Scientists want to place a 4100.0 kg satellite in orbit around Mars. They plan t

Question

Scientists want to place a 4100.0 kg satellite in orbit around Mars. They plan to have the satellite orbit at a speed of 2353.0 m/s in a perfectly circular orbit. Here is some information that may help solve this problem:

mmars = 6.4191 x 1023 kg
rmars = 3.397 x 106 m
G = 6.67428 x 10-11 N-m2/kg2

What radius should the satellite move at in its orbit? (Measured frrom the center of Mars.)
What is the force of attraction between Mars and the satellite
What is the acceleration of the satellite in orbit
What should the speed of the orbit be, if we want the satellite to take 8 times longer to complete one full revolution of its orbit?

PLEASE SHOW STEPS

Explanation / Answer

What radius should the satellite move at in its orbit? (Measured frrom the center of Mars.)

MG/R2 = v2/R

R = MG/v2 = 6.4191e23*6.67428e-11/(2353.0*2353.0) = 7738107 m

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What is the force of attraction between Mars and the satellite

F = GMm/R2 = 6.4191e23*6.67428e-11*4100.0/(7738107*7738107) = 2933.5 N

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What is the acceleration of the satellite in orbit

a = MG/R2 = 6.4191e23*6.67428e-11/(7738107*7738107) = 0.715499 m/s2

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What should the speed of the orbit be, if we want the satellite to take 8 times longer to complete one full revolution of its orbit?

T2/T1 = (2r2/v2)/(2r1/v1) = (r2/r1)*(v1/v2) = (v1/v2)^2*(v1/v2) = (v1/v2)^3

(v1/v2)^3 = 9

v2 = v1/3 = 2353.0/3 = 784.33 m/s

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