I am working on the design of a constellation for academic purposes. I try to describe a phenomenon that appears in the simulations by means of analytic expression and I can't really find a good reference for this issue. I will try to describe the problem and maybe some on here can point me to the right book or an article.
Let assume we have two satellites orbiting the Earth in a near-polar near-circular orbit. The satellites are identical and the two orbits differ only on the RAAN angle. Using a high fidelity simulation I notice a drift between the two satellites, a drift that over time change the node crossing time. Basically, the mean anomaly change rate is not equal between the two satellites. For example, in a 600 km orbit, an inclination of 91 deg and RAAN difference of 60 deg I get a mean anomaly difference of 0.4 deg after 10 days. The effect seems to be secular or maybe with a very long period.
After further analysis, I realize that the cause of this effect is the geopotential, mainly the tesseral part of the geopotential. The initial RAAN difference between the two planes creates an uneven geopotential perturbation.
I am looking of a book or an article that provide equations of the mean anomaly derivative influenced by the tesseral part of the geopotential. I am looking for a straight-forward approximation, something that can help me quantify the effect so I can hopefully design an efficient controller to deal with this drift.