Two Earth satellites, A and B ,each of mass m , are to be launched into circular

Question

Two Earth satellites, A and B,each of mass m, are to be launched into circularorbits about Earth's center. Satellite A is toorbit at an altitude of 7520 km. Satellite B isto orbit at an altitude of 15100 km. The radius ofEarth REis 6370km. (a) What is the ratio of thepotential energy of satellite B to that ofsatellite A, inorbit? (b) What is the ratio of thekinetic energy of satellite B to that ofsatellite A, inorbit? (c) Which satellite (answer A orB) has the greater total energy if each has a mass of 23.2kg? (d) By how much?

Explanation / Answer

   from the given we can see that    rA = (6370 + 7520) km         = ........ km    rB = (6370 + 15100) km         = .........km (a)    the ratio of the potential energies will be    (PEB / PEA) = [-(G mM / rB) / - (G mM / rA)]                    = (rA / rB)                     =.......... (b)    the ratio of the kinetic energies willbe    (KEB / KEA) = [(GmM / 2 rB) / (G mM / 2 rA)]                    = (rA / rB)                     =.......... (c)    satellitte B has the largest energy       (d)    the difference will be    E = EB -EA          = - (G m M /2)[(1 / rB) - (1 / rA)]          =........ J

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