Could someone just run the following bit of physics past them to see if I have got the important point about the Doppler shift right?
If the satellite was absolutely fixed then the Doppler shift would be the same irrespective of whether the plane was heading north or south BUT the sun and moon cause a slight - but predictable - wobble in the orbit of the satellite and since that wobble is also N/S that will add a very small but measurable extra value in the existing Doppler shift. If the satellite was heading south at the same time as the plane then the Doppler effect would be squeezed by a tiny bit and the wavelength decreased - ie very slightly blue-shifted. If the satellite was moving north whilst the plane was heading south then the radio wavelength would be stretched - very slightly red shifted.
Have I got that correct ?