Two satellites of the same mass are in circular orbits of differentradii above t

Question

Two satellites of the same mass are in circular orbits of differentradii above the Earth's equator. Satellite A is in a geosynchronousorbit, that is, the period of its orbit is 24 hours. Satellite B isin an orbit with one-quarter the orbital radius of that ofsatellite A.

-What is the ratio aB/aA of the centripetal accelerations of thesatellites?

- What is the ratio vB/vA of the satellites' speeds?

- How long does it take satellite B to complete one revolution?

- what is the ratio of the satellites angular momenta?

what is the ratio of the satellites' mechanical energies?

Explanation / Answer

Given that RB =(1/4)RA We know the formula for the time period of the satelliteis                   T = (2)sqrt(R3 / GM) From this formula time period is directly proportional to theR3/2. Then TB / TA =RB3/2 / RA3/2                       = (1/4)3/2                  TB= (0.125)(24 hrs) = 3.0 hrs We know the formula for the centripetal acceleration is a = 42R/T2 Then aB / aA = (RB /RA)(TA2 /TB2) We know the formula linear speed is v = 2R /T Then vB / vA = (RB /RA)(TA / TB)

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