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Re: ellipse, mean distance from point on perimeter to a focus ?
Posted:
Feb 11, 2010 12:22 PM


In article <20100211111323.200$wv@newsreader.com>, David W. Cantrell <DWCantrell@sigmaxi.net> wrote:
>Well, as Achava correctly pointed out, it depends on the variable with >respect to which the mean is calculated.
>> Recall the "string and pins" method of drawing an ellipse, which >> depends on the fact that the sum of the distances from a point on the >> ellipse to the two foci of that ellipse is the major axis of that >> ellipse. Since the sum of those two distances is always the major >> axis, the sum of their means is the major axis.
This is true regardless of the variable.
>> By symmetry, the >> means of these distances are the same.
So the mean will be the semimajor axis provided the variable varies symmetrically wrt to the two foci.
(Which it doesn't for time in orbit.)
 Richard  Please remember to mention me / in tapes you leave behind.



