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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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Posts: 62
Registered: 9/15/07
Re: ellipse, mean distance from point on perimeter to a focus ?
Posted: Feb 12, 2010 2:02 PM
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On Fri, 12 Feb 2010 10:22:33 +0000 (UTC), rob@trash.whim.org (Rob
Johnson) wrote:

>In article <20100211111323.200$wv@newsreader.com>,
>David W. Cantrell <DWCantrell@sigmaxi.net> wrote:

>>rob@trash.whim.org (Rob Johnson) wrote:
>>> In article
>>> <a36f3aaf-77d5-499b-bd30-f603613dcc8d@j6g2000vbd.googlegroups.com>, G
>>> 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.


>>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))
>>Doing that, we find instead
>>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).

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