Finding Orbital Period and Speed

Question

A GPS (Global Positioning System) satellites orbit at an altitude of 2.9×107 m.

Part A: Find the orbital period.

Part B: Find the orbital speed of such a satellite.    

Express your answer using two significant figures.

Answer 1

Part B: mv²/(r + h) = GmM/(r + h)²; v² = GM/(r + h), r is radius of earth. M is mass of earth.

On surface of earth mg = GMm/r²; GM = gr². So, v² = gr²/(r + h); v = r√(g/(r + h); r = 6.38·10⁶m

g = 9.81 m/s²

v = 6.38·10⁶m√(9.81m/s²/(6.38·10⁶m+ 2.9·10⁷m)) = 3359.51 m/s

Part A: Period T = 2π(r + h)/v = 2π(6.38·10⁶ + 2.9·10⁷)/3359.51 = 66170 s = 18.38 h