**gravitational force**and

**Satellites**. This topic is important for Upcoming Railway & SSC Exams.

## Physics Notes: Gravitational Force and Satellites

**Gravitation:**

Each and every massive body attracts each other by virtue of their masses. This phenomenon is called gravitation.

**Newton’s law of Gravitation**

The gravitational force of attraction between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

**Gravitational force (F)=Gm1m2****/ r ^{2}**

- Where G is the gravitational constant its value is
**6.67×10**^{-11}Nm^{2}kg^{-2.} - m1, m2 is the mass of two bodies and r is the distance between them.
- Gravitational force is central as well as a conservative force.

**Acceleration Due to Gravity of Earth:**

- The acceleration produced in a body due to the gravitational pull of the earth is called acceleration due to gravity.

g=GM/R^{2 }where M is the mass of earth and R is the radius of the earth. - The value of g changes slightly changes from place to place but its value near the earth’s surface is
**9.8ms**^{-2.} - Gravitational force is the
**weakest**force in nature.

**The condition affecting the value of g:**

**The shape of Earth:**Earth shape also affect the value of acceleration due to gravity that’s why g is maximum at poles and minimum at the equator.**Rotation**of Earth on its axis:

g decreases due to the rotation of Earth

g decreases if the angular speed of Earth increases and increases if the angular speed of Earth decreases.**Effects of Altitude:**The value of g decreases with the increase in height.**Effects of depth**: The value of**g decreases**with depth and become zero at the centre earth.

**Mass and Weight:**

- The mass of a body is the quantity of matter contains in it and it is a scalar quantity and its SI unit is
**Kg.** - Mass of a body does
**not change**from place to place. - The weight of the body is the force with which it is attracted towards the centre of the earth and it is given by w=mg.
- Weight of the body is a vector quantity and its unit is Newton
- The centre of gravity of a body is that point at which the whole weight of the body appears to act.
- The weight of the body is
**a variable**quantity and it changes from place to place.

**The weight of a body in a lift:**

- When the lift is at rest or in uniform motion then the apparent weight is equal to the real weight of the body,
**w=mg**. - When the lift is accelerating upward then the apparent weight is greater than the real weight of the body i.e.
**w=m(g+a)** - When the lift is accelerating downward then the apparent weight of the body is less than the real weight of the body i.e.
**w=m(g-a).** - When the lift is falling freely under gravity the apparent weight of the body is zero i.e.
**w=m(g-g) as a =g****w=0** - The weight of the body on
**the moon**is lesser than the weight of the body on earth as the acceleration due to gravity at the moon is less than the acceleration due to gravity on earth.

Note- Acceleration due to gravity on Earth is**6 times**than that of on the moon.

## Planets:

- Planets are the heavenly bodies which revolve around the sun in a specific orbit or path.
- Our solar system contains eight planets as Pluto losses its planet status.

**Kepler’s Laws of Planetary Motion:**

Kepler gives three laws which are as follows:

- All planets revolve around the sun
**in elliptical orbits**with the sun at its one focus. - The real speed of the planet around the sun is constant.
- The square of the time period of revolution of a planet around the sun is directly proportional to the
**cube**of the semi-major axis of its elliptical orbit

**Satellite:**

- A heavenly body revolving around a planet in an orbit is called a satellite.
- Moon is the natural satellite of the earth.

There are two types of artificial satellites:

**Geosynchronous Satellite:**

- A
**geosynchronous satellite**is a satellite in geosynchronous orbit, with an orbital period the same as the Earth's rotation period. - A special case of the geosynchronous satellite is the
**geostationary satellite**, which has a geostationary orbit – a circular geosynchronous orbit directly**above the Earth's equator**. - They revolve around the earth at the height of 36000 Km
- Their period of rotation is the same as the earth’s time period of rotation around its own axis i.e. 24 hours.
- These satellites appear to be stationary.
- The geostationary satellite is used to telecast TV programmes, weather forecasting, in predictions of floods and droughts.

**Polar Satellite:**

- These satellites revolve around the earth in polar orbits at a height of around 800 km.
- The time period of rotation of these satellites is 84 minutes.

**Period of Revolution of a satellite:**

- Time taken by a satellite to complete one revolution in its orbit is called it is a period of revolution.
- Period of revolution= Circumference of orbit/ orbital speed
- Period of revolution of a satellite depends upon the height of satellite from the surface of the earth, greater its height from earth surface more will be its period of revolution.
- Period of revolution is independent of its mass.

**Escape Velocity:**

- The minimum velocity with which when an object is thrown vertically upwards from the earth’s surface just crosses the earth’s gravitational field and never returns.
- Escape velocity=(2gr)
^{1/2} - When orbital speed is increased by 41% i.e √2 times then it will escape from its orbit.
- Its value on earth surface is 11.2 km/sec
- Escape velocity at the Moon's surface is 2.4 km/s.

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