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A satellite orbiting the moon very near the surface has a period of 110min. What is free-fall acceleration on the surface of the moon?

Short Answer

Expert verified

gmoon=1.58m/s2

Step by step solution

01

Given information

Given in the question that, A satellite orbiting the moon very near the surface has a period of 110min.

02

Period of 

Given:

Tsat=110min

Tsat=110min×60s1min

Tsat=6600s

03

Step 3:A satellite is orbiting the moon 

When a satellite is orbiting the moon at a constant speed, the only force that is acting on it is the gravitational force from the moon.

∑F=mgmoon=mar

m̸gmoon=m̸ar

gmoon=vsat2r

gmoon=vsat21.74×106 (2)

vsat=2Ï€rT

vsat=2π×1.74×1066600
vsat=1.66×103m/s(2)

From (1) and(2)

gmoon=1.66×10321.74×106

gmoon=1.58m/s2

04

Final answer

The free-fall acceleration on the surface of the moon is

gmoon=1.58m/s2

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