Elliptical orbit with non-central force field in celestial mechanics

Equations describing planar motion along a constant elliptical orbit in non-central force field are derived in a simple way and discussed. The angular moment along the elliptical orbit is not a constant of motion. The problem appears to be related to the problem of planar motion with drag force. Relations with related works are discussed. in presence of drag force, conditions for the force field to be derived from the gradient of a function are discussed, and relation of this function with the potential function is indicated.