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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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 Cary Posts: 62 Registered: 9/15/07
Re: ellipse, mean distance from point on perimeter to a focus ?
Posted: Feb 12, 2010 2:02 PM

On Fri, 12 Feb 2010 10:22:33 +0000 (UTC), rob@trash.whim.org (Rob
Johnson) wrote:

>David W. Cantrell <DWCantrell@sigmaxi.net> wrote:

>>rob@trash.whim.org (Rob Johnson) wrote:
>>> In article
>>> Patel <gaya.patel@gmail.com> wrote:

>>> >Is the mean distance from a point on perimeter to a focus equal to the
>>> >semi major axis length?

>>>
>>> Yes.

[snip]

>>But I initially (before seeing Achava's post) calculated the mean distance
>>with respect to theta, thinking of the ellipse in polar coordinates as
>>given by
>>
>>r = a (1 - e^2) / (1 - e cos(theta))
>>
>>
>>mean distance = a sqrt(1 - e^2) = b, the semi-minor axis length.

>
>I get that as well. Furthermore, averaging with respect to time,
>using equal area in equal time, I get a mean of a(1+e^2/2).

This paper may be of interest to those following this thread.

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