Physics Notes: Gravitational Force and Satellites
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 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/R2 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
- 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 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
- 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:
- 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.
- 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.
- 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.