Can you cite a reference for this, or explain a derivation? This sounds fascinating. Perhaps the math is straightforward, but I'm leery of trying to go from Kepler's equal-area-scan result to this one . . . Thanks! -tom On Fri, Jul 15, 2016 at 1:11 PM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
The average position lies on the major axis of the orbital ellipse, on the aphelion side, and half-way between the center of the ellipse and the other focus.
-- Gene
From: James Propp <jamespropp@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Thursday, July 14, 2016 1:35 PM Subject: [math-fun] Average position of Earth
Ignoring the effects of bodies other than the Earth and the Sun, and treating the Earth as a point mass, what is the average position of the Earth over the course of a year as it travels an elliptical orbit with the Sun at one focus?
If you ask me "Are you interested in the average position of Earth relative to the the Sun, or relative to the position of the center of mass of the two-body system?", my answer is "I'm interested in both".
I'm hoping that there's an embarrassingly easy way to see what the answer is using principles from physics that I must've been taught but haven't fully absorbed.
I'm also interested in the limiting case where the ratio of the two masses in a two-body system goes to 0. Even if the answer to my original questions is "It's messy in either coordinate system", this limiting case (in which the two original questions coincide) might behave nicely.
Jim Propp
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