hello can you please type steps with formulas and numbers? there are similar ans

Question

hello can you please type steps with formulas and numbers? there are similar answers on here but i dont understand where the numbers come from or what formulas they are using. thank you

Scientists want to place a 4400.0 kg satellite in orbit around Mars. They plan to have the satellite orbit at a speed of 2659.0 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 is the acceleration of the satellite in orbit: m/s2


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? m/s

Explanation / Answer

The centripetal force is provided by gravity.

mv2/r=GMm/r2

r=GM/v2=6.673*10-11*6.4191*1023/26592=6.06*106m

F=mv2/r=5135N

a=F/m=1.167m/s2

By kepler's third law,

T2=R3

T'=8T

R'3=64T2

Therefore, R'=4R=4*6.06*106=2.424*107m

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