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Hi. I'm just a hobbier of astronomy and have a question about elliptical orbit.

I wonder that can calculate elliptical orbit using just atitude(location) and velocity(vector).

Please look at my picture.

The blue dot is central body and green dot is my interesting body.

Let me assume mass of central body is enough huge to ignore green's gravity.

and assume that there are only those two objects in universe(prevent multi-body problem).

Then we know that the blue dot's mass, gravity and green dot's mass, location and velocity.

I want to get the purple line's length, semi-major axis,

and the orange line's length, semi-minor axis what can calculate from semi-major axis using eccentricity. Finally location of perihelion or aphelion.

Already have seen many questions and answers about calculating orbital speed(scalar) from atitude using vis-viva but velocity(vector).

I think, it's too hard to predict where will be perihelion or aphelion.

How can I solve this problem?

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