Understanding 3D Doppler Shift with Satellites

[Alia_3]

TL;DR Summary

Two satellite circling the earth with different velocities

I am trying to understand a case of doppler shift if I have two satellite circling the earth with different velocities but the same direction and with different altitudes as well. How I will be able to figure out the doppler shift in three dimension between the two satellite if one of the satellites is sending a signal to the other.

 

[Ibix]

Work out the velocity of one satellite with respect to the other, calculate the Doppler factor from the speed velocity (edit: corrected, with thanks to Orodruin) and multiply by the gravitational redshift factor.

 

[Ibix]

If you provide more detail about what you know already, it might be easier to provide more helpful answers

 

[Orodruin]

Work out the velocity of one satellite with respect to the other, calculate the Doppler factor from the speed, and multiply by the gravitational redshift factor.

It is not sufficient to know the relative speed. The Doppler factor also depends on the relative angle between the velocity vector and displacement vector. For example, the transversal Doppler effect is just a gamma factor.

 

[Ibix]

I was going to say "yes, that's why I wrote velocity" but I see I didn't the second time. Will correct that.