to explain that other than as a result of the parallax effect. Might be worth the wait just to watch those contortions.
Ciao for now.
Guess that'll be about the same for the 2015 spring equinox, so the typo there shouldn't matter.
LOLZ. Apart from the fact that the phenomenon we're trying to explain is an asymmetric view of the sun from the same location on two dates, and therefore can't possibly be anything to do with parallax, let's just consider Lee's factoid.
On the equinoxes, the sun crosses the equator, which is another way of saying the axial tilt of the earth is bolt upright with respect to the plane of the earth's orbit on those two dates. For any point on the earth, on any date, the sun rises as that point comes around the limb of the planet. For a point on the equator at the equinox, the sun rises directly east for obvious reasons.
Now consider a point north of the equator, say Dublin or Minneapolis, between three and four thousand miles north of the equator. As they come around the limb at sunrise, the direction the sun must be south of east. Has to be, since they are north of the equatorial plane. On the other hand, if you divide the distance to the sun by their distance above the equatorial plane you only get a fraction of one part in 25,000 or so, so the parallax effect is going to be utterly tiny.
But let's split hairs anyway. The parallax argument says the sun must rise (a very tiny bit) south of east in the northern hemisphere at the equinoxes. timeanddate.com says it rises north of east. Whatever the explanation, it sure as hell ain't parallax.
You need to allow for the effect of measuring the parallax across the disk as opposed to figuring it on point source as one can get away with at the equator. Try again.
Oh, and by the same token, the sunset would have to be south of west. Check that out for Dublin at the equinox. Nope -- that's north of west too. And the magnitudes of the offsets are way higher than could be explained by parallax, even if they weren't in entirely the wrong direction. Oh dear, oh dear. Ain't lookin' good for that parallax explanation (assumin' Lee even understood what he was arguin', which is debatable ... cue some furious Googlin').
"You need to allow for the effect of measuring the parallax across the disk as opposed to figuring it on point source as one can get away with at the equator. Try again."
Sun's disk? Earth's disk? What disk are you rabbitin' on about? Can't be the former, since that appears as a disk wherever you are. Can't be the latter because the line to the sunrise is tangent to the earth's surface wherever you observe it. So you try again.
"What disk are you rabbitin' on about?"
I would have thought the reference to a ‘point source’ would have made that clear enough. But, ya got a full week yet. (Since the sun rises straight up at the equinox, as viewed from the equator, the difference between it being a disk or a point source will manifest itself as a measure of time and not of angle.) Try again.
Very good. Fine piece of Googlin'.
The effect you are referring to is not longitude dependent though. How does that square with this statement:
[Lee C]: "0° longitude 0° latitude is point at sea level on the equator in the eastern Atlantic. The variance is the result measuring the angle at a distance from that 0,0 point."
Seems you've refined your definition of parallax :)
You've got another problem though. Minneapolis is as near as makes no difference to 45°N latitude. Therefore sunrise makes a 45° angle with the horizon. The sun's disk is half a degree wide. Sunrise is measured at the centre of the disk. The translation from time into azimuthal angle compared to the equator doesn't get you more than a quarter of a degree. Better than your last attempt, but still not big enough. Care for another attempt?
Haven't hit google yet. May come a time for that. Probably won't. Ya still got a week.
Fine by me. I think you mean you've still got a week. I don't need any time.
"Seems you've refined your definition of parallax"
Sorta….
"The variance is, technically, a function of the distance from the
nearest point of the equator, the 0° latitude at sea level."
Lee C. @ Mon Dec 08, 07:09:00 am
I'm sure you'll get caught up eventually. Ya still got a week.
"I don't have a degree sign,"
Hold down the left ALT key and hit 0-1-7-6 in sequence on the keypad, and then release the ALT key.
°
That works! :)
We've got the equivalent of more than 12,000 Niagara Falls of warm water circulating up from the Gulf of Mexico, where it starts out at up to 80 F.
At the moment you do. You never know, if that current is slowed or stopped then you're going to be a peoplesickle just like us. :)
"Whatever the explanation, it sure as hell ain't parallax."
Petes @ Mon Dec 08, 11:17:00 am
"And the magnitudes of the offsets are way higher than could be
explained by parallax…"
Petes @ Mon Dec 08, 11:29:00 am
You seem to have yourself way confused. Parallax isn't the cause. It is the observed result.
Your opening question, the one I answered was:
"130° is 40° south of east, while 47° is 43° north of east. The variation
in the position of sunrise is caused by the fixed tilt of the earth's axis in
space, and it must be tilted toward the sun on one side of its orbit by
exactly the same amount as it is tilted away on the other. What gives?"
And the answer is that the dawn opens at around 88°30' at your latitude on the spring equinox, not at 90°. Even you should be able to do the rest of the math yourself from there.
I wonder will we have cannibal season :)
" Parallax isn't the cause. It is the observed result."
You may want to save the meaningless drivel for someone who can't spot meaningless drivel.
"Even you should be able to do the rest of the math yourself from there."
LOL. Google not finding the answers for ya? ;-)
Still ain't been to Google. All that would mean, had I been, is that all it takes to blow your shit up is to know what to google. I do believe I'm gonna check out your date/time.com thing again to see how the variables work for the southern hemisphere and the fall equinox, see if they match what I'd guess without doin’ some scratchin’ on paper.
Earth's rotaton
Does it have to do with the fact that the Earth's orbit around the Sun is in the shape of an ellipse rather than a circle?
*sigh*
"rotaton" should be "rotation"
Okay, why does it keep asking me to prove I'm not a robot? Does my own blog not even know me?
"…an ellipse rather than a circle?"
Probably not. That would effect the observed parallax; you do have that right.
However, Petes' website rounds off to whole degrees. That means any effect of less than a half-degree is the rounding error, and any effect from the out-of-round of the orbit probably ain't near ‘nuff to matter to us here.
(Ignore the cue for the clue; I've just been ignoring it and it posts anyway. Maybe if you'd clear your Blogger cookies and try again, it'd go away--that worked for me once--but now I just ignore it.)
@ Lynnette,
88°30' = 88½°
88½° is 1½° north of dead east.
41½° + 1½° = "43° north of east."
41½° - 1½° = " 40° south of east"
Petes didn't start out with an equinox at dead east is all that he's got goin’ there. The degree and a half that it's off of the 90° mark is the parallax.
LOL. Just as predicted, your stickin' to "because parallax". It's quite entertaining to see you not even understanding the meaning of the word. And the extended disc you are talking about doesn't account for the observed offsets-- how could it? ... the sun's only half a degree wide.
"Petes didn't start out with an equinox at dead east is all that he's got goin’ there."
Yeah, you didn't explain that one either.
"Does my own blog not even know me?"
Yeah, same here. I've been assuming it's because I'm logged into the wrong Google account. I've been switching between my public and private Google Drives today.
"Does it have to do with the fact that the Earth's orbit around the Sun is in the shape of an ellipse rather than a circle?"
That was the first thing that occurred to me, and I thought it was the answer. The sun is at one focus of the ellipse, not in the centre (Kepler's first law). So unless the solstices miraculously happen to be at perigee and apogee (the closest and furthest points in the earths orbit from the sun) the situation at two points six months apart will not be symmetrical, just as we hope to show.
The problem with that explanation is that the solstices are defined to be the most northerly and southerly points of the sunrise (roughly speaking). So if that doesn't happen six months apart, the solstice will occur whenever it does happen. And sure enough, if we look at the dates, its 184 days from the June solstice to the December one, and only 181 from December to June. (Perigee occurs in early January, so the earth is moving faster in the first half of the year).
So no, the solstices really are the most northerly and southerly points of sunrise. It's just that one or both of them seems to be too far north. And it turns out that the equinoctial sunrise is too far north as well. And it turns out all the corresponding sunsets are too far north too. The lack of symmetry is complete. To balance it out, we'll find (or, at least, Lee will) that in the southern hemisphere, all the events are too far south.
P.S. Don't believe anything Lee says about parallax. He's confused.
"It's quite entertaining to see you not even understanding the
meaning of the word."
See Merriam-Webster
"par·al·lax noun \'pa-rÉ™-,laks\
"Definition of PARALLAX
": the apparent displacement or the difference in apparent direction of
an object as seen from two different points not on a straight line with the
object; especially : the angular difference in direction of a celestial body
as measured from two points on the earth's orbit"
First linked at Lee C. @ Mon Dec 08, 07:42:00 am, supra.
Although, technically, the degree and a half that the equinox is off dead east at Dublin is merely a measure of the parallax in degrees, not the parallax itself.
"the difference in apparent direction of an object as seen from two different points"
LOL. "Because parallax" again. What two different points are you talking about? The asymmetry we're discussing is to do with observations from a single point.
"That was the first thing that occurred to me, and I thought it was the
answer."
If I'd had to bet I'd have bet that you were thinking about the atmospheric refraction, but then I realized that'd only get ya less than 4’ of deflection, way too small to ever appear in a chart rounding off to full degrees. Just off the top of my head, I'd still bet that's way higher than any variance introduced by the elliptical nature of Earth's orbit.
"The asymmetry we're discussing is to do with observations from a
single point."
Geometry's not your strong suit is it?
"To balance it out, we'll find (or, at least, Lee will) that in the
southern hemisphere, all the events are too far south."
That would have been my bet, but I hadn't checked it out yet (nor sketched out on a pad either to see if I was missing something, which I'd thought about doin’ before I checked the charts).
"Geometry's not your strong suit is it? "
You're the one that seems to think we're observing from two different place ...
"the difference in apparent direction of an object as seen from two different points"
Hang in there though, ya still got most of a week to try to fix getting your college astrology educated ass clocked by a hillbilly.
"You're the one that seems to think we're observing from two different
place[s] ..."
You are talking about the winter and summer solstices, are you not?
"Hang in there though, ya still got most of a week to try to fix getting your college astrology educated ass clocked by a hillbilly."
So far all ya done is abuse the word "parallax".
"You are talking about the winter and summer solstices, are you not?"
Yup. As viewed from a single terrestrial location.
