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## Main Question or Discussion Point

I've been doing some calculations but am obviously too dumb to work out something which should be straightforward (and no, this isn't homework)

In a circular orbit, the acceleration is related to the tangential velocity and the radius via

a=v^2/r

In an elliptical orbit, both the velocity and the acceleration are constantly changing. At two points in the orbit, the radial acceleration is zero, for example.

Q: Is it possible to infer the distance to the center of mass, knowing the 2-velocity and 2-acceleration at any instance of time?

In a circular orbit, the acceleration is related to the tangential velocity and the radius via

a=v^2/r

In an elliptical orbit, both the velocity and the acceleration are constantly changing. At two points in the orbit, the radial acceleration is zero, for example.

Q: Is it possible to infer the distance to the center of mass, knowing the 2-velocity and 2-acceleration at any instance of time?