Three satellites orbit a planet of radius R, as shown in the figure. Satellites

Question

Three satellites orbit a planet of radius R, as shown in the figure. Satellites S_1 and S_3 have mass m. Satellite S_2 has mass 2 m. Satellite S_1 orbits in 230 minutes and the force on S_1 is 10, 000 N. What is the period of S_2 ? Express your answer to three significant figures and include the appropriate units. What is the period of S_3 ? Express your answer to three significant figures and include the appropriate units. What is the force on s_2? Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

a)

since time period is dependent on radius of orbit

S1 and S2 are in same orbit

so time period of S2

T = 230 minutes

b)

T is directly prportional to r^1.5

T3/T1 = (3R/2R)^1.5

T3 = 230 x1.83

T3 = 422.53 min

c)

F is directly proportional to m and inversely proportional to r^2

F3/F1 = (2R/3R)^2

F3 = 4444.4 N

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