Your ‘single terrestrial location’ will have moved to the other side of the sun between the winter and summer solstice. That's a distance of roughly 186-187 million miles in displacement, measured in a straight line straight through the sun. Traveled distance is much further, of course.
And, now, back to explaining it to Lynnette:
"@ Lynnette,
***
88½° is 1½° north of dead east.
41½° + 1½° = ’43° north of east.’
41½° - 1½° = ’40° south of east’"
Petes didn't start out with an equinox at dead east is all that he's got goin’ on there. The degree and a half that it's off of the 90° mark is the parallax between the equator and Dublin's latitude.
Petes seems to have gone quiet. I suspect there is some ongoing ‘googling furiously’ going on. That's okay.
Google is your friend.
"Your ‘single terrestrial location’ will have moved to the other side of the sun between the winter and summer solstice."
Yep, and the sun will have moved more or less 180° against the background stars. If y'all wanna claim that's the parallax shift yore talkin' about, be my guest. That'd be an even more entertaining line to take. Maybe the answer is the sun has an affinity for certain zodiacal constellations, seein' as you mentioned astrology :)
Petes seems to have gone quiet.
Ya see, there's your problem right there. You'd think someone workin' furiously on the present problem would have a particular understanding that nighttime occurs at different times in different places :-)
"The degree and a half that it's off of the 90° mark is the parallax between the equator and Dublin's latitude."
LOL. "Because parallax". I'll ignore that a minute ago you were claimin' some significance to the parallax due to earth's orbit, and point out a couple of flaws with your present thesis:
1) Nobody moved from the equator to Dublin in makin' the present measurement.
2) The parallax angle of the sun
in movin' from the equator to Dublin is 0.012 degrees -- more than a hundred times smaller than the effect you claim it explains.
Keep tryin'.
"If y'all wanna claim that's the parallax shift yore talkin' about, be
my guest."
I never claimed that. I was, in fact, surprised you tried to go there. As, obviously, it wasn't a comparison of measures taken from ‘a single point’.
"1) Nobody moved from the equator to Dublin in makin' the present
measurement."
Nobody was supposed to move.
"2) The parallax angle of the sun in movin' from the equator to Dublin
is 0.012 degrees…"
Measured from where? obviously not from Dublin.
"Measured from where? obviously not from Dublin."
Well, a parallex measurements involves two places. But allowin' for your ignorance of the definition, yep, from Dublin. Which all comes down to the fact that "parallex" never was the word you were scrabblin' for. Perhaps "declination" would be more apt for your purposes. Or maybe just plain "latitude". I dunno, since I don't have too much idea where you think your goin', apart from it ain't in the direction of the correct answer.
Yeah, typos.
To measure an angle you have to have three (3) points. One is where you're measuring from. The other two are the ones you're measuring the angle between.
How the hell do you manage to calculate the angle between the nearest point on the Earth's equator to Dublin and the sun to be less than .013° as viewed from Dublin?
That's absurd on its face.
"...the apparent displacement or the difference in apparent direction of an object as seen from two different points"
That's the definition of parallax you gave us your very own self. Those are the two points I am referring to.
"To measure an angle you have to have three (3) points. One is where you're measuring from. The other two are the ones you're measuring the angle between."
Nope. The term you are scrabblin' for there is the subtended angle.
"How the hell do you manage to calculate the angle between the nearest point on the Earth's equator to Dublin and the sun to be less than .013° as viewed from Dublin?"
Well, accordin' to your own line of thinkin' that you're tyin' yourself up in knots with, any three points forming a triangle involve three angles, so which one are ya talkin' about? I'll save ya the trouble -- the parallax angle, i.e. "the angular difference in direction of a celestial body" of your definition, is 0.012 degrees. That's when you move the perpendicular distance to Dublin from the equatorial plane.
That's got nothin' to do with what happens when you move around a curved surface. Then you oughta be dealin' with declination. On the rare occasions when the word parallax is used in connection with such a movement, it'll be something like "the horizontal parallax of the moon" (look it up), in which case the distance measured is the chord of a circle through the earth (not the angular distance moved around its circumference), i.e. exactly what I just did there.
Parallex ain't the word you are lookin' for. Get over it.
Post Script:
I think this is the fourth time you've said something was ‘because parallax’. I would remind you again that the parallax effect is not a cause; it's an effect.
"I would remind you again that the parallax effect is not a cause; it's an effect."
Good. That allows us to ignore your total confusion over the definition of parallax. If it ain't the cause of the displacement of sunrise that we are discussin', perhaps you'd like to tell us what is, 'cos yer sure as hell devotin' a lot of column inches to what it isn't.
"Parallex ain't the word you are lookin' for. Get over it."
Ah, I wondered when you'd finally get to here. Yes, the word I was looking for was indeed and remains ‘parallax’, the perceived displacement of an object when viewed from two different points. (In this case, one place being Dublin and the second one on the equator)
However, that argument doesn't change the fact that the reason your measurements of the solstices are 43° north of east and 40° south of east is because it's 1½° north of east at the equinox. The tilt is indeed exactly the same both ways. You just started from 1½° north of east as a beginning point and then got yourself confused from there.
"Nope. The term you are scrabblin' for there is the subtended angle.
Any angle. A measurement between only two points is called a straight line.
"That's when you move the perpendicular distance to Dublin from
the equatorial plane."
That would be in error also. It's not the perpendicular one should use--it's the tangent of the arc between Dublin (at sea level) and the nearest point on the equator. Check the definition again; it says nothing about right angles being required. (Geometry is certainly not your strong suit.)
"You'd think someone workin' furiously on the present problem…"
I'm not the one who hunted up the obscure (and incorrect) reference to a ‘subtended angle’. I've just been coasting (and I took a nap).
Speaking of naps… I think it's time to let you ‘google furiously’ without me for awhile. I'll look in on ya later to see what other foolishness you've managed to come up with. (Well, actually to ask if Lynnette's got it, but I'll look for you too.)
"Yes, the word I was looking for was indeed and remains ‘parallax’, the perceived displacement of an object when viewed from two different points. (In this case, one place being Dublin and the second one on the equator)"
That's not parallax. Not even close. If it's parallax, then how come the displacement of the sun viewed at local noon on the equinox in Dublin from its position at the equator is 53°? Same object -- the sun. Same two points -- Dublin and corresponding longitude at the equator. Displacement is 1.5° of azimuth at sunrise, 53° of declination at noon. That's got damn all to do with parallax.
"You just started from 1½° north of east as a beginning point"
Yeah. Why? That's the question that was posed. All you've done so far is repeat it.
"A measurement between only two points is called a straight line."
Uh uh. Check your own definition. It's from two points to a celestial body (the sun in this case). I presume you're not claimin' you have to go to the sun to make such a measurement.
"it's the tangent of the arc between Dublin (at sea level) and the nearest point on the equator."
LOL. That don't even mean anything. (Not in this context, at least).
Tell ya what. I'm gonna cut ya some slack and ignore that you don't know what parallax is. You already admitted it's not the cause of anything we're interested in, so you can call it "smelly goat's cheese" if you want.
What's the reason for the displacement of the sunrise to the north, as in the original question?
Hint: the answer ain't "because smelly goat's cheese".
Damn near asleep when this thought grabbed me.
"It's not the perpendicular one should use--it's the tangent of
the arc between Dublin (at sea level) and the nearest point on the equator."
If I recall my high school math correctly, that'd be a ‘chord’ not a tangent. Okay now I can sleep.
LOL. Check my post of Tue Dec 09, 02:06:00 am. Chord is exactly the term I used. Are you gonna me this slow to catch up the whole way along? I'm not sure a week's gonna be enough for y'all.
Oh hell, you posted while I's correcting that. I'll do you up later. You don't rate staying up for just now.
Ciao for now.
Damn, couldn't sleep. Knew you'd whine that I was googling instead of sleeping. So, I didn't do either; I typed. (Still don't understand why you think it's helpful for you to point out that anybody who can google up the right terms can blow your shit outta the water.)
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"Check my post of Tue Dec 09, 02:06:00 am. Chord is exactly the
term I used."
You seem to have used every term you could think of to throw at this. ‘Parallax angle’ (I don't think that's a real term; I think you made that one up), ‘declination’, ‘horizontal parallax’ (by the way, Merriam-Webster had twelve separate definitions of separate types of parallax as I recall, including ‘medical parallax’) ‘chord’, ‘angular distance’, ‘azimuth’, just to name a few. Jargon-babble to see if you can get your readers lost, as is your custom when hard pressed. Don't generally work on me; we've been through this before. Didn't work this time anyway.
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"What's the reason for the displacement of the sunrise to the north,
as in the original question."
It's called parallax, i.e.
Merriam-Webster
"par·al·lax noun \'pa-rÉ™-,laks\
"Definition of PARALLAX
": the apparent displacement or the difference in apparent direction of
an object as seen from two different points not on a straight line with the
object;"
‘Parallax’ That's the name of effect that makes the sunrise at equinox appear 1½° north of east in Dublin when the sunrise appears dead due east at the equator some few minutes earlier on that same day.
Do ya got that part yet?
We'll get to the reason it's 1½° different at Dublin and the equator a little later, but first we need to let this much sink in through that thick skull of yours.
Cause it's that 1½° of parallax that caused you to question the readings of ‘40° south of east’ as compared to ‘43° north of east’. That was the question you put on the main page; that's the question I answered.
Why it's 1½° instead of some other number is whole ‘nother question. (But, I can answer that one for ya too.)
And, finally, just about to doze off, I realized that I'd pegged the equinox to the prime meridian, which is not quite right.
Equinox will actually hit in Dublin at 4:57 pm, Dublin time. So scratch that ‘few minutes earlier’ part.
Gawd. How much more verbiage is there gonna be? How about answers?
"‘Parallax’ That's the name of effect that makes the sunrise at equinox appear 1½° north of east in Dublin when the sunrise appears dead due east at the equator"
Nope. It ain't.
"We'll get to the reason it's 1½° different at Dublin and the equator a little later, but first we need to let this much sink in through that thick skull of yours."
