How do I program the orbit of a particle that is experiencing Gravity & Radiation Force Pressure?

How do I turn this equation into a Differential Equation and is it possible to program this analytically? The equation below is Newton's Gravitation with an added term for Radiation Force Pressure. Where 'G' is the gravitational constant, 'M1' is the mass of the particle (i.e. like a dust or a rock), 'M2' is the mass of the object that the particle orbits to (i.e. like a star), 'L' is the luminosity of the source, 'c' is the speed of light, and 'a' is the radius of the particle and they are all constants. The only variable is 'r', which is a function of time, r = r(t).

Answer 1

[James Tursa]

The differential equation is simply Newton's F = ma, where m is the mass of the object (M1) and a is the acceleration of the object (r_dotdot). Solve this for a = F / m and use your nomenclature to get your differential equation:

r_dotdot = F / M1

Just plug in your F from above.

That being said, these really should be vector equations, not scalar equations. I.e., the gravity force should be directed towards the M2 planet and the radiation force pressure should be directed away from the luminosity source. These directions are not the same.