Statement Of The Problem

Give me a lever long enough, and I'll move the world. Give me a scale big enough, and I'll weigh it. This is essentially the problem posed to Electronics students at the Pennsylvania College of Technology in the Spring of 1991. Their innovative solution to weighing their home planet is worthy not only of the best scientific minds, but of the spirit of innovation with which the Amateur Radio Service has always prided itself.

The measurement procedure which they derived is based upon a Newtonian solution to the two-body orbital problem. The forces which hold a satellite in orbit around its primary are gravity (a force pulling in) and inertia (a force pulling out). To achieve a stable orbit, these two forces must of course be in equilibrium. Gravity varies directly with the mass of both objects; inertia, directly with the mass of only the satellite. Thus in setting the forces of gravity arid inertia equal, the mass of the satellite cancels, leaving an expression for the orbit of the satellite which involves only the mass of the primary (plus a constant which Newton threw in for dimensional consistency).

The orbital characteristics of our natural satellite, the moon, are determined through a combination of visual observation and radio ranging. From them, we determine the velocity of the moon as it orbits the Earth. Applying Newton's Laws, we can then calculate the planetary mass required to produce the observed orbital velocity.

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