Find the radius R of the orbit of a geosynchronous satellite that circles the earth?

NetherCraft 0

Find the radius R of the orbit of a geosynchronous satellite that circles the earth. (Note that R is measured from the center of the earth, not the surface.) You may use the following constants:

The universal gravitational constant G is 6.67*10^11 N*m^2/kg^2 .

The mass of the earth is 5.98*10^24 kg .

The radius of the earth is 6.36*10^6 kg

Radius of the earth is in m not kg, sorry

3 Answers

  • mv^2/r=GmM/r^2, where M is the mass of the earth.

    v^2=GM/r

    r=GM/v^2

    To find v, we have w=v/r

    So v=w*r. w=2*pi/Period. Period is 24 hours=3600*24seconds

    Period= 86400s

    w=7.27e-5

    v=7.27e-5*r

    r=GM/(7.27e-5*r)^2

    r^3=GM/(7.27e-5)^2

    r=(GM)^1/3*1/(7.27e-5)^2/3

    r=4.22e7m=42211.85km

    Being the astute student that you are, you’ll recognize this derivation as being quite similar to Kepler’s equation.

  • A Geosynchronous Satellite

  • geo sats are 22,000 miles out and how can a radius be in kilograms?

    but my guesstimate would be about 25,000 miles

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