I am looking to determine the acceleration vector of a satellite orbiting the earth at a certain point in time given its ephemeris data for that same point in time. I am taking into account the effects of an oblate earth, but not of third-body forces, aerodynamic forces, or solar radiation pressure.
To find the ephemeris data for a satellite, I use JPL's HORIZONS Web-Interface (https://ssd.jpl.nasa.gov/horizons.cgi), and I use the VECTORS ephemeris type, which gives me the following information for a given point in time (key included as well): (I apologize for including this information for anyone that is already familiar with this tool, as I only wanted to make the data format I am working with more accessible)
Information given for one point in time: JDTDB X Y Z VX VY VZ LT RG RR Key (units can be changed): JDTDB Julian Day Number, Barycentric Dynamical Time X X-component of position vector (au) Y Y-component of position vector (au) Z Z-component of position vector (au) VX X-component of velocity vector (au/day) VY Y-component of velocity vector (au/day) VZ Z-component of velocity vector (au/day) LT One-way down-leg Newtonian light-time (day) RG Range; distance from coordinate center (au) RR Range-rate; radial velocity wrt coord. center (au/day)
How would I solve for the acceleration vector given this information?
I know that assuming a spherical earth, the magnitude of the acceleration is given by
|Ā| = GM / R^2 (where R is the distance between the satellite and the center of the earth),
but would that work for an oblate earth? In addition how can I determine the direction of the vector? Assuming a spherical earth, the direction of the acceleration vector would be opposite to that of the position vector, but I do not think that would work either.
I appreciate the help! Also, if my problem is beyond the scope of a StackExchange question, I would appreciate references to source material that I could look into.