Washington Post now has a link to Inmarsat's analysis documents: http://apps.washingtonpost.com... http://s3.documentcloud.org/do... I've no idea what variable D1 is. Maybe some inherent frequency offset in the system that has to be subtracted. Maybe that's the minimum 85 Hz offset in the data. The difference between northbound and southbound flightpaths is almost 100Hz at times (e.g. 19:40 UTC). That's pretty big ; 100Hz from a 131 MHz signal (the higher 137MHz bands are North America only, I think) I get 100Hz / (131E6 Hz) ~ 7.63E-7, and (7.63E-7 x c = 229 m/s = 445 knots. That's a difference of 445 knots in plane-satellite line-of-sight closing speeds between north and south tracks. The 270 Hz peak at 18:20 UTC is an additional 100Hz, or 445 knots directly towards the satellite. The satellite is west, but also really high up. How could an airplane following the surface of the Earth achieve 445 knots closing speed towards a satellite? I still don't see all the details here.

The satellite we're talking about, Inmarsat-3 F1, is not perfectly geostationary. Nothing's perfect. This one's orbit is inclined 1.7 degrees with respect to the equator, which means it oscillates North-South and crosses the equator twice a day. If you know the motion of the satellite at the time of the flight (say it was moving south), then the Doppler shift between north and south tracks would be a little different (the south track would have a smaller shift). Of course, with a 130MHz signal you're talking about a shift of 1Hz or less. How much resolution do their tuners have? Maybe enough.

I think 'geostationary' satellites wobble more than you think. This one is inclined 1.7 degrees to the equator, and whether that Doppler shift is detectable... it depends on your detector. Maybe it's really that good.

I'll give you two hints to how they probably did this: 1. Nothing's perfect. 2. Re-read the quote, at face value "Effectually we looked at the doppler effect, which is the change in frequency, due to the movement of a satellite in its orbit." ;)