Determining The Gm Product

At the Pennsylvania College of Technology, second year electronics students have recently come up with an independent estimate of the Earth's mass, based upon recovering echoes from radio signals bounced off the surface of the Moon. Their novel EME experiment, which involved observing the lunar orbit and solving Equation 6 above for M, has already been treated in the literature [Shuch, 1991]. Their published result for the mass of the Earth, 6.037 x 1024 kg, appears to be in error by about1

Let's utilize a more widely accepted value for the mass of the Earth: 5.975 x 1024 kg. Now we've already stated that Newton's Universal Gravitational Constant, a fudge-factor for dimensional consistency, is equal to 6.673 x 10 " Nt m2 / kg2. Thus we see that the GM product encountered in Equations 7 and 8 above is not a Chevy at all, but rather 4 x 1014 m3/s2, a constant which relates radius to velocity for any satellite orbiting the Earth.


The change in frequency of electromagnetic waves as a function of relative motion is now known as the Doppler shift. The phenomenon was first described by Johann Christian Doppler, a mathematics professor at the State Technical Academy in Prague, in 1842, in a paper delivered to the Royal Bohemian Society of Learning titled "On the Colored Light of Double Stars and Some Other Heavenly Bodies" (Magnin, 1986). Doppler shift varies directly with both the transmitted frequency and the relative velocity between the transmitter and receiver, and inversely with the speed of light. It is utilized in fields as diverse as aircraft radar (Shuch, 1987), spacecraft navigation, remote sensing, biomedical imaging, and of course satellite orbital analysis (Davidoff, 1978).

To understand the Doppler shift for electromagnetic waves, imagine the headlight on the front of an approaching train, which is traveling at a substantial velocity—let's say, mach 100,000, a tenth the speed of light. Now we know the radiation leaves the headlight at the speed of light, 3 x 108 meters per second. Since it appears that the train is adding its forward velocity to that of the light beam, we would naively expect the light from the moving train to

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