How to calculate perihelion precession

[Bjarne]

Let’s say that a space probe orbiting the Sun in an elliptical orbit prove would emit heat towards the motion direction., and hence causing resistance against motion.
Let’s say it would happen only when it was moving from aphelion towards perihelion, - and that the motion resistance is 1E-9 m/s.
After passing Perihelion the opposite did happen, instead of resistance the heat escape would be turned to acceleration, also 1E-9 m/s.

I believe this would cause the space prove to get its own perihelion precession anomaly.

How can a such be calculated ?

 

[D H]

Lagrange's planetary equations, which you can find in most astrodynamics texts.

 

[lpetrich]

Those are equations for the object's orbit elements as functions of the forces on it. One can find equations for long-term behavior by averaging over orbit times.

 

[Bjarne]

This math is above my head, can someone show an example?

 

[Bjarne]

I am willing to reward the one that will spend time on showing an example of calculation.