welt-verstehen/Relativity, stw2069R

Unsere Welt zu verstehen:  Relativity

 Beitrag 0-317

GPS and Relativity

General relativity dictates that a clock runs slower in a gravitational field, the stronger the field the slower the clock:
    A GPS satellite's clock runs faster when observed from a receiver on the earth as the satellite is in a weaker gravitational field. Conversely a consequence of special relativity is that a clock moving with respect to the observer appears to run slow.
As a GPS satellite is moving in the reference frame of an observer on the earth, a time dilation effect occurs and the satellite's clock appears to run slower.
So the general and special relativistic effects work in opposition to one another, with the gravitational effect being the more dominant for a GPS satellite. Thus an uncompensated satellite master clock would appear to run fast to the earth-bound receiver.
In the real GPS satellites the relativistic effect is nominally compensated by reducing the master 10.23 MHz clock down by 0.00457 Hz before launch. For an ideal satellite in a circular orbit, this would remove the effect.
With an elliptical orbit the satellite clock will still not be correct to an earth observer as it speeds up and comes closer to the earth on one half of it's orbit (clock slows down) and slows down and goes further from the earth in the other half of it's orbit (clock speeds up). Thus the receiver must make compensation for this according to the eccentricity of the orbit and the satellite's position within the orbit at a given time.
Note: One can also calculate the Doppler effect (which is much greater than the effects mentioned above) and obtain the relative speed, which may also be included in the calculation of position.
Quelle: Understanding GPS


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tags: stw1540R: Relativity

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