  Formula Sheet

## Gravitation

- All the formulas in one go
1
Universal Law of Gravitation
or
where is the universal gravitational constant.
Newton's Law of Gravitation in vector form :
and  Now, , Thus
Comparing above, we get
2
Gravitational Field Gravitational field across mass due to the mass , Gravitational potential: and Ring and or  Gravitational field is maximum at a distance, and it is
Thin Circular Disc
and  Non conducting solid sphere
(a) Point P inside the sphere. , then
and , and at the centre and
(b) Point P outside the sphere. , then
and  Uniform Thin Spherical Shell / Conducting solid sphere
(a) Point P Inside the shell. , then
and
(b) Point P outside shell. , then
and  3
VARIATION OF ACCELERATION DUE TO GRAVITY: Effect of Altitude
when  Effect of depth  Effect of the surface of Earth
Here,
is the mass of earth.
is the height above the earth surface.
is the depth below the earth surface.
is the gravitational constant.
is the acceleration due to gravity.
Variation of g due to Rotation of Earth  At a latitudinal position on earth, where is rotational velocity of the earth, the variation on gravitational acceleration follow above relationship.
4
SATELLITE VELOCITY (OR ORBITAL VELOCITY)
when , the
Time period of Satellite
Energy of a Satellite
; then total energy
5
Kepler's Laws Law of area : The line joining the sun and a planet sweeps out equal areas in equal intervals of time. Hence, Law of periods :