THE PROBLEM Suppose you are building a satellite to travel in a circular orbit a

Question

THE PROBLEM Suppose you are building a satellite to travel in a circular orbit around the Earth. The Earth has radius r = 6.37 × 106 m and mass m = 5.97 × 1024 kg. To complete one orbit every T-2.7 hours, what altitude should the satellite have? PAPER SOLUTION Solve the problem on paper first, including all four IDEA steps. You will become a better physicist that way! Have you finished your paper solution already? yes INTERPRET DEVELOP Derive an algebraic expression for the satellite's altitude. EVALUATE ASSESS

Explanation / Answer

here,

radius of earth , r = 6.37 * 10^6 m

mass , M= 5.97 * 10^24 kg

time period , T = 2.7 hours 2.7 * 3600 s

let the height above the earth surface be h

time period , T = 2 * pi * sqrt( r^3/G*M )

2.7 * 3600 = 2 * pi * sqrt((6.37 * 10^6 + h )^3 /( 6.67 * 10^-11 * 5.97 * 10^24))

solving for h

h = 3.47 * 10^6 m

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