# How to calculate azimuth and elevation angle between aircraft and GEO satellite (in aircraft coordinates)

Given a fixed ground station, it is known how to calculate the azimuth and elevation.

If changing it to an aircraft which is changing its data (location, altitude, angles) and working with same satellite, the antenna shall change its direction on each parameter change.

I have some issues with my calculations of those angles.

Can you please assist me with the computation.

Numeric example would also be assist (to verify my code is doing right). For example aircraft located at (long=100E, lat=2N, height=35kft pitch=4, roll=10, yaw=315) and the GEO satellite is located at (long=88.22E, lat=10.15).

Generally: I perform azimuth & elevation calculation when all the angles are 0, then multiply by Euler matrix and the result is the final results (I've omitted cos/sin of angles on the elevation and azimuth). However the final results are pretty close to original results which can't be

The general strategy for this sort of situation is to construct a set of frames for the problem, then find rotation matrices for all of the frame transformations (possibly symbolically), then compute your output azimuth and elevation based on the matching rotation matrix.

Frames at work in this problem:

• A: Earth-fixed (GEO sat is static)
• B: Aircraft Vertical Frame (uses lat/long, axes on cardinal directions)
• C: Aircraft Body-Fixed Frame (aircraft is static)

The relative rotation from Aircraft Body-fixed Forward to Pointing at GEO Sat would be this (might need to check me):

B->C * A->B * (GEO sat pointing rotation from Earth Fixed Frame)

• thanks for your reply. Can you please assist also with the the actual numeric example? Commented May 22, 2020 at 5:40