Hi there.
The more I am trying to understand the D2 doppler (plane->satellite doppler, not compensed and measured by the ground stations) profile presented by the AAIB, the more I get confused. Maybe some tech guys here can help.
I understand that this D2 doppler is the plane-satellite relative speed (the 3D vector Vplane-Vsat) projected (using a dot product) onto the line of sight, the 3D vector POSplane-POSsat. This is also the 1st order derivative of the range between the plane and the satellite.
The Inmarsat satellite in geostationary orbit is moving (in the earth referential) with a Vz speed, I have modelled the Inmarsat satellite trajectory using (the sat. parameter are derived using the AGI Satellite Toolkit or STK):
Duncan Steel | Space Scientist, Author & Broadcaster
As I modelled it, the max Vz speed of the Inmarsat satellite (65 m/s) is far lower than the plane speed (235 m/s), so that the plane's heading changes are primarily shaping the D2 doppler graph.
I have also modelled the plane trajectory (but with a constant altitude) in spherical coordinates with the varied heading changes.
I get a D2 doppler which can be either positive (the plane is moving away from the satellite) or negative (a closing speed meaning the plane is moving closer to the satellite). For exemple on the 1st protion of the trajectory (heading toward Beijing), my D2 doppler is positive, and just after the large heading change toward the south, my doppler is negative (plane coming closer to the satellite). Another point: the magnitude of my doppler (from -750 Hz to 750 Hz) cannot compare with the presented D2 doppler (between 100 and 275 Hz).
My resultats are there:
https://imageshack.com/i/eun1u9p
https://imageshack.com/i/jjxqdup