Cross-polarization loss between a circularly polarized antenna and vertical or horizontal polarized antenna is known to be -3dB. This is one of the reasons why Circular Polarized antennas are preferred for satellite based communications. However, practical mismatch loss between a RHCP and LHCP antenna can be -20 to -30 dB (theoretically $-\infty$).
I am trying to understand what happens between a RHCP satellite and a LHCP ground emitter as the satellite crosses from horizon to horizon as the LoS geometry changes. Is there any rule of thumb in terms how the losses will look like as satellite rises, culminates, and then finally sets? If I know the azimuth and elevation at each rise, culminate, and set instance can I say something about the mismatch loss?