Scientists want to place a 3300 kg satellite in orbit around Mars. They plan to

Question

Scientists want to place a 3300 kg satellite in orbit around Mars. They plan to have the satellite orbit a distance equal to 2.3 times the radius of Mars above the surface of the planet. Here is some information that will help solve this problem: mmars 6.4191 x 1023 kg mars 3.397 x 106 m G 6.67428 x 10 11 N-m2/kg2 1) What is the force of attraction between Mars and the satellite? 1125.027 Submi 2) What speed should the satellite have to be in a perfectly circular orbit? 1954.91 m/s Submit 3) How much time does it take the satellite to complete one revolution? 91.07 hrs

Explanation / Answer

1] Gravitational force = Gm1m2/r^2 = 6.67e-11*3300*6.4191e23/[3.397e6+3.397e6*2.3]^2

= 1124 N

2] Here centripetal force F = mv^2/r

1124 = 3300*v^2/[3.397e6+3.397e6*2.3]

v = sqrt(1124*[3.397e6+3.397e6*2.3]/3300)

= 1954 m/s

3] time period T = 2pi r/v

= 2pi*[3.397e6+3.397e6*2.3]/1954

= 36046 s = 36046/3600 hrs

= 10.01 hrs

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