I think you should cut to the chase. 'Cos your use of "parallax" is gettin' embarrassin'. By way of incidental education, I drew you a little picture showing actual parallax. Dublin is the red star. That vertical line is a chord through the earth. It's sunrise at the equinox. The line from the equator is due east. You claimin' the line from Dublin to the centre of the sun is anything other than south of east? By 0.012 degrees of parallax as it happens :)
But don't pay that no never mind. Over to you to explain why it's displaced 1.5 degrees to the north. After you explain it I don't care if you choose (erroneously) to call the cause "parallax" or "smelly goat's cheese".
" So scratch that ‘few minutes earlier’ part."
I didn't even bother correctin' you on that. At this stage I'm wonderin' if you're throwin' in asinine comments just as a smokescreen.
"Knew you'd whine that I was googling instead of sleeping."
What, like you did to me? I'd never be that unreasonable ;-)
But seen as yer claimin' to be awake ... where y'all at? Is that the sound of furious Googlin'? Did the fact that parallax deflects the sun to the south, not the north upset y'all that much? Well it should have, 'cos it blows your shit outta the water.
You still don't get it. I'll try again:
Merriam-Webster
"par·al·lax noun \'pa-rÉ™-,laks\
"Definition of PARALLAX
": the apparent displacement or the difference in apparent direction of
an object as seen from two different points not on a straight line with the
object;"
(emphasis added)
The apparent difference--NOT what the parallax would otherwise be if the axis weren't tilted relative to the orbit or the horizons weren't variable with point selected. (Neither of which is true.)
"…then how come the displacement of the sun viewed at local noon
on the equinox in Dublin from its position at the equator is 53°?"
Combination of the tilt of the Earth's axis relative to it's orbit, and the difference in the planes of the horizons at the different points on the Earth's surface. (Plus or minus what the parallax would otherwise be absent either or both of those things as a variable.)
"Over to you to explain why it's displaced 1.5 degrees to the north."
First, there's the angle of the tilt of the axis to the Earth's plane of orbit to figure in. Second, there's the shift in the direction (the plane) of the perceived horizon from point to point as one moves across the globe. Then there's the actual degree measurement to get, what would be measured across the relevant distance between the two points on Earth if the two horizons were in the same plane (which they are not often and never in the case of Dublin and the equator), then there's the arc and width of the sun to consider, and we're now down to half a degree (as the width of the sun according to you earlier), and your charts round off the measurments to the nearest degree, so we're at the margin of error right here and don't need to throw in any further factors which would lead to any changes of less than 30 minutes, like perhaps refraction or the variable distance to the sun from the elliptical orbit. It's gonna be a fairly complicated math problem and I don't even intend to try to set it up and solve it, even with a computer. That's why they publish those charts.
You said you were gonna tell us why it's 1.5 degrees?
And, now that you've obviously figured out that the 1½° off dead east at equinox explains the difference between ‘43° north of east’ and ‘40° south of east’, I figure I've answered both your original question, and the one you thought up later to try use as cover for having not been able to figure out the first one.
And I will bid you ado for the evening.
"You said you were gonna tell us why it's 1.5 degrees?"
‘Cause when they figured out all that stuff I listed at Tue Dec 09, 04:48:00 am, that's what it calculated out to be.
No, I did not tell you I was going to show you the math calculations.
"No, I did not tell you I was going to show you the math calculations."
Lee, seven posts earlier:
"Why it's 1½° instead of some other number is whole ‘nother question. (But, I can answer that one for ya too.)"
So we just have to take your word for it that all those factors combine to give the right number? Shucks, for a minute I thought you were gonna do something other than just make your standard declaration of yourself to be correct.
Tell ya what, to make it easy, just tell us how you combine them. No need to crunch the actual number. I'll do that for y'all as a free service (no really, no need to thank me). Just gimme the procedure.
;-)
"So we just have to take your word for it that all those factors combine
to give the right number?"
My word for it? Hell no. I'm talkin’ their word for it. I'm just assuming you got us accurate charts. If you didn't then it won't be 1½° after all, but that's not my problem.
My problem you can't give it up when you're whupped, and everybody knows it.
(I told you this wasn't the one you wanted. I warned ya. You're needin’ to learn patience; chose your fights, pick your shots.)
Hell, I don't even know that it's really ‘43° north of east’ and ‘40° south of east’; I never been to Dublin during a solstice. I'm just assuming your chosen experts in the field came up with the right numbers.
"Just gimme the procedure."
Don't think it'd do you any good. We've pretty much established that geometry ain't your strong suit. (Probably should have realized that when you built your shed too small for your telescope.)
LOLOLOL. Hey, I can do that too. Watch this:
Well, first, there's the angle between Jupiter and Mars to figure in. Second, there's the shift in the direction of the perceived roof line of my house as you proceed across the garden. Then there's some other number that you'd get if you measured some relevant factor. Then there's the arc and width of the sun to consider, and we're now down to half a degree (the width of the sun), and the charts round off the measurments to the nearest degree, so we're at the margin of error right here and don't need to throw in any further factors blah blah bleurgghhh. It's gonna be a fairly complicated math problem and I don't even intend to try to set it up and solve it.
Voila: 1.5 degrees right there, 'cos otherwise the charts are wrong.
See how that works?
"I told you this wasn't the one you wanted. I warned ya. You're needin’ to learn patience; chose your fights, pick your shots."
LOL. I think it worked out quite well. We established once again, that you ain't just a dunce, you're a lyin' dunce who'll sink to any depths to declare hisself correct. Another good giggle for the audience.
"…'cos otherwise the charts are wrong."
If the charts are wrong then it's because the charts are wrong. That'd be your problem, not mine. I got the 1½° (roughly) at equinox from the charts. Wasn't hard to notice it matched up with the 3° difference between 43° and 40°.
"Wasn't hard to notice it matched up with the 3° difference between 43° and 40°."
In fact, I'm still at a loss for how you could have missed that, what with you bein’ all college educated in astro-whatever it was. Still got yer ass clocked by a hillbilly.
Ok, I have every faith in Lynnette to be able to detect the smell of bullshit. So I'm gonna lay out your instructions, and trust Lynnette to know if a value can be calculated from them, even in principle. What's more, I'm even gonna fill in the values that you didn't. Here we go:
1) "First, there's the angle of the tilt of the axis to the Earth's plane of orbit to figure in". Ok, that's easy. It's the equinox so that's zero degrees.
2) "Second, there's the shift in the direction (the plane) of the perceived horizon from point to point as one moves across the globe". That's easy too -- the perceived horizon is always a circle surrounding you no matter where you are. At the earth's surface the direction to it is the local horizontal. Never changes. So the shift is zero.
3) "Then there's the actual degree measurement to get, what would be measured across the relevant distance between the two points on Earth if the two horizons were in the same plane (which they are not often and never in the case of Dublin and the equator)". Well, that one's meaningless bullshit. But seein' as how you've been rabbitin' on about Dublin and the equator for reasons you never explained, I'm gonna assume this simply means the angular distance between the two, i.e. the latitude of Dublin, i.e. 53 degrees.
4) "then there's the arc and width of the sun to consider". Dunno what you mean by the arc. We'll take the width as half a degree.
And just for good measure we'll give honourable mention to the factors you said could be ignored:
5) "refraction"
6) "the variable distance to the sun from the elliptical orbit"
So now, I'll combine the name of each variable, it's value, and your instruction for what to do with it. Lynnette's job will be to use them to arrive at a value of 1.5 degrees, the assumed correct answer.
1) Tilt of axis to plane of orbit; 0 degrees; "figure it in"
2) Shift of the perceived horizon; 0 degrees; No instruction
3) Angular width from equator to Dublin; 53 degrees; No instruction
4) Arc(?) and width of sun; 0.5 degrees; "Consider it"
5) Refraction; unknown; "ignore it"
6) Variable earth-sun distance; unknown; "ignore it"
Now, if Lynnette can't figure out that you just laid a pile of meaningless bullshit at all our doors, I'll be quite surprised. Marcus too. Maybe even Canadian John, but I expect he'll have trouble expressing it in a way that won't get instantly deleted ;-)
You really wanna leave this as your "solution" to the problem? :) :) :)
The hilarious thing is the hillbilly announcin' ponderously that "it's gonna be a fairly complicated math problem and I don't even intend to try to set it up and solve it".
Actually, it's a completely trivial math problem that doesn't need half the variables he mentioned, and can be written in just eight characters.
1) …It's the equinox so that's zero degrees.
Nope, incorrect. The tilt of the axis relative to the plane of the orbit is somewhere between 20 and 25 degrees (I'll not bother to google it up). It remains thus tilted at all times, equinox, solstice, all points in between. It does not get straight with the plane of the orbit ever, except maybe on, I believe you said, it was a 26,000 year ‘wobble’ cycle (and I'm not sure how much it wobbles). The tilt changes relative to how it's positioned towards the center of the plane (i.e. it's tilted straight in towards the sun on the north at the summer equinox, straight out on the north at the winter equinox--but it stays fixed tilted relative to the plane of the Earth's orbit.). How much it's tilted towards or away from the sun at any particular dawn changes the distance from the sun to Dublin at dawn. The equator stays the same (or would if the orbit were round); Dublin ‘wobbles’ relative to the sun with a wobble period of one year.
"2)…The local horizon…Never changes. So the shift is zero."
Again, incorrect. The local horizon extends I think about 12 miles in a circle (figuring sea level flat) for a man with eyes about 5' 6" from the ground; figure a guy 5' 9" or 5' 10" tall has eyes at around 5' 6" above the ground. This circle has him at the center, so his horizon is angled approximately 53° differently in Dublin than would be the horizon he'd see at the equator (assuming you got that part correct), and one has to adjust any reading taken in Dublin to correct for that difference from a reading taken at the horizon at the equator. (The two ‘local’ horizons, if extended sufficiently, would intersect at a roughly 53° angle.)
And then it begins to get kinda tricky from there on out, so I'll just quit there. But, you didn't get a single one of them right. I'd have thought you'd have to get one right just by accident.
Are you just pretending to be this stupid? Or are you really this incompetent at perceiving spatial relationships?
"The equator stays the same…"
This was assuming we were talking about the distance to the equator at dawn. Dublin's dawn wobbles, changes day by day, with a wobble period of one year.
