M

total mass of the satellite + star system

From this total mass subtract now the mass, Mstar of the star (or whatever that center of attraction may be), measured by the same method before the satellite was added to the system. The difference gives the energy of the small satellite as sensed by a far-away observer, the beacon In geometric units

E = Wtotalstar

To speak of satellite energy as a constant of the motion is to say that the quantity E—the satellite's energy measured at infinity—always keeps the same value during free flight of the satellite

SAMPLE PROBLEM 1 Energy of a Clock Bolted to a Spherical Shell

A shell clock of mass m is bolted to a spherical shell at r-coordinate r0. What is its energy E that we measure using the orbit of a remote beacon?

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