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Re: (OFF-TOPIC) Flight 370
From: Don Seltzer
Date: 2014 Mar 27, 09:34 -0400
From: Don Seltzer
Date: 2014 Mar 27, 09:34 -0400
On Thu, Mar 27, 2014 at 2:01 AM, Frank Reed <FrankReed@historicalatlas.com> wrote:
..If you were just saying that there is a geometric factor to deal with, then yes, of course that is true. But it's symmetrical, north and south of the equator yielding the same pattern. The only way that I can think of to "de-symmetrize" the north and south arcs via a Doppler shift, as reported, is through the satellite's own north-south motion.
Yes, I was writing about the geometry, in relation to the magnitude of your numbers. I have squirted some WD-40 into my rusty brain, and have finally remembered the term for which I was searching: Dot product. We are dealing with satellite motion and airplane motion that are in different planes. The Doppler effect from the satellite is dependent upon that component of its motion that is directed along the vector between the two.
If the Inmarsat were at the earth's surface on the equator at 64°E, the dot product would be obvious. When Flight 370 was directly east, the component of the satellite NS velocity that contributed to Doppler shift would be Vns * cos 90°, or zero. At the end of its projected flight path, when to the SE of the satellite location, the dot product would have been approximately Vns * cos 45°. Using Frank's suggested numbers, approximately 70 - 120 mph along the vector contributing to Doppler shift.
The calculation becomes a bit trickier when the plane of the satellites motion is displaced to 22,200 miles above the earth. The vector from the satellite to flight 370 is now, by my back of the envelope calculations, only about 6° from the satellite's perpendicular, or 84° from the plane of the satellite's motion. The dot product is now Vns * cos 84°. This knocks down the Doppler contribution by a factor of ten. The component of the satellite's NS motion that is directed along the vector from the satellite to flight 370 is only about 7 - 12 mph towards the end of the flight.
From Gary's posting, it would seem that even these small velocities would be observable through Doppler shift.
Don Seltzer
