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25 September 98

The Inconstant Year

The Autumnal Equinox was last Wednesday, September 23. This was the first day of autumn. It's also a special day for the earth, along with the Vernal Equinox on March 20, and the Summer and Winter Solstices on June 21 and December 21. On the solstices, the earth is most tilted toward or away from the sun. On the equinox, it's in the middle, and day and night are (nearly) the same. I counted days on my calendar and found that there are 186 summer days between the spring and fall equinoxes, but only 179 days between fall and spring. What gives?

There are more summer days between the equinoxes than winter days because the Earth's orbit is slightly elliptical and not quite a perfect circle. It's pretty cool to "discover" this fact in a couple of old calendars! The odd thing is that our summer is longer because the Earth is actually farther from the sun and takes longer to go the distance. If this seems like another stumper, remember that it's just the opposite south of the equator. The seasons are actually caused by the tilt of the Earth's axis. Distance has little to do with it.

Note: The Autumnal Equinox occured on September 23 at 1:37 a.m. Eastern Daylight Time. But that was on on September 22 at 10:37 p.m. Pacific Daylight Time here in California. I guess the official start of the seasons is figured from the East Coast only. This could create a wobble of a day or two in the exact count of summer and winter calendar days, but our northern hemisphere summer will always be longer than our winter, as measured between the equinoxes.

The actual distance from the Earth to the Sun varies from about 91.5 million miles at perihelion when it is closest, to about 94.5 million miles at aphelion when it is most distant. This is not enough to make a difference in any model or drawing you could construct, but it does slightly effect the length of the seasons. On a true Endless Summer trip, you would spend more time north of the equator.

Graybear sent his usual interesting reply:

I remember learning a LONG time ago that Earth is farther from the sun during the summer, and closer in the winter and that's why the northern hemisphere is more populated - the summers are not as hot and the winters are not as cold, but I think that was just a mnemonic device.

My almanac says that the distance to the sun ranges from 91.4 to 94.6 million miles, but couldn't find when perihelion and aphelion take place. I remember, too, that a planet's velocity varies with the distance from the sun such that the pie-shaped area that it circumscribes is constant for a constant time period. Using the small angle theorem, the velocity is inversely proportional to the distance from the sun.

The changing distance from the Earth to the Sun does have a slight effect on temperature. A planet's temperature varies with the inverse square root (not inverse square) of the distance to the sun. I figure the change in temperature is about

                   94,500,000 miles
     square root ( ---------------- ) = 1.02
                   91,500,000 miles
That's about 2 percent. On the absolute Kelvin scale, the Earth's average temperature is something over 300 degrees, so a 2% change is about 6 degrees Celsius. This seems enough to notice, but the usual temperature swings between summer and winter are much greater. Atmospheric factors and the tilt of the earth have a much greater effect. See the Bad Astronomy Page for more details.

I find it curious that Earth reaches perihelion on about January 4, and aphelion about six months later on July 4. Is it significant that these events are so close to the solstices? Graybear thinks not:

I don't see any connection between peri-/ap-helion and the solstices. An evolutionist would probably say it is coincidence, a creationist would say it's part of a greater plan that we can't comprehend. The seasonal range of temperatures is based primarily on the solstices which determine how much sunlight is received.
I'm still not sure.

The U.S. Naval Observatory has a data page on the Web with exact times of the equinoxes, solstices, aphelion, and perihelion for the years 1992 - 2005.

My MSDOS TBC program can generate lots of useful ephemeris data and maps, and can literally play the music of the spheres in MIDI! TBC is available for download (with BASIC source code) at Treebeard's Basic Vault.

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