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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:
>In article <20100211111323.200$wv@newsreader.com>, >David W. Cantrell <DWCantrell@sigmaxi.net> wrote: >>rob@trash.whim.org (Rob Johnson) wrote: >>> In article >>> <a36f3aaf77d5499bbd30f603613dcc8d@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 semiminor 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>



