A satallite orbiting the moon very near the surface has a period of 110 mintues.

Question

A satallite orbiting the moon very near the surface has a period of 110 mintues. Use this information, together with the radius of the moon from the table on the inside of the back cover, to calculate the free fall acceleration on the moons surface. My book says the radius of the moon is = 1.74 x 10^6

Please slove this by step by step explaining how to do each step. Thank you

Spacecraft have been sent to mars in recent years. Mars is smaller than earth and has correspondingly weaker surface gravity. On mars, the free fall acceleration is only 3.8 m/s^2. What is the orbitial period of a spacecraft in a low orbit near the surface.

Please slove this by step by step explaing how to do each step. Thank you.

Explanation / Answer

g on moon = GM/r^2

mass of moon is 7.32 e22 Kgs

g = 6.67e-11* 7.32e22/(1.74^2*10^12)

g = 1.61 m/s^2

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Vo = (sqrt(GM/R)

Vo = sqrt(gR)

Vo = sqrt(3.8 * 3390000)

Vo = 3.589 Km/s

Vo = 2*3.14* 3390000/T

T = 21289200/(3589)

T = 5931.79 secs

T = 1.64 hrs

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