# Centripetal Acceleration of the Moon

by • 04/07/2012 • GeneralComments (0)428

## Gravitation

The property of all objects in the universe which carry mass, by virtue of which they attract one another, is called Gravitation.

## Centripetal Acceleration of the Moon

Newton, after determining the centripetal acceleration of the moon, formulated the law of universal gravitation.

Suppose that the moon is orbiting around the earth in a circular orbit.

If V = velocity of the moon in its orbit,

Rm = distance between the centres of earth and moon,

T = time taken by the moon to complete one revolution around the earth.

For determining the centripetal acceleration of the moon,.Newtonapplied Huygen’s formula which is

a(c) = v2 / r

For moon, am = v2 / Rm ………………… (1)

But v = s/t = circumference / time period = 2πRm/T

Therefore,

v2 = 4π2Rm2 / T2

Therefore,

=> a(m) = (4π2Rm2/T2) x (1/Rm)

a(m) = 4π2Rm / T2

Put Rm = 3.84 x 10(8) m

T = 2.36 x 10(6) sec

Therefore,

a(m) = 2.72 x 10(-3) m/s2

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