Tuesday, June 22, 2010

the solstice

Happy Belated Summer Solstice!

This is my favorite time of the year, when it stays light until well into the evening and even in Berkeley I can wear short sleeves on my motorcycle, and of course, there's no school obligations to get me out of bed before I darn well feel like it.

I was thinking about the mechanics of the solstice yesterday as I was trying to answer someone's question on Quora (the new Q&A website that has no real purpose except to waste time, but hey sometimes that's fun when you're on summer vacation and in denial about the need to get back down to business). I guess the first thing to understand is that the summer solstice is not defined by the longest day of the year, but by the maximal tilt of the Earth's axis towards or away from the Sun. This animation explains the mechanics:

So, in addition to the seasons changing as we move around the sun, the length of daylight also changes, because when the northern hemisphere is pointed towards the sun, more of it is illuminated than the southern hemisphere. So it takes longer to rotate from one edge of the illuminated hemisphere to the other.

Here's where I'm working from my own logic in a simplified celestial mechanical system, so someone correct me if I'm wrong. The exact time of the summer solstice can occur at any time of day. On half of the Earth at that time, it's daytime, and that day will be the longest of the year. But in other parts of the world it is nighttime, and then either the day before or the day after might be the longest day of the year. That is, the shortest day might not be the same calendar day as the actual solstice. Say the time of the solstice, in your time zone, is 12:01 am on June 21. The sun set on June 20 at 9pm and rose on June 21 at 6am. Therefore, the solstice was closer in time to the daylight hours of June 20, so actually June 20 is your longest day of the year. Meanwhile, on the other side of the planet where the solstice occurred at 12:01 pm on June 21, June 21 was their longest day. Likewise for the nighttime: either the night that begins the calendar date of the solstice, or the night that ends it, might be the shortest of the year.

There is at least one confounding factor that might make me wrong though. The Earth revolves around the sun in an elliptical orbit, moving slowest at aphelion (its farthest point from the sun) and fastest at perihelion (its closest). Aphelion occurs in July and Perihelion in January (no, that's not backwards - the tilt of the Earth causes the seasons, not the distance from the sun, hence reversed seasons in the Southern hemisphere and the slightly more extreme seasons there.) These are NOT the same times as the solstices. Since the Earth is moving at slightly different speeds around the sun on the day before and the day of the solstice, the lengths of days are also changing at different rates, so that screws up the calculation a bit. I imagine it is a negligible effect though.

Unfortunately, the only sunrise/sunset times that I can find are only accurate to the minute, not second. Since they change by less than a minute each day, rounding errors are an issue, and I can't verify my intuition. Anyone know where to get daylight times to the second? Or have a different answer for what is the longest day of the year?

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