The Asymetric Sunrise

The story of heliocentrism -- the idea that the Sun, not the Earth is at the centre of the "universe" -- is a fascinating tale, full of twists and turns, that spans over 2,000 years. By the time Galileo first turned a telescope on the heavens, the evidence was literally in front of our eyes: it was clear that Jupiter had satellites that orbited it, not the earth, and Venus had phases owing to being lit from different angles on its path round the sun.

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.