00:02
Hello guys, using the given data we have to find out the time taken by moon to rotate about earth in its orbit.
00:14
That is the period of moon rotation about earth.
00:21
Now, the gravitational force between earth and moon equals g times the product of the mass of moon with the mass of earth over the square of the moon's orbit, say this as equation 1.
00:39
The centipotal force, because the moon is moving in circular motion, is defined as the mass of the object, which is the mass of the moon, times the square of the circular speed or the orbital speed over the orbital radius are.
00:56
And we can write the speed v as 2 pi r over the period t so from this we can write the centipital force equals the mass of the moon times 4 pi square r over t square say this as equation two now for the moon in its orbit the gravitational force provide the necessary centipital force so from equation one and two we can right, g times the mass of moon times the mass of earth over r square equals, the mass of the moon times four pi square, r over t squared.
01:48
And we get the equation for the period t as 2 pi times square root of r -q over g times the mass of earth...