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when a object is thrown from a orbiting satellite, does the orbit of the object pass through point of projection while orbiting (Of the velocity is less than escape velocity). If it does so why?

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All two-body orbits in a inverse-squared force law are closed.

If the orbiting body passes through a point on one orbit (in the CoM frame) then it will pass through that same point on all subsequent orbits. An impulse change to it's motion does result in a new orbit, but that orbit includes the point where the change occurred.

Nor can you guarantee that the new orbit is elliptical the impulse could circularize a previous elliptical orbit.


An interesting computation that you will find in many upper-division mechanics is texts to to find the period of the new orbit compared to the old one under the assumption that the impulsive delta-vee is small (compared to the orbital velocity). It turns out that the difference in periods is also small and you could conceivably try to catch something thrown overboard on the next pass with a net on a stick.

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