This code can transform orbital elements to state vectors and vice versa. It can also predict the state vectors of the satellite, given the initial state vectors and time of travel.
It uses the Newton Raphson method to iteratively solve for the eccentric anomaly at another epoch.
The code is in the form of Python Notebooks, and hence the equations used have been explained then and there.
Assumptions:
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The satellite orbits the earth.
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Mass of satellite is negligible as compared to mass of earth.
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The motion of the satellite is affected only by the gravitational field of the earth. Other bodies are neglected. (2 body problem)
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The earth is uniformly dense and is a perfect sphere.