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** Gravitational Motion**

**Solar system**

- It consists of sun which is stationary at the centre of the universe, a source of light and energy and eight planets (Pluto has lost it planet status) which revolve around the sun in separate orbits.
- The order of the planets in the solar system with their increasing distance from the sun is-
**Mercury****Venus****Earth****Mars****Jupiter****Saturn****Uranus****Neptune**

- John kepler found important regularities in the motions of the planets.
- He gives three law in this context called kepler’s laws of planetary motion.

**Kepler’s laws**

- all planets move around the sun in elliptical orbits having the sun at one force of the orbits.
- The Areal speed of the planet remains constant.
- The square of the period of revolution of any planet around the sun is directly proportional to the cube of its mean distance from the sun, i.e.,
- T2 or r3

**Newton’s Universal Law of Gravitation**

- Every two objects in the universe attract each other.
- “The force of attraction is directly proportional to the product of masses and inversely proportional to the square of the distance between the two masses”
**F ∞ m**_{1 }m_{ 2 }/ r²

(or) F = G . m_{ 1 }m_{ 2 }/ r²**where, G = universal gravitational constant.****G = 6.67 x 10**^{ -11}N m^{ -2}kg^{ -2}

**Acceleration Due to Gravity**

- When a body falls freely, then the increase in velocity per second is called acceleration due to gravity.
- It is represented by g.
- g = GM
_{e}/ R_{e}²- where, M
_{e}= mass of the earth, - R
_{e}= radius of the earth.

- where, M
- Value of g depends upon the radius of the earth as g ∞ 1 / R.
- So, value of g is maximum at poles and minimum at equator.

**Variation in the Value of G With Height**

- Value of g at the surface of the earth is 9.8 m / s²
- Value of g at the centre of earth is zero.
- Value of g at infinity becomes zero.
- If the body is taken inside the earth, acceleration due to gravity decreases linearly with the distance from centre of the earth.
- If the body is taken above the surface of the earth, acceleration due to gravity varies inversely as the square of the distance from the centre of earth.
- g is a vector quantity. Its direction is towards the centre of the earth.
- Its value is independent of the shape, size, mass, etc of the body but depends upon mass and radius of the earth or planet due to which there is a gravity pull.

**Geostationary Satellites**

- Geostationary satellites are stationary with respect to an observer on the earth.
- Their time period is 24 hrs. Their height above the surface of earth is 36,000 km.
- They are always in equatorial plane and their orbits are circular. They are also called parking orbits.
- the speed of satellite depends upon its height from the earth’s surface. The farther is the satellite from the earth’s surface, the lesser will be its speed.
- The velocity of a satellite does not depend upon its mass. There force, if various satellites of different masses revolve around the earth in same orbit then orbital velocities will be the same.

- In an artificial satellite reaction of a person is zero; therefore the person does not experience any weight. This state is known as the state of weightlessness.

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