I am trying to model the motion of a planet in the following scenario:
A planet is orbiting a star in an elliptical orbit. The star is located at one of the foci of this ellipse. The planet's motion obeys Kepler's second law.
I am looking for a reasonably accurate approximation of the planet's location on a coordinate grid as a function of the time elapsed. However, I am not quite sure how to approach this problem. It would be very helpful if someone could point me in the right direction. Thanks!
(As a side note, I am only familiar with math up to a high-school level of calculus.)
There is no explicit formula that gives the position of the planet as a function of time but there is an implicit one that give the time as a function of the eccentric anomaly, see for example wikipedia for a detailed explanation.
If you want to avoid solving implicit equations you can make an asymptotic expansion with the eccentricity as the small parameter.