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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