"Actually, it's a completely trivial math problem that doesn't need half
the variables he mentioned, and can be written in just eight characters."
Now comes the show part of your little show and tell story. Show us your eight character, completely trivial math problem.
And then I will tell you why you're fulla shit.
Correction: Got out my scratch pad out and drew a planet with tilt. Should have done that earlier. Summer equinox has the tilt 90° away from the sun (directly at the sun is summer solstice, so I'd spun it 90° out of phase in my head--knew that didn't feel right--which is why I got the pad out and drew the axis. Otherwise, the game remains the same.)
"Nope, incorrect. The tilt of the axis relative to the plane of the orbit is somewhere between 20 and 25 degrees"
Yep, yore right. 23.5 degree if memory serves me. Due to the symmetry of the problem at the equinox I thought you might want to use just it's component in the direction of the sun. That's 0 degrees. Thought I'd help y'all out there, but hey, if you think it needs to be more complicated I'll leave y'all to it.
"Again, incorrect. The local horizon extends I think about 12 miles in a circle (figuring sea level flat) for a man with eyes about 5' 6" from the ground ... blah blah blah blah blah ...The two ‘local’ horizons, if extended sufficiently, would intersect at a roughly 53° angle."
Yep, another stunning insight. Most people would just say Dublin's at a latitude of 53 degrees, but if y'all need to deal with the height of an average man (assuming gender doesn't matter to your Byzantine calculations too), be my guest.
"And then it begins to get kinda tricky from there on out, so I'll just quit there."
Thank God for that.
"Are you just pretending to be this stupid? Or are you really this incompetent at perceiving spatial relationships?"
Truth be told, I wasn't payin' that much attention. Most of yourn parameters don't matter a shiney shite to the required calculation. But you know that, right? You're just makin' it complicated so that you can spring it on me how you knew it was simple all along? That's gotta be it. You couldn't actually be pretendin' to need any of this stuff, knowin' full well I'm gonna show you up to be full o' crap?
Happy Googlin'. Y'all still got six days. If ya like I'll actually give you the formula and you can take the (somewhat) easier option of showin' how it's derived?
"Now comes the show part of your little show and tell story. Show us your eight character, completely trivial math problem. And then I will tell you why you're fulla shit."
Ooh. Now I'm all offended. Nah, go and figure it out yourself. I'll put you a different proposition. When you've got yer multi-parameter Byzantine maths all figured out (which we both know is never gonna happen, but I'm givin' you the benefit of the doubt for now), I'll pit my 8-character formula against yours and if it don't come up with the right answers I'll eat humble pie. Can't say fairer than that, now, can I?
"Summer equinox has the tilt 90° away from the sun..."
Hmm. Maybe check that. Last I looked, there warn't no equinox in summer. LOLZ.
"I'll pit my 8-character formula against yours and if it don't come up
with the right answers…"
You've already come up with the wrong answer. We've already seen that.
" Merriam-Webster
"par·al·lax noun \'pa-rÉ™-,laks\
"Definition of PARALLAX
": the apparent displacement or the difference in apparent direction of
an object as seen from two different points not on a straight line with the
object;"
(emphasis added)
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"Last I looked, there warn't no equinox in summer."
Yeah, March, spring. Not near ‘nuff sleep at this point. I mean to fix that soon as I can.
The only reason I'm still up now is I thought I'd get a read from Lynnette on whether or not she got that 1½° variance from what one would maybe expect to be a 90° reading, and how that translated into ‘40° south of east’ and ‘43° north of east’.
By the way, I have assume that you've finally figured that part out. But perhaps I should ask--you having any trouble finally figuring that piece of math?
Yawn. Now yore getting boring. I've got the 8-character formula. You got jack shit and don't know how to get jack shit, as you showed in yore smoke'n'mirrors attempt at Tue Dec 09, 04:48:00 am. Yore wastin' precious Googlin' time. Lemme know when you want to compare formulas. After all, it was you who took it on yoreself to turn this into a pissin' competition (at Mon Dec 08, 09:09:00 am). To which my reply is the same now as it was then:
"Trust me. Yer talkin' through yer anus -- it's nothing to do with parallax. I'd have happily given you the real explanation. Now we're just gonna have to watch you make a fool of yourself. Except, knowin' yer M.O., I'm gonna predict right now that you just keep mutterin' "because parallax" til the cows come home, and never elaborate on what you mean. Fact is, you don't mean anything, you just found a fancy word to misapply."
Tee minus six days and countin' ...
"Now yore getting boring."
And you're getting evasive. I will put the question again. ‘40° south of east’ and ‘43° north of east’. You having any trouble with the math of that coming off the center reading of 41½°
And now back to normal service while Lee furiously Googles. I see the US is worried for its embassy's safety due to the release of a report about how all that "enhanced interrogation" was just grubby torture after all. Same as abusive tyrants have been practicin' since time immemorial. Dems will want to avoid any more Benghazi incidents.
What is this thing with you and ‘googling furiously’?
I will put the (not google related) question again. ‘40° south of east’ and ‘43° north of east’. You having any trouble with the math of that coming off the center reading of 41½°? Or you got that now?
Yep, got that. Indeed, I've got a compact formula that calculates it. Have you?
(By the way, it's 1.4 degrees, not 1½. Did I mention my 8-character formula is also a lot more precise than timeanddate.com? How's yours comin' along ... must be very precise indeed with all those extraneous parameters you're feedin' it. LOLZ)
"Yep, got that.
Okay, then here's the final piece. I'll skip the stuff in the middle.
"Displacement is 1.5° of azimuth at sunrise"
Petes @ Tue Dec 09, 02:37:00 am
There's that same 1½° variance under another name. Although it took you until early in the morning to cough it up.
You want us to not use the Common English term¹ for the phenomenon generally known as ‘parallax’ in deference to your preference for the jargon heavy term ‘displacement of azimuth’ as the right name for that same phenomenon More of your jargon games; that's all this has been.
------------------------------
¹ ‘Parallax’ may not be a common English term for most people, but it is Common English, standard Merriam-Webster stuff.
Seems Lynnette is maybe not close to making a morning appearance. I'll drop off while you figure out how to phrase your coming claim that your preference for jargon is due the deference you demand.
LOLZ. You really are scrapin' the dregs of the barrel. Tell you what -- if you can find an authoritative reference that refers to this as a "parallax" effect, I'll happily concede your point. Hey, just find something approximately similar referred to as parallax. But you won't, cause that's not what it is. And if you could you wouldn't be spoutin' dictionary definitions here. Common English it may be, but as a term for changes of perspective around the curve of the earth, no it certainly ain't and you won't find a reference to that effect. So I'm calling your bluff on that.
A displacement around the azimuth is exactly what it is. It's got nothin' to do with the direction of the sun in space -- I already gave you the value for that: it's 0.012 degrees.
However, while we may entertain ourselves with yer misapplication of the terms, that's not what the original question was. And the answer still ain't "because parallax".
How's that formula comin' on? Y'all must have yer precision down to milliarcseconds at this stage! LOLZ. My poor 8-character one's probably only good to about a tenth of a degree.
"So I'm calling your bluff on that."
You're not calling my ‘bluff’ on anything. I'm not bluffing. I'm simply not granting you deference for your preferred jargon definition simply because you demand it. I speak English whenever I can; I was speaking English then. I'm giving you plain English now. I do not intend to change that for you.
And you can't change the Common English definition just by declaring it to be not from an ‘authoritative reference’ defined as techie source who shares your usage of jargon in this instance.
"And the answer still ain't ‘because parallax’."
Never was. Trying to redefine the parallax effect as a cause of something was always your endeavor; I never went along with it. How many times we gotta go down this road?
"How's that formula comin' on?"
Ah, that… First time I mentioned that was:
"It's gonna be a fairly complicated math problem and I don't even
intend to try to set it up and solve it, even with a computer. That's why
they publish those charts."
Lee C. @ Tue Dec 09, 04:48:00 am
So far, it's comin’ on just as I intended. And I must say I'm quite pleased with that.
Basically, it all boils down to this: You keep demanding that I have to use your preferred jargon definitions instead of Common English. But, I don't have to do that. Deal with it.
The only reason I'm still up now is I thought I'd get a read from Lynnette on whether or not she got that 1½° variance from what one would maybe expect to be a 90° reading, and how that translated into ‘40° south of east’ and ‘43° north of east’.
Yes, I understand what you were saying.
Seems Lynnette is maybe not close to making a morning appearance.
lol! Between getting some work done and reading the comments section it took me this long to come up for air!
I haven't done any trig or geometry since high school, or astronomy since college. It's a wonder I can dredge up anything from those classes considering all of the garbage that has been stuffed into my brain since then! lol!
This puzzle actually makes me want to retake some of the astronomy classes. Sometimes I think college is wasted on all those teenagers and twenty somethings out there. I would find it more interesting now.
P.S.
I did rather like that video I found about the Earth's rotation. It made it much easier to visualize the Earth's travels.
P.P.S.
Ignoring that test for robotic life did work.
I see the US is worried for its embassy's safety due to the release of a report about how all that "enhanced interrogation" was just grubby torture after all. Same as abusive tyrants have been practicin' since time immemorial.
Yup. Idiots. I doubt anyone will cut us any slack for going overboard. It's too good a propaganda coup to pass up. Never mind that other people are merrily chopping off heads willy nilly.
*sigh*
No, it boils down to this. I'm not demandin' anything. You can call it anything you like. If you check back up thread you'll see this is the third time I've said that. You're just lookin' for an excuse to get your panties in a twist, 'cos at this stage you reckon pantie-twistin' makes you look slightly less of a fool than not bein' able to come up with any goods. Pantie-twistin' lets you go on diversionary rants that you hope will stop folks from noticin' that you haven't actually come up with jack shit.
Fortunately I've set it all out for Lynnette at Tue Dec 09, 06:20:00 am above -- your wrong parameters and lack of any clue as to what's to be done with them. You think anyone's gonna think that pile of steamin' shit is the answer to somethin'?
I can see why you want to stick to yer rant about my imagined "demands". You ain't foolin' nobody.
