Hello together,
I am looking for a way to describe the roll angle between a LEO satellite and a Ground Station antenna.
The ITU has a nice recommendation for calculating the polarization angle based on the G/S position and the LON position of a GEO satellite. However, I am looking for a general approach not limited to geostationary orbits (Rec. ITU-R BO.791, Appendix 1).
Background of this question is a communication link, that only uses linear polarization on both terminals. Therefore, the polarization angle needs to be corrected on one side and I am looking for a way to predict this roll angle - best case depending on the current El/Az of the G/S antenna. (This problem is quite similar to the field rotation for telescopes)
Does anyone have an idea how to analytically describe it?
Well, you're talking about a rather sticky problem in spherical coordinates where you have two different origins. A GEO satellite isn't too bad because you can more or less ignore the radius of the Earth as the offset in origins, but for LEO, you can't. Assuming the satellite is pointing straight down (i.e. to the Earth coordinate system) and the ground station is pointed at the satellite, you have to deal with both the off-axis behavior of the satellite plus the apparent polarization rotation of the GS antenna around its axis. If the satellite is beamforming to the GS, then there's another degree of freedom to deal with.
I'm not going to try to work it out here, but I'd start with GS elevation and work on the triangle from the Earth center to the GS to the satellite. That lets you solve for the corresponding angle of the beam at the satellite (and distance to the satellite). For azimuth, there's a reference frame problem, but for low elevations and low enough orbits, you can probably approximate it with planar coordinates vs. having to do all the spherical transformations. However, to get the "correct" result, you really need to get both objects in the same coordinate system.
Finally, however, regardless of what you do you have the problem of trajectory, which can get ugly if you try to look at it in the alt-az coordinates of the GS. You're right that the behavior is similar to the tracking of an alt-az mount for astronomy, but the dimensions and coordinates are all wrong. A LEO could be traversing in any orientation relative to azimuth, whereas a star will always track east to west with a relatively easily calculable arc that is mirrored/symmetrical on either side of the meridian. Likewise, the field rotation then follows the angle between the tangent of that arc and the horizon. That's the angle you're asking to solve for. If you can work out the trajectory from the POV of the GS, you can solve for that tangent and figure out the rotation of the polarization angle (field rotation).
A Google search will find you the formula for astronomical field rotation (like this link http://www.stargazing.net/david/doublestars/fieldrotation.html) which may help you work back to the LEO calculation.
I know that doesn't work the answer out for you, but hopefully this helps you get moving in the right direction.
Please have a look at the article that could be helpful for your question. "Comparison of the Self-Piloting Constructive and Destructive Interference in 7 and 23 GHz Band Over the Seawater Surface"
https://ieeexplore.ieee.org/abstract/document/9465895
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