A 20 kg satellite has a circular orbit (period = 2:24:00; circumference = 5.00 t

Question

A 20 kg satellite has a circular orbit (period = 2:24:00; circumference = 5.00 times l07 m) around a planet of unknown mass and size. Find the speed of the satellite in its circular orbit Find the radial acceleration of the satellite Find the mass of the planet. Local g on the surface of the planet is found to be 8.00 m/s2. Find the radius of the planet. At what minimal radial speed (directly away from the planet) would the satellite need to be moving in order to escape from the planet's gravitational field?

Explanation / Answer

period = 2hour, 24 min = 144*60 = 8640s

circumference = 5*107 m

by definition, period = time taken to complete one cycle.
so the satellite travels 5*107m in 8640s

1) speed = distance/time = (5*107)/8640 = 5787 m/s
2) radial acceleration = v2/r

r = circumference/2 =7957747.15 m

therefore, radial accn = 4.21 m/s2

3)

F = GmM/r2 = ma

Therefore, M = ar2/G = 4.21 * (7957747.15)2/(6.67 * 10-11)

= 3.99 * 1024 kg

4)

accn = GM/R2

Therefore, R = (GM/a) = 5.77 x 106 m

5) escape velocity = (2GM/R) = 8178.42 m/s

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