A satellite moves in a circular orbit around the Earth at a speed of 5 km/s. Determine the satellite’s altitude above the surfac
e of the Earth. Assume the Earth is a homogeneous sphere of radius 6370 km and mass 5.98 x 10^24 kg. The value of the universal gravitational constant is 6.67259 x 10^−11 N* m^2 /kg^2 . Answer in units of km.
Writing Newton's 2nd Law and Newton's Gravitational Law on the satellite (of mass <em>m,</em> experimenting an acceleration <em>a)</em> orbiting Earth (of mass <em>M</em>) with <em>r</em> as the distance between their centers we have:
Since this acceleration is centripetal, we can write:
So we have:
Or:
This distance <em>r</em> is the sum of Earth's radius <em>R</em> and the satellite's altitude <em>h </em>(<em>r=R+h</em>), so for our values we have (in S.I.):