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A satellite is revolving very close to a planet of density . The period of revolution of satellite is

Options

  1. A3 G
  2. B3 2 G
  3. C3 G
  4. D3 G

Correct answer

C. 3 G

Step-by-step solution

We know that, Period of revolution Let, T be the time of one revolution of the satellite. Then, aligned T & = 2 r v₀ = 2 (R_p+h ) v₀ T & = 2 (R_p+h ) [G M_ / (R_ +h ) ]^ 1 / 2 v₀ & = G M_ (R_p+h ) T & =2 (R_p+h )^3 G M_p aligned Again, G M_e=g R_e^2 T=2 (R_p+h )^3 g R_ ^2 If the planet is supposed to be a sphere of mean density , then the mass of the planet is given by aligned M_ & = volume density & = 4 3 r_ ^3 aligned So, T= 3 (R_p+h )^3 G R_p^3 If a satellite is orbiting very close to the planet's surface (h R_p

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