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A recent NASA report says that a large meteor impacted the Moon on March 17th in Mare Imbrium creating a momentary bright flash of light.

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A recent NASA report says that a large meteor impacted the Moon on March 17th in Mare Imbrium creating a momentary bright flash of light.

The International Geophysical Year spurred the launch of the first artificial Earth satellites. The year was devoted to a study of the Earth and led to major gains in the field of geodesy. There is a good review on the subject at NOAA entitled Geodesy for the Layman. In the chapter on Satellite Geodesy there is a figure with a close-approach diagram similar to the one I used. I could not find a formula for the frequency vs time curve but that could mean at the time it was available elsewhere. Some of Guier's papers are cited in Kaula, Theory of Satellite Geodesy, 1966.

Here are a few papers on the history of doppler satellite tracking:

Yionoulis, The Transit Satellite Geodesy Program (1998)

Guier, Weiffenbach & George, Theoretical Analysis of Doppler Radio Signals from Earth Satellites (1958)

Unclassified reports available to the public:

Guier & Weiffenbach, The Doppler Determinations of Orbits (1959)

Guier, W. H., Ionospheric Contribution to the Doppler Shift at VHF from Near-Earth Satellites (1963)

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Doppler shifts were used to determine Sputnik's orbit in 1957. Subsequently, the US Navy's Transit satellites which were part of its NAVSAT system used the Doppler effect to determine positions on the Earth.

ESA, the European Space Agency, has made space more accessible to some new users as can be seen from the Vega VV02 launch Tuesday morning. Riding up with the Proba-V was Vietnam's VNREDSat 1A and Estonia's ESTCube-1 student satellite. Tracking satellites visually can be difficult because they have to be in sunlight to be seen and then daytime is too bright and at night this just leaves times just before sunrise and after sunset when they are not in the Earth's shadow. ESTCube-1 sends out coded messages on two amateur radio frequencies. This suggests the possibility that one can use the Doppler Effect to acquire some information about the satellite's location. Consider what happens when the satellite makes a close approach to a known position, x

To use this information we need to relate the shape of the frequency curve to range and velocity of the object. One can derive the following set of formulas where omega is the angular frequency and c the velocity of the transmitted wave.

One gets the formula used to plot the frequency curve which contains two unknown parameters, the minimum distance, x

As was mentioned in previous blogs the maximum precision available in Mathcad 11 is about 15 decimal places. The limit is somewhat fuzzy and the roundoff errors can accumulate with the sum of a large number of terms. If the roundoff error is δ=0.5x10

Note that Mathcad made a roundoff error on the sum of u and v above. The correlation matrix for the curve fit procedure involves the sum of squares and other even powers of x

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