Calculating the Solstice and shortest day (Shallow Thoughts)

Akkana's Musings on Open Source Computing, Science, and Nature.

Thu, 22 Dec 2011

Calculating the Solstice and shortest day

Today is the winter solstice -- the official beginning of winter.

The solstice is determined by the Earth's tilt on its axis, not anything to do with the shape of its orbit: the solstice is the point when the poles come closest to pointing toward or away from the sun. To us, standing on Earth, that means the winter solstice is the day when the sun's highest point in the sky is lowest.

You can calculate the exact time of the equinox using the handy Python package PyEphem. Install it with: easy_install pyephem for Python 2, or easy_install ephem for Python 3. Then ask it for the date of the next or previous equinox. You have to give it a starting date, so I'll pick a date in late summer that's nowhere near the solstice:

>>> ephem.next_solstice('2011/8/1')
2011/12/22 05:29:52
That agrees with my RASC Observer's Handbook: Dec 22, 5:30 UTC. (Whew!)

PyEphem gives all times in UTC, so, since I'm in California, I subtract 8 hours to find out that the solstice was actually last night at 9:30. If I'm lazy, I can get PyEphem to do the subtraction for me:

ephem.date(ephem.next_solstice('2011/8/1') - 8./24)
2011/12/21 21:29:52
I used 8./24 because PyEphem's dates are in decimal days, so in order to subtract 8 hours I have to convert that into a fraction of a 24-hour day. The decimal point after the 8 is to get Python to do the division in floating point, otherwise it'll do an integer division and subtract int(8/24) = 0.

The shortest day

The winter solstice also pretty much marks the shortest day of the year. But was the shortest day yesterday, or today? To check that, set up an "observer" at a specific place on Earth, since sunrise and sunset times vary depending on where you are. PyEphem doesn't know about San Jose, so I'll use San Francisco:

>>> import ephem
>>> observer = ephem.city("San Francisco")
>>> sun = ephem.Sun()
>>> for i in range(20,25) :
...   d = '2011/12/%i 20:00' % i
...   print d, (observer.next_setting(sun, d) - observer.previous_rising(sun, d)) * 24
2011/12/20 20:00 9.56007901422
2011/12/21 20:00 9.55920379754
2011/12/22 20:00 9.55932991847
2011/12/23 20:00 9.56045709446
2011/12/24 20:00 9.56258416496
I'm multiplying by 24 to get hours rather than decimal days.

So the shortest day, at least here in the bay area, was actually yesterday, 2011/12/21. Not too surprising, since the solstice wasn't that long after sunset yesterday.

If you look at the actual sunrise and sunset times, you'll find that the latest sunrise and earliest sunset don't correspond to the solstice or the shortest day. But that's all tied up with the equation of time and the analemma ... and I'll cover that in a separate article.

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[ 10:28 Dec 22, 2011    More science/astro | permalink to this entry | comments ]
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