Gravitational Force and the period of Rotation of Satellite.

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 Nm²kg^-2.
• m1, m2 are the mass of two bodies and r is the distance between them.
• Gravitational force is central as well as conservative force.

Acceleration Due to Gravity of Earth:

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

g=GM/R²  where M is the mass of earth and R is the radius of earth.

• The value of g changes slightly changes from place to place but its value near the earth's surface is9.8ms^-2.
• Gravitational force is the weakest ce in nature.

Condition affecting the value of g:

• 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:
• 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 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 whole weight of the body appears to act.
• Weight of the body is a variable quantity and it changes from place to place.

Weight of a body in a lift:

• When lift is at rest or in uniform motion then apparent weight is equal to the real weight of the body, w=mg.
• When lift is accelerating upward then apparent weight is greater than the real weight of the body i.e. w=m(g+a)
• When lift is accelerating downward then apparent weight of the body is less than the real weight of the body i.e. w=m(g-a).
• When 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

• Weight of the body on 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.  Acceleration due to gravity on Earth is 6 times than that of on the moon.

Planets:

• Planets are the heavenly bodies which  revolves 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 areal speed of 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:

Geostationary Satellite:

• It revolves around the earth in equatorial orbits which is also called Geostationary or Geosynchronous orbit.
• They revolve around the earth at the height of  36000 Km
• There period of rotation is same as the earth's time period of rotation around its own axis i.e. 24 hours.
• These satellites appear to be stationary.

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 satellite is 84 minutes.

Period of Revolution of a satellite:

• Time taken by a satellite to complete one revolution in its orbit is called its 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 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
• Its value on earth surface is 11.2 km/sec
• When orbital speed is is increased by 41% i.e √2 times then it will escape from its orbit.

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