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Topic: ellipse, mean distance from point on perimeter to a focus ?
Replies: 8   Last Post: Feb 12, 2010 5:56 PM

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 Richard Tobin Posts: 1,409 Registered: 12/6/04
Re: ellipse, mean distance from point on perimeter to a focus ?
Posted: Feb 11, 2010 12:22 PM

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 semi-major 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.

Date Subject Author
2/10/10 gaya.patel@gmail.com
2/10/10 Achava Nakhash, the Loving Snake
2/11/10 Rob Johnson
2/11/10 David W. Cantrell
2/11/10 Richard Tobin
2/12/10 Rob Johnson
2/12/10 Cary
2/12/10 Rob Johnson
2/12/10 Rob Johnson