On Fri, 12 Feb 2010 10:22:33 +0000 (UTC), email@example.com (Rob Johnson) wrote:
>In article <firstname.lastname@example.org>, >David W. Cantrell <DWCantrell@sigmaxi.net> wrote: >>email@example.com (Rob Johnson) wrote: >>> In article >>> <firstname.lastname@example.org>, G >>> Patel <email@example.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).