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 a distance equal to 1.9 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
rmars = 3.397 x 106 m
G = 6.67428 x 10-11 N-m2/kg2

How much time does it take the satellite to complete one revolution
hrs

Which of the following quantities would change the speed the satellite needs to orbit at
the mass of the satellite
the mass of the planet
the radius of the orbit

5) What should the radius of the orbit be (measured from the center of Mars), if we want the satellite to take 8 times longer to complete one full revolution of its orbit?

Explanation / Answer

F=GMm/r2

=6.673*10-11*4400*6.4191*1023/(2.9*3.397*106)2=1942N

Let the speed be v.

The centripetal force is provided by gravity.

mv2/r=1942

v=2085.2m/s

time=2r/v=2*2.9*3.397*106/2085.2*3600=8.25 hours

The following willl change the speed of orbit:

the mass of the planet
the radius of the orbit.

T2=R3

T'=8T

R'3=64T2

Therefore, R'=4R=4*2.9*3.397*106=3.94*107m

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