Goddard Space Flight Center
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The spring equinox of 2004--night and day equal--occurred on March 20, day 80 of the year. Fall equinox will be on September 22, day 266. The difference of 186 days is definitely longer than half a year (close to 183 days). How come?

If Earth moved around the Sun in a circle with constant speed, the time from one equinox to the next would always be exactly half a year.
Looking at the orbit from above, the two lines, equinox-to-equinox and solstice to solstice (shortest day to shortest night), cross at right angles, and each would divide the circle in half (a drawing might help here!).

Actually, however, the orbit is an ellipse, an elongated oval, so the two lines divide it unequally. Furthermore, by Kepler's second law of planetary motion, Earth moves a bit faster when it is closer to the Sun. These two features explain the discrepancy.

By Kepler's first law of orbital motion, the Earth's orbit is an ellipse with the Sun at one focus, displaced from the center towards one end. Actually, with Earth the orbital ellipticity (aka "eccentricity") is very small. If you looked at a scale drawing of our orbit on paper, you would have a hard time telling it from a circle--although, if the Sun was also included, you would easily see that it was off-center.

Now it so happens that Earth comes nearest to the Sun around January 4, quite close to our winter solstice (about December 21). The solstice-to-solstice line is therefore almost exactly along the long axis of the ellipse, and the line between equinox positions divides the ellipse quite unequally. During the winter segment (fall to spring) Earth is closer to the Sun, its path is "the shorter half the ellipse" (=less than half the ellipse length), and it moves a little faster. During the summer segment the Sun is more distant, Earth must cover a little more than half the length of the ellipse and it moves a little more slowly. That is why it takes 3 extra days to cover this stretch.

 


This week's question comes from David P. Stern, a retired GSFC physicist. His educational web collection "From Stargazers to Starships" discusses many aspects of the Earth's motion in space; the above feature is covered in "More about Kepler's Second Law" at:
http://www.phy6.org/stargaze/Skepl2A.htm
For the entire index of "Stargazers," click on "Site Map" at the top of that file.