Oops. Hi Lynnette :-)
That last was, of course, in response to Lee C @ Tue Dec 09, 01:17:00 pm.
"You can call it anything you like."
Very good.
"…you haven't actually come up with jack shit."
There's nothing else to come up with. The Common English definition of parallax covers it all, including the part you once wanted to sequester out under the alternate name of ‘displacement of asimuth’.
(That's where the math gets rather more complicated than ‘can be written in just eight characters.’)
"That's where the math gets rather more complicated than ‘can be written in just eight characters."
LOLZ. No it dudn't. I've got 8-characters that'll give you the location of the rising sun at the equinox from any place on earth. You got jack shit.
Yeah, I already knew that only worked during the equinox--no surprises there.
Nope. Check the very first post on this thread. The very original question from Lynnette. My 8 characters calculates the discrepancy for any location on earth, any time.
What does yours do? Oh yeah, I forgot ... you ain't got jack shit.
:) :) :)
Ok, I'm bein' a bit ungenerous. You got this:
"There's nothing else to come up with. The Common English definition of parallax covers it all".
Just as I predicted right back at the start. You got "because parallax". LOLZ.
Then your formula must necessarily only work for your restrictive definition of a ‘parallax’ which means it won't get you the observed 1½° variance from due east at equinox at Dublin. You're just playing jargon games again, redefining the ‘parallax’ from what I was talking about, to exclude that displacement you prefer to call ‘displacement of asimuth’
And just what is it that is supposed to happen ‘because’ of the observed parallax (Common English definition)? I've been wondering where you thought you were gonna go with that, but not enough to further complicate the issue.
LOLOLOL. Now yer really crackin' me up. :)
What restrictive definition of parallax are you yakkin' on about? I never had such a thing. My approach dudn't need any definition of parallax. As for the observed variance, y'all pointed out yourself that timeanddate is only good to an accuracy of half a degree. My 8-characters gives a more accurate value of 1.4 degrees.
I ain't redefinin' parallax. I don't need no steenkin' parallax -- not the real version, and certainly not your version.
But by all means, let's compare formulas to see where parallax enters into yours. Oh yeah, that little thing again ... you ain't got no formula. You ain't got jack shit.
I'm gonna ignore your descent in jargon-babble, there for the time being anyway; been there; done that. Just ‘cause you want to do it again don't mean it's worth doin’ again, at least, not now.
What is it you've been rambling on about that supposedly happens ‘because parallax’?
Ok, enough of yer boring diversions. I got an 8-character formula that calculates the discrepancy mentioned in the first comment on this thread.
You got nothin'.
The end.
‘Because parallax’ and then what happens? What happens ‘because parallax’? You've been at that ‘because parallax’ six or eight times now. Surely you were going somewhere with that beyond it just being smoke and dust and mirrors tossed in for the sake of the distraction?
I've been working on the assumption that your supposed eight character equation was supposed to calculate the parallax (at least, at equinox). I kinda figured you must have a point there beyond it being just a diversionary tactic. Looking back over your jargon-babble now, with a more inquisative bent, I have reason to question that assumption.
What is this eight character equation of yours supposed to actually do with or about the parallax (by any definition)?
typo just ‘cause it bugs me for some reason this time: inquisitive
"‘Because parallax’ and then what happens? What happens ‘because parallax’? You've been at that ‘because parallax’ six or eight times now."
That'd be six or eight failures of comprehension on your part then. "Because parallax" is your answer, just as I predicted. Or rather, to be exact, it is a paraphrase of your statement: "There's nothing else to come up with. The Common English definition of parallax covers it all".
Against all common sense, you appear to be claimin' you've actually come up with somethin'. So far you've got no formulas, and a bogus list of parameters, amounting to jack shit. So your statement that there's nothing else to come up with is aptly summarised as "because parallax" ... a vacuous statement devoid of meaning.
"What is this eight character equation of yours supposed to actually do with or about the parallax (by any definition)?"
Aha. We've got to the goin' round in circles stage. That figures. You always get there in the end when you have to cover for the fact you got nothin'. So I refer you to Tue Dec 09, 03:04:00 pm.
And I repeat:
I got an 8-character formula that calculates the discrepancy mentioned in the first comment on this thread.
You got nothin'.
The end.
"Or rather, to be exact, [‘because parallax’] is a paraphrase of your
statement: "There's nothing else to come up with. The Common English
definition of parallax covers it all’."
That has got to be the single most peculiar syntax I've ever seen for what you claim is supposed to be a paraphrase of two complete sentences. I presume there's some reason for such a peculiar syntax, but I'm not gonna try to guess what it is, on account of I don't think I care and it almost certainly doesn't matter.
"Against all common sense, you appear to be claimin' you've actually
come up with somethin'."
Ah, well then, let me disabuse you of the notion that I've ‘come up with something’. The Common English definition for ‘parallax’ that I gave you is, in fact, a quote from Merriam-Websters Online Dictionary. I have a link.
The ‘formula’ you mention, which would cover both what you want to call ‘parallax’ and also what you want to call not-parallax but rather ‘displacement of azimuth’… That's way too complicated to be worth the bother, as I mentioned much, much earlier, to wit.
"It's gonna be a fairly complicated math problem and I don't even
intend to try to set it up and solve it, even with a computer. That's why
they publish those charts."
Lee C. @ Tue Dec 09, 04:48:00 am
(I presume you would agree that there is a formula for calculating what you call ‘displacement of azimuth’ out there somewhere. As well as a formula for calculating what you wish to call ‘parallax’ But, it simply ain't worth all the trouble for me to work it out for myself, nor do I need to watch you whine about Google if I decided to just look it up instead.)
"I got an 8-character formula that calculates the discrepancy
mentioned in the first comment on this thread.
Yeah, you keep sayin’ that. I presume this ‘formula’ along with your reading of just what is ‘the discrepancy mentioned’ will now join the growing list of closely guarded personal secrets of ‘The Great and Wonderful Petes’, along with the secret magical mystery maths that prove that Einstein didn't actually mean what he said when he applied a base frame of reference to his proof for his Theory of Relativity, and the secret of whether the Pope is head of Maronite Church instead of the Patriarch being its head, or whether they're both head of the Maronite Church, it effectively having two heads instead of just the customary one.
Have fun with that.
"…nor do I need to watch you whine about Google if I decided to just look
it up instead."
By the way, just what is your recurring deal ‘bout Google? You got a grudge agin those folks or what?
"Ah, well then, let me disabuse you of the notion that I've ‘come up with something’. The Common English definition for ‘parallax’ that I gave you is, in fact, a quote from Merriam-Websters Online Dictionary."
Parallax has got nothing to do with the discrepancy mentioned in the first comment. Nothing. Nada. Zippo. You sayin' "parallax" and citing a dictionary means nothing. I've got a formula that calculates the discrepancy and it don't consider no parallax. It also happens to get the right answer. You able to explain that, genius?
If you wanna stake a claim that parallax has got the remotest connection to what we're talkin' about, go ahead prove it. Be my guest. Here's a hint for ya: just sayin' parallax over and over again (as you are doin') dudn't make your case for ya.
Here's another hint: just Google "parallax formula". It's given to you on a plate. If you're able to use that formula in any way connected to the problem at hand, I'll concede your point. Hell, if you find one single reference to parallax concerning a shift of position around a globe, I'll concede it. Note: that means where the arc of the globe's surface, as opposed to a chord through it, is used.
"The ‘formula’ you mention, which would cover both what you want to call ‘parallax’ and also what you want to call not-parallax but rather ‘displacement of azimuth’…"
Let me stop you there. What I refer to as parallax has got nothing to do with the problem at hand. The proof of that pudding is that I've solved the problem without any reference to it. The displacement around the azimuth is the discrepancy that has been referred to all along. That's the only thing that needs explaining and I've done it, with an 8-character formula. You wanna add some more complexity, you're gonna need to explain why the hell you think it's necessary.
The ‘formula’ you mention, which would cover both ... That's way too complicated to be worth the bother, as I mentioned much, much earlier"
I didn't mention any such formula. I've got a formula that fully explains the discrepancy in every case. It doesn't need to take anything else into account, and certainly not any kind of parallax. It's 8 characters long.
Tell ya what. If y'all think there's a formula that's too complicated for y'all (which would be no surprise) then come up with the simple version. The one that does any one of the two things you claim need doin'.
That gives you three chances to get away with this without lookin' like a fool:
1) Just use the parallax formula that you can find online in any way loosely connected with the problem at hand.
2) Find any reference to "parallax" around a globe (other than in connection with a chord between two points). Just a simple reference anywhere.
3) Derive a formula for either of the two aspects you claim need explainin'. The simpler of the two, if there are two. (I claim there is only one, and I got it).
Do any one of those three simple things. You don't have to come up with actual results. Just any one of those partial steps, and I'll concede the whole argument.
I will take your further silence on the matter to mean you are full of shit.
And just to point out once more:
I got an 8-character formula that calculates the discrepancy mentioned in the first comment on this thread.
You got nothin'.
The end...
...Except for this part:
"I presume this ‘formula’ along with your reading of just what is ‘the discrepancy mentioned’ will now join the growing list of closely guarded personal secrets of ‘The Great and Wonderful Petes’."
Nope. You're gonna see it in five days time. Funny thing is, you won't be able to deny it gets the right answer, but you still won't understand it. LOLZ.
"You sayin' "parallax" and citing a dictionary means nothing. ***
You able to explain that, genius?"
Yeah, I think I can explain that. I think I can explain that your cavalier dismissal of customary Common English is based on you decideding that what you want to be true must necessarily be true, and it's the rest of the world's responsibility to play to your wants. In this particular case you want to pretend that changing the name, using a different, rather more arcane definition, a different, rather more arcane set of words, as the name for the apparent displacement we both now see, that will somehow change the actual cause of the displacement, and you don't have to deal with the fact that I knew right off the top of my head that either you…
1) Took your own readings and found a local "out of round" discrepancy, or
2) Took your own readings and forgot to adjust magnetic north back to true north, or
3) You had merely neglected somehow to allow for the opening, initial, apparent displacement of the sun displayed at latitudes above 0°
(Turns out it was the third one.)
