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Cary
Posts:
62
Registered:
9/15/07
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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.
[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))
>>
>>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).
This paper may be of interest to those following this thread.
<http://faculty.matcmadison.edu/alehnen/kepler/kepler.htm>
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