I have a theoretical problem that merges the effects of a gravitational field and the Sun radiation pressure. The problem goes as follows:
A spacecraft orbits the Sun in absence of any other body interaction. The spacecraft surface is not negligible compared to its mass and it faces the Sun with the same orientation at all times. Does the trajectory satisfy the conditions of a Keplerian motion (i.e. is the trajectory a conic section?) Same question when the Sun is not a sphere but a flat disc whose axis is pointing always in the direction of the spacecraft.
My answer is that in both cases we can consider that the spacecraft will move in a conic section. If you consider that SRP is always acting in the opposite direction of the gravitational pull of the Sun, both forces would form a central vector force field, where the gravitational force would be decreased by the SRP. If the motion described by the S/C only considering gravity is a conic section I do not see any reason why it should be different in that case.
For the case of the Sun as a flat disc, considering that it would be pointed always to the S/C, the force is again central (although the potential would not be circular).
I have not found a better explanation for this, although I feel there is some kind of theoretical insight that I might be missing.
Thanks for the help!