So, now you want to argue like hell about the name of the phenomenon to cover up the fact that you initially neglected to consider it, but I knew right off that it had to be one of only three reasonable possibilities. You think fussing ‘bout the name to give it might somehow change those things--it won't.
"If you wanna stake a claim that…[through]… as opposed to a chord
through it, is used."
Continued argument over the name. Needs no further explanation.
"The displacement around the azimuth is the discrepancy that
has been referred to all along."
If you had an eight character formula that would have gotten you to 1½° of apparent displacement at Dublin, and not on the date of an equinox, we'd have seen you strutting it proudly long ago. I therefore conclude you got squat and are highly unlikely to come up with squat in the next few days.
"That gives you three chances to get away with this without lookin'
like a fool:"
I'm quite content with hangin’ in here and watchin’ you babbling on and producing nothing except the same tired arguments over names of terms and definitions in the dictionary. I see absolutely no need to ‘get away’. I'll therefore pass on your offer, it being empty of substance.
(And do know that I will be here waiting to call ya on it when your time's up if that's what I have to do. I ain't gonna forget and wander off. You can kiss that hope good-by right now.)
Post Script:
Producing an equation that works only in Dublin, or, rather, only at 53° latitude ain't gonna fool nobody either. I don't know that it can be done, but I'd not put the attempt past ya.
"You're gonna see it in five days time."
No point in waiting; nothing's gonna change. Do it now!
And, in the meantime, what's your repetitive deal with Google? You got a grudge agin those folks or something? You got money in Bing maybe? What is that bit of weirdness all about.
As I said, you think obfuscatin' while jumpin' up and down with your panties in a twist is gonna save face.
Let me address it one more time. After that your repeated pathetic lies are gonna make you look a complete fool in everyone's eyes. You say:
"In this particular case you want to pretend that changing the name ... will somehow change the actual cause of the displacement"
1)
I said at Tue Dec 09, 02:40:00 am: "you can call it "smelly goat's cheese" if you want. What's the reason for the displacement of the sunrise to the north, as in the original question?"
See that? I told you 17 hours ago I don't care what you call it. Quote any dictionary definition you want. Your dictionary don't say "1.5 degrees to the north". You're gonna have to provide that bit, whatever you call it. Get it?
2)
I said at Tue Dec 09, 04:09:00 am: "Over to you to explain why it's displaced 1.5 degrees to the north. After you explain it I don't care if you choose (erroneously) to call the cause "parallax" or "smelly goat's cheese".
See that again? Another hour later after you repeatedly bleated about your naming obsession, I told you again you can call it anything you like.
3) At Tue Dec 09, 01:51:00 pm I said: "I'm not demandin' anything. You can call it anything you like. If you check back up thread you'll see this is the third time I've said that. You're just lookin' for an excuse to get your panties in a twist, 'cos at this stage you reckon pantie-twistin' makes you look slightly less of a fool than not bein' able to come up with any goods."
Now, three times is enough. This is the fourth and last time I'm gonna say it. I ain't imposin' any naming restriction on you, nor am I accepting any from you on me. Show your formulas, with descriptions, and let the maths do the talkin'. (That's assuming you got some maths, which we all know you don't.) I already told you I'd concede the whole argument if you just use any parallax formula that you can find online.
I ain't gonna treat you like a idiot no matter how much you keep actin' like one. Any more bleatin' about naming from here on in, you will get no more from me than the timestamp on this comment.
If you had an eight character formula that would have gotten you to 1½° of apparent displacement at Dublin, and not on the date of an equinox, we'd have seen you strutting it proudly long ago. I therefore conclude you got squat and are highly unlikely to come up with squat in the next few days.
Just to tie you weasel ass down on this ... the blog post refers to an asymmetry between the most northerly and most southerly azimuth of sunrise in a year. The magnitude of that asymmetry is the "discrepancy" that Lynnette referred to in the first comment. Explaining that asymmetry and its magnitude is the only thing this thread is about. That's the definition of the problem. You observed that the asymmetry is twice the offset of sunrise from due east on the equinox. That's fine, now we've got another value which is half the original one. It still needs explaining. But our definition can now refer to either of two values if you like, one being half the other.
Now, I got an 8-character formula that calculates the magnitude of that offset from east at the equinox, equal to one half the asymmetry referred to earlier. If you want the formula to produce the latter value, I can just insert an x2 in it. It it able to calculate the value for any location on earth. Your comment about "not on the date of an equinox" is meaningless. The discrepancy at the equinox is part of the definition of the problem.
You need to rapidly start gettin' a clue here or I'm gonna have to consider you unable to understand the problem, let alone come up with a solution.
"Your dictionary don't say ‘1.5 degrees to the north’."
Of course it doesn't. The apparent displacement is function of the latitude. It's lower in Minneapolis, for example. I believe Lynnette gave it to us at 1° (producing a combined swing of 2° which she noticed on the charts).
The eight character equation you think you're going to produce has to actually work in the real world--many, many different latitudes for it to actually work with in the real world. Many places it'll have to match up in the real world--and 365 days a year. It has to match the real world, or it's obviously not the explanation after all. Does match the real world, doesn't it?
So, why not show it to us now? No reason to wait. Nothin's gonna change.
And what is your weird recurring fixation ‘bout Google all about?
Hmmmmm... It appears you posted another note (timestamp Tue Dec 09, 08:48:00 pm) while I was typing.
"Just to tie you weasel ass down on this ..."
Oh come now… You really think you're gonna fool anybody with that crap? After all this you're gonna produce an equation that solves out to 3° no matter what the latitude and nobody's gonna notice that you swapped the target for something you could hit?
Good luck with that.
(I can, however, now see why you think you need to wait as long as possible on makin’ the swap--that's suddenly obvious. Don't think the wait will help ya though, but I guess there's no use urging you to give up on that fairly forlorn hope. So, guess we'll just have to wait.)
"Producing an equation that works only in Dublin, or, rather, only at 53° latitude ain't gonna fool nobody either. I don't know that it can be done, but I'd not put the attempt past ya."
For the third time, my formula works for any location on earth (except the poles, at which a singularity occurs).
"No point in waiting [for five days to show the formula]; nothing's gonna change. Do it now!"
Nope. I'm giving you five days to make good your claim about bein' able to understand the solution to the problem. Problem is, you listed a bunch of factors that my solution doesn't use, and failed to list ones that it does. Most sane people would conclude -- assuming my approach works -- that you have failed to understand the problem.
"Of course [the dictionary] doesn't [say ‘1.5 degrees to the north’]. The apparent displacement is function of the latitude. It's lower in Minneapolis, for example."
At Tue Dec 09, 04:48:00 am above, you listed at least five things that it's a function of (plus a couple more that it's not a function of). You didn't even mention the word latitude. Have you changed your mind?
"The eight character equation you think you're going to produce..."
I don't "think" I'm gonna produce it. I have produced it. I can run it for any location on earth right now, including ones that timeanddate.com can't do, since it is limited to a list of cities.
"...has to actually work in the real world--many, many different latitudes for it to actually work with in the real world. Many places it'll have to match up in the real world"
See earlier. And earlier than that. And all the other times I've told you it works for any location.
"--and 365 days a year."
The date is not part of the original problem posed. The problem concerns the asymmetry in direction to the earliest and latest sunrises, equivalent to twice the offset of the equinocteal sunrise from due east. There is no date parameter in that problem statement. You'd think after 150 comments you'd get this by now.
"It has to match the real world, or it's obviously not the explanation after all."
And I'm very glad you brought that up. Because your solution's gonna have to do the same. The dictionary definition of parallax doesn't match the real world in this case, as you agreed above. That means the mere mention of parallax is not the solution. Contrary to this, you said there was "nothing else to come up with. The Common English definition of parallax covers it all". Now you've clearly contradicted yourself. The common definition of parallax doesn't deal with the real world of this case at all.
"After all this you're gonna produce an equation that solves out to 3° no matter what the latitude and nobody's gonna notice"
Try not to be a complete idiot.
"For the third time, my formula works for any location on earth
(except the poles, at which a singularity occurs)."
If I understand you correctly, your version of ‘works for any location on earth except the poles’ means it solves out to 3° no matter what the latitude (any latitude less than 90° that is).
I was expecting something at least semi-clever. This is a major disappointment.
You are no longer lookin’ to worth any of my time on this.
If this fools anybody, that's their problem; they're too far gone for me to help.
Ciao for now. But, I'll be here waiting when your time's up.
"You are no longer lookin’ to be worth any of my time on this."
"If I understand you correctly, your version of ‘works for any location on earth except the poles’ means it solves out to 3° no matter what the latitude (any latitude less than 90° that is)."
You give imbeciles a bad name. At least they can't help it, while you're just tryin' to divert attention from your lack of understanding of this whole problem.
Got any formula yet? For even a trivial part of the problem? Got any uses of parallax formulas. Any references to parallax on a globe? Got any kind of clue at all?
Was that supposed to be a denial that it works out to 3° no matter the latitude? Or do you not know yet?
Well, I don't know about either of you, but I'm actually finding it rather interesting Googling around. lol!
I'm fine with waiting the five days. :)
"I'm fine with waiting the five days. :)"
I guess that's the deciding vote. Wait we shall.
A rather cool animation of Earth's orbit around the Sun.
It seems to have been a little short on polar ice. Hope that's not an accurate preview of things to come.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
And, while we wait…
"I'm giving you five days to make good your claim about bein' able to
understand the solution to the problem."
I'm pretty much done with my doin's. If you think you're waiting on something more from me then you're most certainly just lost and confused. And waiting to discover that this is your condition.
Lynnette, here's my favourite set of astronomy applets... just beautifully written and very illustrative of loads of concepts in a compact way. The first half dozen are relevant to motion in the solar system.
For a visualisation of sunrise and sunset at the equinox in Dublin I used the "motions of the sun" applet. Here's two screenshots I took of summer and winter solstice sunrise. Although it doesn't specifically address the present problem, it helped me draw a diagram that does, and thus come up with the very simple formula that reproduces the timeanddate variations that I mentioned in the post. (And no, contary to Lee's bleatings, the formula isnt: "3" ;-)
P.S. Dunno about you, but Blogger started letting me use my login again for posting comments. Dunno what changed.
