Gravitation

Kepler's laws

1.   Kepler's first law :      The orbit of each planet is an ellipse which has the 

                                             Sun at one of foci.

2.    Kepler's second law   :

       The line from the Sun to each planet sweeps out equal areas in equal times.

3.   Kepler's third law :     

        The squares of the periods of revolution of the planets about the Sun are

        proportional to the cubes of their mean distances from it.

Newton's law of universal gravitation :

Gravitational field strength :             

Gravitational potential and gravitational potential energy

The gravitational potential V at a point in the gravitational field is defined as being numerically equal to the work done in bringing a unit mass from infinity to that point.

The gravitational potential energy, U, of a body of mass m at a point where the

gravitational potential is V is given by         U = m V

If the test mass, m, is moved from potential V₁ to a different potential V₂, its

change of P.E. is equal to m(V₂ - V₁).

Relation between gravitational field and gravitational potential :

Acceleration due to gravity

1.      Outside the Earth ( i.e. r > R ) :  

2.      At the surface of the Earth :         

3.      Inside the Earth ( i.e. r < R ) : 

Satellite orbits. :  

Parking satellites ( or called Synchronous satellites ) :  

Escape Velocity : (By principle of conservation of energy)