# Modeling satellite attitude for propagation of orbit

I recently obtained good results with a high-precision numerical orbital propagator using a constant effective area for drag and radiation pressure. I have now become interested in checking if the accuracy can be improved by using a variable effective area, i.e., values that vary along propagation to provide a more accurate calculation of the drag and radiation pressure to which a satellite is subject.

My understanding is that this requires knowing what is known as satellite attitude, i.e., its orientation in 3D, in addition to a model of the shape of the satellite. By combining these, we can get an estimate of the cross-section of the satellite at a given time, and an estimate of the effective surface of the satellite subject to radiation pressure.

To simplify things, let's assume a simple box-wing model, with a central body with 2 flat panels attached. Is there any simplified model that allows predicting the satellite attitude as a function of the position, speed, acceleration and forces at a given instant?

Is there a way to model such improving the accuracy of a high-precision numerical propagator by using a variable

• box-wing and attitude for modeling solar radiation pressure are pretty standard, but most drag models are so uncertain themselves that most propagators I can think of assume spherical satellites for that portion of the calculation. If you get it to work, that would be really nifty, but getting good truth data is going to be difficult, because most things with well-known orbits are well away from drag. The ISS is probably your best bet at a target to compare with, and it is also very different from a sphere. Dec 21, 2021 at 5:53
• Thanks a lot! Then, for the case of atmospheric drag, most propagators use a constant effective area, right? Since treating the satellite as a sphere, would mean that its attitude does not affect the cross section. Would you have by any chance any source for reading on how attitude modeling for solar radiation pressure is performed in the simpler case of a box-wing model? Thanks!
– Rafa
Dec 21, 2021 at 9:23

The most extensive attitude modeling I've ever seen is for GPS, but that's for calculating solar radiation pressure. There is a vast literature on the topic, ranging from the Proceedings of the First International Symposium on Precise Positioning with the Global Positioning System in 1985 to things published just a few months ago. The most recent survey of all that history I've read is Duan & Hugentobler, "Enhanced solar radiation pressure model for GPS satellites considering various physical effects", GPS Solutions 25 (42) 2021, which also has lots of good stuff on the content of the models themselves. Furthermore, that article is open access, since it's creative commons licensed. The probably most historically significant article, on the other hand, which I would otherwise have suggested you read first, is paywalled: Springer, Beutler, & Rothacher, "A new solar radiation pressure model for GPS", Advances in Space Research 23 (4) 673-676, 1999.

Detailed attitude modeling for drag, however, I have not seen in any propagator I've used, probably because the available density models of the atmosphere itself, and the data to feed them, are so uncertain that the extra effort to use anything but a "cannonball" (hard, dense sphere) model isn't considered worthwhile. As a quick introduction to the topic, I recommend this page at the NOAA Space Weather Prediction Center. If you can show results from making the effort, I think some people would be very interested in seeing them, but I would also be quite concerned about how you could manage to verify them! This is particularly problematic since most of the orbits that are really well known are for satellites that feel very little drag, which is partly causal (that is, if they did feel a lot of drag, their orbits would not be as well known, or last very long). The only major exception I've thought of is the ISS, which is relatively low, very closely monitored, and definitely not spherical. The only article I recall encountering on the topic is Nwankwo & Chakrabarti, "Theoretical Model of Drag Force Impact on a Model International Space Station Satellite due to Solar Activity", Transactions of the Japan Society for Aeronautical and Space Sciences 12 47-53, 2014.

• – uhoh
Dec 22, 2021 at 1:16
• Thanks a lot for the very nice explanation and references! This is great material, I will go through it in detail. The ISS example looks really interesting, I'll try to play with it and see what can be done in terms of modeling somehow attitude for drag!
– Rafa
Dec 22, 2021 at 2:27