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March 27, 2017

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A satellite moves in a circular orbit around the Earth at a speed of 5.8 km/s.
Determine the satellite’s altitude above the surface of the Earth. Assume the Earth is a homogeneous sphere of radius 6370 km and mass 5.98 × 1024 kg. The value of the universal gravitational constant is 6.67259 × 10−11 N · m2/
the gravitational force is the centripetal force

  • physics - ,

    When orbiting at 5.8km/s:
    From Vc = sqrt(µ/r) where Vc = the velocity of an orbiting body, µ = the gravitational constant of the earth and r the radius of the circular orbit,with µ = GM, G = the universal gravitational constant and M = the mass of the central body, the earth in this instant,

    r = µ/Vc^2
    = 6.67259x10^-11(5.98x10^24)/5800^2

    The altitude is therefore
    (r - 6370)/1000 km.

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