A GPS satellite orbits at an altitude of 20,200 km above the surface of Earth. What is the speed of the satellite? (Recall that RE = 6.37 ✕ 106 m.)

Answer 1

Equate the centripetal force = mv²/R and the gravitational force = GM_em/R²

Rearrange to solve for v = sqrt(GM_e/R)

You need to look up G, M_e and R = R_e + height above the earth (in meters!)

You can also solve this by equating mv²/R = mg where g is g_e (R_e²/R²) which only requires knowing g of the earth at sea level, g₀^.

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