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Is there an analytical technique for determining the effect of a small variable transverse acceleration upon the rate of precession of a planet orbitting around the Sun according to Newtonian gravity law?

I have modelled such effects in a reiterative computer model and would like to verify those measurements.

The transverse acceleration formula is

$$K*V1*V2/c^2 * A.$$

Where K is a constant, A is the acceleration of the planet towards the Sun due to Newtonian gravitational influence of the Sun, c is speed of light, V1 is planet radial velocity relative to the Sun and V2 is planet transverse velocity relative to the Sun. Assume planet mass is small relative to the Sun and no other bodies are in the system and all motions are confined to a two-dimensional plane.

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