So, now that Lee seems to have piped down and gone to ground to wait for the glorious formula, I'm gonna do what he accused me of doing -- pour scorn on his abuse of the word parallax. Although, I hasten to add, he's still free to call it anything he likes -- how could I stop him?
Parallax is intimately associated with triangulation, a technique familiar to any school child. If you move along a baseline and measure the changing angle to some object, then armed with the length of the baseline, and the change in angle you can calculate the distance to the object. You need to know what sort of triangle it was -- it's mostly arranged so that the triangle is a right triangle or an isosceles triangle that can be divided in half to give a right triangle.
Here's an example of parallax on a small scale on the surface of the earth. On a grand scale, astronomers have used parallax to measure the distance to celestial objects for thousands of years, although measurements beyond our solar system had to wait until we were able to accurately measure very tiny angles.
We even have a fundamental distance unit in astronomy called the parsec -- the distance that subtends an angle of one arc second (i.e. 1/3600 degree) on a baseline whose length is the diameter of the earths orbit round the sun. In other words, a star that appears to move by one arc second of angle against more distant background stars during the course of the earths annual motion around the sun is one parsec away. A parsec is about 3.3 light years.
One thing that parallax is most definitely not is any general apparent change in position of an object. Turning around on your feet doesn't cause a parallax shift. Looping the loop in an aeroplane doesn't cause a parallax shift. Rolling down the side of a hill in an oil drum is not a parallax shift. Likewise, travelling around the circumference of the globe is not a parallax shift. To be sure, things will appear to have a relative motion. But not one that is ever referred to as parallax, because it does not have the essential association with triangulation.
When Eratosthenes of Cyrene discovered that the sun was at a different in mid summer between Alexandria and Aswan, and used it to calculate the circumference of the earth, he was not using parallax. The first picture in the Wikipedia article on Parallax is not affected by whether viewpoints A and B are on the surface of a globe, and certainly not by whether they are on 180 degree opposite sides of a small globe or one degree apart on a big globe. It simply doesn't matter -- only the distance along the AB baseline (not around the surface of the globe) matters.
"Parallax" simply is not used to describe changes in perspective other than along a baseline used in triangulation. There are different words for the apparent movements of the sky associated with movements around the globe. Parallax isn't a useful concept in such circumstances, as exemplified by the fact that the ancients measured sky angles perfectly well without knowing whether the celestial objects were pinned to a fixed celestial sphere, or to many concentric shells, or whether the sphere or shells were nearby or infinitely distance, or something in between.
Unfortunately, dictionary definitions are not written to withstand the Jesuitical parsing of ole' Lee. So they're not going to contain all the nuance I've just mentioned here. However, the fact that I've offered to concede the entire argument of this thread if Lee can turn up a single counter example to the usage I've talked about here is a pretty much surefire proof that he can't find any such example, because you can be damn sure he'd jump on the chance. Lee's constant harping on about terminology around parallax is evidence of his muleheadedness and incorrigibility, nothing else.
Here's a summary of the CIA torture-program:
http://www.theguardian.com/us-news/2014/dec/09/cia-torture-methods-waterboarding-sleep-deprivation
People are outraged again, although those who cared to find out have known about this for quite some time. That "rectal feeding"-stuff was news to me but it doesn't surprise me one bit that sadistic torturers feel a need to venture up their victims ass for whatever reason.
I'd like to add that bad as these techniques sound it's really the prolonged time they were used on prisoners that's the worst factor.
Just a concrete cell, an AC set low enough for the naked prisoner to shiver, a pair of handcuffs and then all you need is time. A day of that would be seriously uncomfortable, stressful and frighening. After a week or a month I'd imagine you'd be close to losing your mind. And they did that and much worse to many prisoners.
Seems they even accidently froze one of 'em to death in the "salt-pit" in Afghanistan only to find out he was apparently innocent. Ooops!
2 weeks later the interrogator in charge got a $2500 cash bonus for his outstanding work.
And now I'm going to write something about the systems of coordinates for measuring angles on the sky. It's not because I'm insisting on any particular terminology, but simply because there is a set of existing terminology that can be used to compare any concepts against, regardless of how we choose to call them colloquially. Also, I'm sick to the back teeth of being accused of using "jargon", so you can treat this as a jargon buster.
Everyone's familiar with the spherical coordinate system of latitude and longitude that we use for measuring angles on the surface of the earth. Lines of longitude are great circles (i.e. complete circumferences) drawn through the poles. The zero of longitude is the Prime Meridian, arbitrarily chosen to be the line running through the poles and through the site of the original Royal Observatory in Greenwich, England. The zero line of latitude is the equator. Lines of longitude intersect lines of latitude at right angles.
There is an exactly analogous system of celestial coordinates used for the sky. Simply project rays from the centre of the earth through the lines of latitude and longitude, projecting them onto the sky and that's it. There are minor changes, mostly around terminology, and I'm not going to delve into the reasons for this here. The latitude measurement on the sky is referred to as declination. The longitude measurement is referred to as Right Acension. Declination, like latitude, is measured in degrees above or below the equator. Right Acension, on the hour hand, is measured in hours and minutes (not the same as minutes of arc). But there's an easy translation -- an hour of RA is 15 degrees of longitude.
Now, you are fixed to the earth so if you do nothing your latitude and longitude don't change as the earth rotates. The distant stars are fixed to the sky, so their Dec and RA don't change either. Obviously as the earth rotates, the sky seems to move above our heads. The lines of latitude on earth stay aligned to the declination in the sky, but the lines of RA in the sky progress westward. (That's why we measure them in hours -- the amount they move in an hour). Unlike the equator for latitude and declination measurements, the earth-based zero of longitude is no use to us in the sky -- we need a separate definition for a zero of Right Ascension. We use the vernal equinox for this. The sun moves north and south of the celestial equator during the year, owing to the tilt of the earth's axis. It crosses the equator (both terrestrial and celestial -- it's the same thing) at the equinoxes. The location where it crosses the celestial equator at the vernal equinox defines the zero of RA, also known for historical (and anachronistic) reasons, as the "first point of Aries". (It used to be in the constellation of Aries, but that 26,000 year wobble of the earth's axis has moved it. It'll be back there again in 24,000 years time).
(cont'd...)
(...cont'd)
Ok, that's enough on Dec and RA. But there's a whole other sky coordinate system that can be used. Instead of defining fixed positions of stars in the sky, this other coordinate system is completely local and relative to your current location. Simply put, you see the sky as a big hemispherical bowl above your head and if we paint lines of longitude and latitude on this, with the "north pole" directly above your head, this is the Alt-Azimuth system of coordinates. As implied by the name, the lines of "latitude" are called "altitude" (since they measure heights above the horizon). The lines of longitude are called azimuth or azimuthal angle, and they measure angles around the horizon. The horizon, of course, corresponds to your local equator in this system. The zero of azimuth is the line passing through the zenith from the northern compass point on your horizon. Lots of the terms in astronomy come from Arabic, hence the strange sounds of e.g. azimuth, zenith (the "north pole" point above your head), and nadir (the opposite point below your feet).
The local coordinate system is useful for knowing what you are going to see at a particular time and place. If I told you that Sirius would be at 25 degrees altitude and 180 degrees in azimuth at 10pm tonight at your location, you'd be able to go out and spot it. Of course, to calculate that for you that, I'd have to know your latitude and longitude on the earth, and the declination and Right Ascension of Sirius, so that I could convert from the never-changing Dec and and RA of Sirius to Alt-Azimuth coordinates for a particular time and place on earth.
And now, abandoning almost all that useful knowledge, I'm gonna relate it to the problem we've been discussing in this thread. The sunrise is, of course, a local event by definition. The sun doesn't rise in the same direction or at the same time for observers at different places on earth. Sunrise, again by definition, is always fixed to the horizon, i.e. an altitude of zero. So the only local positional coordinate we need is its azimuth. The problem we've been discussing is that the most northerly azimuth of sunrise on the summer solstice and the most southerly azimuth on the winter solstice display an asymmetry with respect to their distance from due east. It turns out, as Lee C explained, that it can be thought of as each of them being shifted northward by an amount which we also see the equinocteal sunrise being shifted by. It is the magnitude of this azimuthal discrepancy that we are interested in.
typo: "on the hour hand" = "on the other hand".
Oh, and I should also mention why this equinocteal shift can be referred to as a "discrepancy". Geometric intuition tells us that the sun has to rise due east at the equinox. The equator is aligned with the sun. The point of sunrise for everyone on earth should therefore be aligned due east. Well, ok, there is a parallax shift (and that's real parallax, not the baloney Lee is spouting). If we're north of the equator we're looking "down" toward the sun in the equatorial plane. But because we're a massive 93 million miles from the sun and only a couple of thousand from the equator, this parallax shift is completely negligible and can be ignored. (In fact, it's 2*pi times smaller even than I mistakenly said earlier -- so about 0.002 degrees). So the fact that sunrise is significantly offset from due east needs explanation. The explanation is not because we're offset from the equator, and it's not "because of parallax".
And finally I'm gonna say something briefly about the mathematical concept of a function. Wikipedia says it's "a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output". The way that the inputs are related to the outputs is what differentiates one function from another. Examples are given in the article. The inputs are often referred to as parameters of the function and the outputs as results of the function.
In our case, we're looking for one specific output: the magnitude of that azimuthal discrepancy of sunrise. By producing the correct general function, we show that we understand what inputs are needed, and how they are processed to produce the output. In short, it shows we understand the problem and its solution. I said the function has to be correct -- in our case it produces the observed change in azimuth. And it has to be general -- we can't just "hardcode" a result of 3, to match the desired output for Dublin. It must work everywhere.
Part of our understanding of the problem is knowing what parameters are required. A parameter that has no bearing on the result is not required, and strictly speaking cannot even be thought of as a parameter, since it's absence would have no effect on the result. I gave a nonsense example earlier of needing the angle between Jupiter and Mars. That obviously can't have any bearing at all on the position of sunrise!
