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Frank:

By "distance moved" I mean the change in great-circle distance between the sun and Aries.  I then looked at Kepler's Second Law, which... apparently doesn't get as much attention online as Kepler's Third Law.

Rearranging things, the area swept out by a line between the sun and the earth, over the course of a day, is supposed to be constant.  I couldn't find said constant (see above lament), but (assuming I understand things correctly) the Gaussian gravitational constant is supposed to be the "average" or "standard" angular velocity of the earth, expressed as radians per day.  I converted the radians to arcminutes so I could have something to compare almanac data to.

Since the area is constant, and the area is a product of the angle and the square of the radius, I formed a ratio of the angles and took its square root to find the raio of the distances to the sun (treating the "standard"/"average"/whatever distance as 1).  Then I assumed the ratio for the sun's SD would be the same.

(Speaking of, it seems a "more better" number for its standard SD is 15.994'.  The 15.987' came from throwing together some numbers I found on Wikipedia, because of insomnia and hypomania and my bookshelf was all the way on the other side of the room.)

As a side note, counting the days from perihelion requires knowing when perihelion is (turns out it's not in the Nautical Almanac).  You can go with memorizing an average date, but that average goes stale over time (it's a tropical calendar after all, not an anomalistic one), and that's basically what started me down this garden path to begin with.

(And the way almanacs calculate perihelion/aphelion versus how they calculate equinoxes/solstices is a whole other bugbear of mine...)