Monday, April 26, 2010
Physics of a Sunset
About six weeks ago I slept for the first time in the Berkeley apartment, I noticed that first night the sun was setting just a degree or two north of the Marin side of the Golden Gate Bridge. Since that was mid-March the sun was progressing north and I wondered when I would see a sunset directly over the bridge. After reaching its furthest point north on June 21st, a rough estimate would have the sunset back to the bridge around the fourth week of August. So the second part of the question was: just how far does the sun move each day?
I wondered if my distance from the Marin Headlands was a factor (that's the land on the other side of the Bay those of you who don't live around these parts) but I quickly realized that the horizon (where the sun sets) is nearly equidistance from me at all times and the intervening land masses had nothing to do with my calculations. I did, however, correctly intuit that latitude had to make a mathematical difference. Since I was dealing with a tilting planet around a semi-constant axis. I made the only rational decision I could with my decades old calculus.
I went to google.
Between the solstices (approx. June 21st & Dec. 21st), the sunset point changes by about 62.6 degrees in half a year (about 183 days), for an average of 0.34 degrees per day. Near the equinoxes (March 21st, Sept. 21st), the sunset point changes about 0.51 degrees per day; near the solstices, it hardly changes at all. Which means the sunset appears to shift faster around the equinoxes and almost not all all near a solstice.
If you live south of 40 degrees, the change from solstice to solstice is less; if you live north of 40 degrees, the change is greater. Berkeley is at 37 degrees 87 minutes.
The earth's axis is inclined to its orbit by 23.5 degrees. The shift in the sunset point between solstices is roughly given (in degrees) by the formula [2 * 23.5 / cos (latitude)] but this is only an approximation. For a precise calculation, we need to use spherical trigonometry, which I will hold for another time. Nerds may proceed on their own.
What I clearly did notice was that the point of sunset did move quickly right around the time I moved in, near the equinox, in fact by the second week just a line of sight projection seemed to suggest that by the summer solstice the sun would be out of sight to the north. This, of course, assumed a constant movement, which google has help me discover is not the case. Already the daily progression to the north has slowed from the near breakneck half a degree a day when I moved in.
Come summer solstice, I will still have a sunset and somewhere in late August, I will post a week or so of pictures when the sunset beams through the Golden Gate.