One thing that Lee has demonstrated so far is that he doesnt't know what parameters are required for the present problem. He mentioned them up thread (Tue Dec 09, 04:48:00 am). Another curiosity is that he keeps referring to the problem as "a function of latitude", when he didn't even mention latitude as a parameter. Now, I'm pretty certain that one of things he did mention translated straightforwardly into latitude, although it begs the question why -- as the chief whinger about use of jargon -- he used such ridiculously complicated lingo. Anyway, the fact of the matter is that he has the number and type of the parameters wrong. That proves he doesn't understand the problem. His assertion that "it's gonna be a fairly complicated math problem and I don't even intend to try to set it up and solve it, even with a computer" is just a pathetic cover for the fact he has no clue what he's talking about.
I got a quote you should keep in mind when you consider what I'm going to tell ya here. First, the quote for you to keep in mind.
"…you ain't just a dunce, you're a lyin' dunce who'll sink to any
depths to declare hisself correct."
Petes @ Tue Dec 09, 05:34:00 am
Then the thing I'm gonna tell ya ‘bout…
"His assertion that "it's gonna be a fairly complicated math problem…
is just a pathetic cover for the fact he has no clue what he's talking
about."
Now, you figure out how to also include what you prefer to denominate as not-parallax but instead as ‘displacement of azimuth’ along with that smaller portion of the apparent displacement that you are willing to actually call parallax. And you tell us again how damn easy that calculation is gonna be be.
Go for the the real world apparent displacement that the ancient navigator was actually gonna see when dawn broke. That's the number he needed. Your much different technical definition of parallax sans ‘displacement of azimuth’ was gonna be of no particular use to him. So, you tell us all now how easy that combined calculation is gonna be. ‘Cause that's the reading the navigator needed to start his morning off right. (Which is probably why it is the Common English definition.) Jackass!
I'm kinda bored bein' rude for the time bein'. You kinda wore me out on that score. So I'm gonna explain this nice and simple and gentle.
In fact, I don't so much have to explain it, as to quote yerself back to yerself: "we're at the margin of error right here and don't need to throw in any further factors which would lead to any changes of less than 30 minutes, like perhaps refraction or the variable distance to the sun from the elliptical orbit."
So you accept that there are factors that can be left out of a calculation, having been roughly determined to be of no practical importance due to their small magnitude and the precision required.
Now, I already told you what the magnitude of the sun's displacement due to parallax is. It's 0.002 degrees. I'll happily show you how that calculation is done if y'all want since it's of no import at all to our main issue. To convert that into an azimuthal movement is a tiny bit more involved, but seein' as I've already had to do that for the other, main, component of the discrepancy, it's not remotely a problem. I assure you -- and you can choose to take my word for it or work it out yourself -- that the 0.002 degrees of parallax has NO practical bearing whatsoever on the issue. I can also tell you that the "ancient navigator" (LOL) had got no instrument whatsoever at his disposal that could possibly measure such a small angular offset, so to say that omitting it was "of no particular use to him" is, uh, well let's just say it's wrong. Badly wrong.
"So, you tell us all now how easy that combined calculation is gonna be."
Gladly. It's fairly trivial. Not as trivial as my 8-character one. I'd probably need 20 or 30 characters.
"Which is probably why it is the Common English definition."
That rhetorical flourish doesn't even make sense.
Best o' luck.
Oh, I should also have mentioned that converting the 0.002 degrees of parallax into a movement around the horizon cannot produce an azimuth angle higher than 0.002 degrees. That's the max. Actual value will be smaller in almost all cases. In this particular case, it is smaller the further you get from the equator. But in all cases it is simply, utterly, negligible.
Dealin' with Lee's episodic appearances feels like the movie Jaws. You know where they're shovellin' crap into the water to attract the shark, and every now again he rears his big ugly snout, to gasps from the audience. Then it's back to the tense music ... dah ... duh ... dah .. duh ... dah-duh dah-duh DAH-DUH DAH-DUH-DAH-DUH ... BLAM! Big snout appears again.
The tense music is Lee Googlin' furiously. Then it's back up to the surface for a barrage of wrong ideas bein' thrown out. After he's repelled by the boat's occupants, it's back to the depths once more.
:)
"I assure you -- and you can choose to take my word for it or work it
out yourself -- that the 0.002 degrees of parallax has NO practical
bearing whatsoever on the issue. *** I can also tell you that the
‘ancient navigator’ (LOL) had got no instrument whatsoever at his
disposal that could possibly measure such a small angular offset"
Which is almost certainly why the ancient navigator would not have been interested enough in that limited measure of displacement for it even have it's own common name.
"…to say that omitting it was ‘of no particular use to him’ is, uh, well
let's just say it's wrong. Badly wrong."
I was thinking of combining calculations, not omitting anything. I thought I was fairly clear on that. I have no clue what the hell you think you're talking about.
"Now, I already told you what the magnitude of the sun's
displacement due to parallax is. It's 0.002 degrees."
So you've given up on getting 3° as the result everywhere and are instead going for a formula that only works on exquinox. That wasn't what you were promising a little while back. But then neither of your propositions would be useful for navigation in the real world, so I don't guess it much matters which way you go with it. Still, I'm not sure you can do even that small thing in only 30 characters. I guess we'll see.
My guess is you're not gonna fool either Lynnette nor Marcus with that; neither of those numbers would have been useful to common folk for navigation or much else for that matter. Other than showing to other astronomers they're of no real practical application that I can see.
I'll just wait now to see how impressed they are with whatever it is you finally settle on displaying before the grand ♪♫ta-da♫♪.
Oh, yeah, and what is it with this persistent recurring weirdness you got ‘bout Google? I notice that's back this morning.
Yer post of Wed Dec 10, 09:43:00 am is far too confused to be bothered pickin' apart line by line.
I will say it again. There are several factors affecting the offset of the sun from due east on the equinox. Some are negligible. That means they can be neglected. I have neglected them. One of the negligible factors is parallax.
You may choose to include parallax. (Although you previously said the whole calculation was too complicated for y'all). If you do include it, you are on a fool's errand to include a factor of maximum approx. 0.002 degrees which is vastly, vastly, smaller than other inherently unpredictable random factors in the position of sunrise. In the context of the explanation of the discrepancy this thread is discussing, it's beyond idiotic to include it.
And although our purpose is not to be "useful to common folk for navigation" such negligible factors can, by the common definition of "negligible", be ignored, even for navigational purposes. Not sure which aspect of "negligible" you cannot get through your skull.
As for "So you've given up on getting 3° as the result everywhere and are instead going for a formula that only works on exquinox."
All explained on previous posts which you can look up, although I seriously doubt you have the intellectual capacity to grasp them since you keep asking the same questions I've already answered. My solution is entirely general. You don't understand what that means, I can't help you any further.
Should have been a question mark here:
"So you've given up on getting 3° as the result everywhere and are instead
going for a formula that only works on exquinox?"
And, since I'm correcting that: I'm not really sure whether to expect the grand ♪♫ta-da♫♪ to come before or after your display, but it'll be what it is when it is.
"You may choose to include parallax."
In what?
Here -- I'm gonna try a little experiment, if Lynnette would be so kind as to be the guinea pig.
Lynnette: my calculation of the magnitude of the discrepancy in the sun's position at sunrise is general in that 1) it is not specific to any location on earth, it works for all locations and yields the correct result for that location; 2) the discrepancy is the same for all dates to within a negligible margin, so the solution for a given location on earth works on all dates, not just the date of the equinox.
In short, the solution is general to all dates and places.
Do the above statements make sense to you, more or less? I've made them to Lee umpteen times and he keeps coming back and ignoring them. Any idea what his mental block might be? Just pure dumbness?
"And although our purpose is not to be ‘useful to common folk for navigation’"
So what use you ‘spect those sextants actually had? Why would the navigators have carried those charts around with ‘em? (This could get amusing.)
Oh, yeah, and then there's this:
"You may choose to include parallax."
In what?
And then there's that Google thing that keeps coming back to you. What's with that?
Christ almighty, yer gettin' tedious. Here's a sextant. Can you show me where the 0.002 degree interval markings are? No, scratch that. You're not even going to understand the question. This is pointless.
"In short, the solution is general to all dates and places."
But is it useful? Would observational instruments available to pre-industrial revolution have been able to use it to navigate? You also gonna tell her what use it might have been put to?
And, of course, there's couple more questions pending, those being:
"You may choose to include parallax."
In what? What would I include parallax to?
And then there's that Google thing that keeps coming back to you. What's with that?
Ok, you're gonna play dumb, I'm gonna resume normal service.
I got an 8-character general formula that calculates, to within a margin at least ten times smaller than the effect itself, the discrepancy mentioned in the first comment on this thread.
You got jack shit.
The end.
So, not useful then? Basically worthless to any normal, non-astronomy folks?
[Lee C]: "So, not useful then."
Useful for the exact purpose for which it was created. Your transparently snide little whinge as to what it "ought" to be usable for counts for jack shit.
I got an 8-character general formula that calculates, to within a margin at least ten times smaller than the effect itself, the discrepancy mentioned in the first comment on this thread.
You got jack shit.
Get over it. The end.
"…the discrepancy mentioned in the first comment on this thread."
You got a name for that, or a description sufficiently not-evasive that allows us reality based folks to figure out what the hell you think that might actually be?
Given that at the time of writing I had no idea what was causing the discrepancy, you might suspect it's a tad unlikely I had a name for it. Now that I do know, any name I give it would reveal its cause. And given you decided to go all adversarial on it, that's for you to figger out. You already pronounced confidently on it many times, so I presume you weren't just talkin' through yer ass. (LOL, scratch that ... of course you were).
So that's also a no on the not-evasive description question. Okay I can handle that; not a problem. I'll just take that as a negative on the is it useful in any way question too. Pretty sure you'd have mentioned that if you'd had any good news on that front.
So, what's with this thing you got goin’ on with Google?
Just spotted this:
"Useful for the exact purpose for which it was created."
Must have posted while I had a screen up, maybe while I was typing. You were good for a good laugh this morning at least. Made the effort to engage you in bit of sanity worth the effort, unsuccessful thought it might have been.
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