If a body is falling freely, under the effect of gravity, then the acceleration in the body is called acceleration due to gravity.

#### Variation in acceleration due to gravity with height

Acceleration due to gravity at a height h above the surface of earth is,

$$g’ = g (1 – \frac{2h}{R_e})$$

Where,

R_{e} is the radius of the earth.

g is the acceleratin due to gravity.

#### Variation in acceleration due to gravity with depth

Acceleration due to gravity at a depth d below the surface of earth is,

$$g’ = g (1 – \frac{d}{R_e})$$

Where,

R_{e} is the radius of the earth.

g is the acceleratin due to gravity.

#### Variation in acceleration due to gravity with rotation of earth

Acceleration due to gravity, when rotation of earh is taken into account is,

$$g’ = g – R_e \omega^2 \cos^2 \lambda$$

Where,

R_{e} is the radius of the earth.

g is the acceleratin due to gravity.

λ is the lattitude of earth

#### Variation in acceleration due to gravity with shape of earh

Equatorial radius of the earth is about is 21 km greather than the polar radius. It means value of acceleration due to gravity is increases as we go from equator to the pole.

Acceleration due to gravity on the earth surface is 9.8 m/sec^{2}.

### Gravitational potential energy

Gravitational potential energy of the body of mass m is given by,

$$ U = – \frac{GMm}{r}$$

where,

M is the mass of earth.

r is the distance between M and m and r>R.

### Escape speed

Escape speed from earth’s surface is given by

$$v_e = \sqrt \frac{2GM}{R}$$

Where,

M is the mass of earth.

R is the radius of the earth.

G is the universal gravitational constant.

### Kepler’s law of planetary motion

#### Law of elliptical orbits

Every planets move around the sun in elliptical orbits, the sun being at one of the focus.

#### Law of Area

The radius vector, drown from the sun to planet, sweeps out equal areas in equal time.

#### Law of periods

The sqare of the period of the revolution of the planet around the sun is proportional to cube of the semi-major axis of the ellipse.