- #1

snorkack

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The distance from focus can be expressed as a function of position angle θ:

r=a(1-e

^{2})/(1+e cos θ)

The length linearly along the ellipse famously cannot be expressed analytically.

The total time spent on ellipse depends on a alone (Kepler 3rd).

If the angular speed at any r of θ were known then the angular speed at any other r would be because r∂θ/∂t=cost for any a and e.

But is there any analytic expression to find r∂θ/∂t given a and e?

Also, is there any way to find

_{0}

^{θ}∫∂θ/∂t, or

_{0}

^{t}∫∂t/∂θ? These are different questions because many analytic expressions cannot be reversed.