Question

The moon orbits the earth in an approximately circular path of radius 3.8 x 10^8 m. It
takes about 27 days to complete one orbit. Calculate the mass of the earth from this data.​

Answer 1

Answer:

The centripetal acceleration = Net centripetal force / mass

Net centripetal force =

R

2

GMm

−m(ω)

2

R

ω=

27.3×24×3600

2π

,R=3.8×10

8

,M=5.92×10

2

4

centripetal acceleration =

m

R

2

GMm

−m(ω)

2

R

=

(3.8×10

8

)

2

6.67×10

−11

×5.92×10

2

4

−(

27.3×24×3600

2π

)

2

×3.8×10

8

=2.7×10

−3

m.s

−2

Explanation:

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