# Gravitation

**Newton’s Law of Universal Gravitation:** Every two bodies in the universe attract each other with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The value of g near the equator is 9.78 ms^{-2} and near the poles it is equal to 9.83 ms^{-2} and is zero at the centre of the earth.

### Variations of g

Variations of g are due to

- Shape of the earth (Pear shaped, more flattened at the S–pole than at the N–pole)
- Spin of the earth
- Latitude
- Altitude
- Local conditions

**Shape:** Earth is flat at the poles and some what bulky at the equator. The polar radius is lesser than the equatorial radius by 21 km. Hence g is greater at the polar regions than at the equatorial region.

**Latitude:** Because of the spin of the earth, more centrifugal force acts on bodies near the equator. Hence g value is less at the equator.

**Altitude:** As the height from the surface of the earth increases, the value of g decreases.

**Depth:** As the depth from the surface of the earth increases, the value of g decreases.

### Kepler's Laws

**Kepler’s first law of motion (Law of orbits):** All the planets revolve round the Sun in elliptical orbits with the Sun at one of the foci.

**Kepler’s second law (Law of areas): **The radius vector joining a planet to the Sun sweeps out equal areas in equal intervals of time. This law is a direct consequence of the law of conservation of angular momentum. According to second law a planet moves faster when it is nearer to sun and moves slower when it is far a way from the sun.

**Kepler’s third law (Law of periods):** Square of the period of any planet (T^{2}) about the sun is proportional to cube of the mean distance (R^{3}) of the planet from the sun.

### Orbital Velocity

The velocity required for a satellite to orbit round the earth very close to it is called orbital velocity (v_{o}) or first cosmic velocity.

### Geo Stationary Satellite

An orbit in which the time period of revolution of a satellite is 24 hours is called geostationary orbit or parking orbit or synchronous orbit. It appears stationary with respect to the earth.

Radius of the geo–stationary orbit is approximately 42,400 km. Speed of geo–stationary satellite in it is 3.1 kms^{-1}. The relative velocity of a geostationary satellite with respect to the earth is zero.

### Escape Velocity

The velocity which a body must be projected so that it never returns back or goes out of the earth gravitational field.

It depends upon: (a) Mass M of the earth or planet, (b) Radius R of the earth or planet. It is independent of mass of the body and angle of projection. Its value on earth surface is 11.2 km/s.