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.

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# Tag: Gravitation

## What is the formula of gravitational potential energy?

## What are the Kepler’s law of planetary motion?

#### Law of elliptical orbits

#### Law of Area

#### Law of periods

## What is the formula of Escape speed?

## What is acceleration due to gravity?

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

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

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

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

### Gravitational potential energy

### Escape speed

### Kepler’s law of planetary motion

#### Law of elliptical orbits

#### Law of Area

#### Law of periods

## What is the Universal law of gravitation?

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.

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

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

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.

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.

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

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.

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.

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

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 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 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.

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

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

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.

Force of attraction between two masses \(m_1\) and \(m_2\) is given by,

$$ F = \frac{m_1 m_2}{r^2}$$

Where,

r is the distance between two masses \(m_1\) and \(m_2\).

G is a constant, called the Universal gravitational constant.

That is called Universal law of gravitation.