Gravitation and its Laws
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| Discuss Gravitation and its Laws GRAVITATION
Gravitation is the name given to the universal attraction between bodies. The term gravity in day to day context refers to the force, as a consequence of which the members of the solar system maintain their orbits.
NEWTON’S LAW OF GRAVITATION
According to this law, there is a force of attraction between any two massive particles in the universe. The force between two point masses m1 and m2, separated by a distance of d is given by
|
F = G m1m2 /r2 |
Where G is the Gravitational constant, and has a value of 6.666 X 10-11 N m2 kg-2.
Thus it can be stated as
Every particle of matter in the universe attracts every other particle with a force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This force acts in the line the line joining their centre.
GRAVITATIONAL POTENTIAL ENERGY
Gravitational potential energy of a body at any point in a gravitational field is defined as the work obtained when a body is brought from infinity to that point.
The gravitational potential energy of a two particle system is given by
|
U = -G m1m2 /r |
The above expression gives the gravitational potential energy of the mass m1 in the gravitational field of m2 at a distance r from it.
On the surface of the earth m1 = Me and r = Re. Thus the expression for the gravitational potential energy of a mass m on the surface of the earth is given as
|
U = G Mem /Re |
|
U = G Mem /(r+Re) |
GRAVITATIONAL POTENTIAL
The change in gravitational potential energy per unit mass when the mass is brought from the reference point to the given point is called the gravitational potential at the given point.
The change in gravitational potential V = Vf - Vi = V is given by
|
V = ( Uf - Ui )/m |
the potential due to a point mass m at a distance of r from it is given by
| V = -Gm/r |
The potential at a point on the axis of the ring, of radius a and mass m, at a distance of r from the centre of ring is given by centre
|
V = -GM/(a2+r2)1/2 |
Consider a spherical shell of mass M and radius a, for a point inside the shell the gravitational potential is given as
| V = -GM/a |
And for a point outside the shell, at a distance of r from the centre of the shell, it is given as
| V = -Gm/r |
Consider a sphere of mass M and radius a, for a point inside the sphere the gravitational potential is given as
|
V = -GMr2/a3 |
At the centre of the sphere the gravitational potential is
| V = -3GM/2a |
And at a point outside the sphere at a distance of r from its centre the gravitational potential is given as
| V = -GM/r |