Hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I've been banging my head against this problem for a few days now so I'm ready to find some help with it.

In short, I have a set of orbital state vectors(a position vector and velocity vector) describing an object's starting position, as well as the mass of the focus, and I need to figure out the math of how to convert to conventional orbital elements.

The biggest hitch seems to be determining the length of the orbit's semi-major axis. I've found one formula which describes near-circular orbits very well, but it seems to fail on highly eccentric orbits:

a = (2 / r - v^2 / ( m * G))^-1

In the case of a circular orbit, the equation is perfect. For example, plugging in earth's orbit about the sun produces an answer very close to 1 AU, which is satisfactory to me.

Now, however, consider the case of a highly eccentric, or even radial orbit. Let's say that the orbit has zero initial velocity, and starts at a distance of 1 AU. The orbiting body will fall in towards the sun and (considering an ideal case with point masses) continue through the other side, and come to rest 1 AU on the other side. That yields an ellipse with a semi-major axis equal to r, or 1 AU, however simplifying this equation will give you one half r as the semi-major axis.

So I guess that comes down to if anyone knows or can find a better equation for me to use; one that will hopefully work in the case of elliptic, hyperbolic, parabolic, and radial trajectories.

Thanks in advance for any help

--Firestorm--

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# Find Orbital Elements given Orbital State Vectors

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