Show that if a satellite orbits very near the surface of aplanet with period T,

Question

Show that if a satellite orbits very near the surface of aplanet with period T, the density of the planet is
= m/V = 3/GT2. Using these results,estimate the density of the Earth, given that a satellite near thesurface has an orbital period of 88min. I plead you to respond in detail, because I'm not evenunderstanding the problem. I don't know from where to start. Thank you very much for your help! Show that if a satellite orbits very near the surface of aplanet with period T, the density of the planet is
= m/V = 3/GT2. Using these results,estimate the density of the Earth, given that a satellite near thesurface has an orbital period of 88min. I plead you to respond in detail, because I'm not evenunderstanding the problem. I don't know from where to start. Thank you very much for your help!

Explanation / Answer

   Timeperiod , T = 2R /V0    [ Where Vo = orbital velocitynear the surface = ( GM /R) ]                        T = 2R / ( GM /R)                            Here G = universal gravitational constant = 6.67 X 10-11 N m2 / kg2                                   M = mass                                     R= Radius                         T2 ( GM/R) = 4 2 R2                                   M = 42 R3 / G T2                    But, mass = density () * volume (v)                             v = 42 R3 / G T2                        here volume, v = (4/3) R3                                [  (4/3) R3]=  42 R3 / GT2                          density, = mass /volume = 3 / GT2 Given that Timeperiod, T = 88 min = 88 * 60 s = 5280 s                      density, = 3 / ( 6.67 X 10 -11) (5280)2 = 5065.9 kg /m3 Given that Timeperiod, T = 88 min = 88 * 60 s = 5280 s                      density, = 3 / ( 6.67 X 10 -11) (5280)2 = 5065.9 kg /m3

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