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Old 26th Mar 2014, 00:01
  #8089 (permalink)  
hamster3null
 
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Latest charts are extremely interesting, but they don't quite add up to me.

I actually sat down and tried to derive Doppler offsets by hand.

* The range of values in the chart is not right for 1.6 GHz - they should be much larger.
* It looks like we're looking at absolute values, not raw frequency shifts. The peak at 18:25 UTC corresponds to the time when the aircraft was flying directly westwards, towards the satellite. At 00:11, it was flying away from the satellite. These two points should have opposite signs of Doppler shift.
* The difference between "predicted north track" and "predicted south track" is WAY too large to explain by nonzero satellite orbit inclination or eccentricity. Satellite has inclination of 1.7 degrees, apogee of 35816 km and perigee of 35769 km. That's maximum speed of ~175 knots perpendicular to Earth-satellite axis in the north-south direction, and something negligible like 4 knots along the axis. Perpendicular component enters with a factor of at most ~0.11. Its absolute contribution is largest at the end of the track, when the satellite is contributing 20 knots and the aircraft is flying away from the satellite at the speed of 230 knots (total speed 450 kts, projecting on the aircraft-satellite axis leaves 230.) During the period up to ~21:00, when the aircraft is still near the equator, the effect of satellite inclination should be very small. Anyone is welcome to repeat these calculations.

Ultimately, I don't think that the chart is comparing the south track towards south Indian Ocean against its mirror image. In fact, a good fit for the "north track" would be the route that goes to Straits of Malacca and then turns and heads for Beijing. That's the only way to arrive at a high Doppler shift early on, at 20:00 to 21:00 (because the aircraft is to the east of the satellite and moving northeast, while the satellite is moving south). They could also be comparing against a track that heads northeast initially and then hugs the 40 degree arc through Burma and Tibet.
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