Gravitation
Important Points (Part -I)
Gravitational force is attractive force between two masses 
and 
separated by a distance r. It is given by
F = - G (M1M2/r2), where G is universal gravitational constant, G = 
. The negative sign shows that force is attractive.
Dimensional formula of G is 
.
The gravitation is the central force. It acts along the line joining the particles. It is a conservative force. The work-done by it is independent of the path followed. This force is attractive in nature.
It is the weakest force in nature. It is 
times smaller than unclear force and 
times smaller than electric force.
Gravitation is independent of the presence of other bodies around it.
The gravitational pull of the earth is called gravity.
The gravitation forces between two bodies are action-reaction paris. The law of gravitation is called universal as it is applicable to all bodies, irrespective of their size, shape or position. This force does not depend upon the state of the bodies nature of the intervening medium, temperature and other physical condition of the bodies.
In motion of the planets and satellites, force of gravitation provides the necessary centripetal force due to which earth revolves around the sun and moon around the earth.
The value of acceleration due to gravity increases as we go from equator to the pole.
The value of the acceleration due to gravity on the moon is about one sixth of that on the earth and on the sun is about 27 times that on the earth.
Among the planets, the g is minimum on the Mercury.
Acceleration due to gravity on the surface of the earth is given by,
g = 
, where M is the mass of the earth and R is the radius of the earth.
Acceleration due to gravity at a height h above the surface of the earth is given by
= 
.
The approximation is true when h < < R.
Value of g at depth d from earth's surface
(a) 
= 
(b) 
= 
The value of g at height h from the surface and h < < R is 
= g
.
The value of g at latitude 
is
(a) 
= 
(b) At the equator 
= 0. 
= 
(c) At the poles 
= 
. 
= g.
The decrease in g with latitude is caused by the rotation of the earth about its own axis. A part of g is used to provide the centripetal acceleration for rotation about the axis.
The rotation of the earth about the sun has no effect on the value of g.
Decrease in g in going from poles to the equator is about 0.35%.
The weight of the body varies in the same manner as the g does. (W = mg).
The gravitational force to attraction acting on a body of unit mass at any point in the gravitational field is defined as the intensity of gravitational field 
at that point.
= 
=