CIRCULAR MOTION AND GRAVITATION
 
 
 
GRAVITATION

 Every object in our universe attracts the other object with certain fore towards its center. This force of  attraction is known as GRAVITATIONAL FORCE and the phenomenon is called GRAVITATION. This is  gravitational force which is responsible for the uniformity or regularity in our daily astronomical life. The  whole system of the universe is in order only due to this force. Due to gravitation, the system of our  universe is working uniformly and smoothly. The planets around the earth or around the sun moves in an  orderly motion due to gravitation.

NEWTON’S LAW OF GRAVITATION
 In order to explain the gravitational force between two bodies, Newton formulated a fundamental law known after his name i.e. "NEWTON'S LAW OF GRAVITATION"
Newton’s law of gravitation states that
every object in the universe attracts the other object with a force and :
 (1) The gravitational force of attraction between two bodies is directly proportional to the product of their  masses.
F a m1 x m2 ------- (1)
 (2) The gravitational force of attraction between two bodies is inversely proportional to the square of the  distance between their centers.
F a 1/d2 --------- (2)
MATHEMATICAL REPRESENTATION
   
 Combining (1) and (2)
F a m1m2 /d2
F = G m1m2/d2
 Where G = universal gravitational constant
 Value of G:
 G = 6.67 x 10-11 Nm2/kg2
MASS OF THE EARTH
 Consider a body of mass ‘m’ placed on the surface of the earth. Let the mass of the earth is ‘Me’ and  radius  of earth is ‘Re’ .
 Gravitational force of attraction between earth and body is
F = G m Me/ Re2
 We know that the force of attraction of the earth on a body is equal to weight the weight of body.
 i.e
F = W
 therefore
W = G m Me/ Re2
 But W = mg
mg = G m Me/ Re2
or
g = G Me/Re2
or
Me = g x Re2/G
 From astronomical data:
 g= 9.8 m/s2
 Re = 6.4 x 106 m
 G = 6.67 x 10-11 N-m2/kg2
 Putting these values in the above equation.
Me = 9.8 (6.4 x 106)2/6.67 x 10-11
or
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