Question

The Moon orbits the Earth once in 27.3 days in almost circular orbit. Calculate the centripetal acceleration experienced by the Earth. (Radius of the Earth is 6.4×10^6m)
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Answer 1

Answer:

The centripetal acceleration is given by a=

6

v

2

This expression explicity depends on Moon's speed which i s non trivial . we can work with the formula w

2

R

m

=a

m

Since,

a

m

→ centrifugal acceleration of the moon due to earth's gravity

w→ angular velocity

R

m

=60R=60×6.4×10

6

=384×10

6

m is the distance between earth and the moon, which is 60 times the radius of the earth.

w=

T

2π

angular velocity w=

T

2π

.

and T=27.3days=27.3×24×60×60

Seconds=2.358×10

6

sec

putting these values in the formula for acceleration

a

m

=

(2.358×10

6

)

2

(4π

2

)(384×10

6

)

=0.00272ms

−2

Explanation:

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Answer 2

Explanation:

moons centripetal acceleration is 2.7×10^-3m/s^2