A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2014 Mar 25, 19:22 -0700
Well, I wanted to comment on this last night, but I restrained myself, in order to follow my own advice and post just once a day on this topic. I do apologize in advance if this tries anyone's patience, but clearly there's still an enormous amount of interest in the mystery.
We learned ten days ago from Inmarsat, which recorded simple "handshake" pings from the aircraft without positional information, that they were able to determine a rough "circle of position" for the aircraft at the last (or second-to-last?) ping that placed it either on a great arc extending across western China and maybe as far as Kirgizstan or on a southern arc extending deep into the southern Indian Ocean.
The circles on the chart that was published by media sources are circles of equal angular altitude. But I think (and Peter Monta agrees; private discussion) that this is probably range data based on the round-trip speed-of-light travel time of the quick "handshake" conversation between the satellite, 23,000 miles out in space, and the hardware in the aircraft. They could thus determine the distance of the airplane from the satellite or equivalently from the spot near the equator on the Earth directly beneath the satellite. The satellite in question is Inmarsat 3-F1 (or Inmarsat III F-1, depending on the catalog) which hangs in geosynchronous orbit nearly above the equator south of India. The circles are concentric on that spot beneath it on the Earth's surface though the circles of "equal light travel time" would not be evenly spaced as in the published diagram (but close enough in the ranges in question).
What other information could they get from those pings? How did they narrow things down? Articles published in the past few days refer to "Doppler effect" and make vague references to spooky "mathematics" --it's all "boffin" stuff, way beyond mere mortals. There's very little detail in the published reports, but it seems like there's a huge problem. The Doppler effect for a satellite in geosynchronous orbit would seem to be symmetrical. If the aircaft was on the northern arc and headed generally north, then it would be moving away from point on the equator at its cruising speed, maybe 600mph. If the aircraft was on the southern arc and headed generally south, then it would ALSO be moving away from a point on the equator at the same speed. So Doppler effect alone would not seem to help solve the problem.
The key seems to be that Inmarsat 3-F1 is not exactly in an equatorial orbit. It's inclined by 1.7° with respect to the equator. So that means that if you were standing on the equator directly under its mean position and you could see it with a telescope, you would observe that it shifts north and south of the equator (and also a little east and west but that doesn't matter here) moving north to a bit more than 1.7° Declination and then to the same Dec south of the celestial equator, completing a cycle in every 24-hour orbit. That means that the satellite is usually travelling north or south relative to an observer on or near the Earth's surface. Moving up and down a mere 1.7° of latitude in a 24-hour cycle may not sound like much, but this is all happening in an orbit with a radius of 23,000 miles. So the actual speed of the satellite relative to the Earth's surface can be as high as 180 mph (approximately) and on average it's about 100 mph. This is the north-south component of the speed. And of course, the orbit of the satellite is exactly determined and known so we know exactly how rapidly the satellite is moving in the north-south direction at any instant of time. I haven't checked details, but suppose for the sake of argument that the satellite is travelling southbound (on the descending branch of the orbit) at a speed of 150 mph at the time it receives a signal from an aircraft. If the aircraft is travelling mostly northbound at a speed of, let's say, 600 mph, then the relative speed between the two would be 750 mph. If the aircraft is instead travelling southbound, then the relative speed would be 450 mph. The Doppler shift at 750mph is obviously greater than the Doppler shift at 450mph. By comparing a series of pings (I think they have at least four that they trust) and getting estimated ranges and approximate speeds, it would be possible to definitively exclude one of the range arcs in the original circle of position. One direction could yield a consistent set of range and Doppler values. The other could not. That's my best guess as to how they were able to further analyze the signals and make the most recent determination that the aircraft must have ended up somewhere near 45°S and 90°E.
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