A satellite moves in a circular orbit around the Earth at a speed of 6.7 km/s. D

Question

A satellite moves in a circular orbit around
the Earth at a speed of 6.7 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/kg2.
Answer in units of km.

Explanation / Answer

The equation you need to solve is this: F = G * m1 * m2 / r² You are given F, G, m1, and m2 F = 8.93e-11 G = 6.673e-11 m1 = .881 m2 = .881 --> solve the equation for r: F * r² = G * m1 * m2 --> r² = G * m1 * m2 / F --> r = v(G * m1 * m2 / F) so just plug in your values to that formula (with the parenthesis around the square root)!

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