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Gravitation

Gravitation – Gravitation oftentimes also termed as Gravity is a force which found among all material objects in the universe. For any two objects or particles having non-zero mass, the force of gravity tends to attract them toward each other. Gravity works on objects of all sizes, be these subatomic particles or clusters of galaxies.


Newton's law of gravitation: The Newton’s Law of Gravitation is the law which explains the force of gravitational attraction between two bodies as a function of their mass and their distance.

Mathematically, the force of attraction between two bodies in the universe having non zero mass can be expressed as

F = Gm1m2/d2

Where, F is the force in Newtons, m1 and m2 are the masses of the bodies in kilograms, G is the gravitational constant which equals 6.672x10-11Nm2/kg2, and d is the distance between the bodies in meters.

Newton’s Law of Gravitation also referred as law of gravitation or universal law of gravitation.

Gravity- The earth has a tendency to pull other universal bodies towards its center with some force; this force is called Gravity.

The acceleration developed in body because of force of Gravity is called acceleration due to gravity, denoted in symbol ‘g’; g = 9.8 ms-2

Variation in ‘g’

  • The acceleration due to gravity ‘g’ decreases with height or depth from earth’s surface.
  • The acceleration due to gravity ‘g’ is found maximum at poles.
  • The acceleration due to gravity ‘g’ is found minimum at Equators.
  • The acceleration due to gravity ‘g’ decreases due to rotation of earth.
  • The acceleration due to gravity ‘g’ decreases if angular speed of earth increases and increases if angular speed of earth decreases.
  • If angular speed of earth becomes 17 times its present value, a body on the equator becomes weight less.
Weight of a body in a lift
•    If lift is stationary or moving with uniform speed either upward or downward, the apparent weight of a body is equal to its true weight.
•    If lift is going up with acceleration, the apparent weight of a body is less than the true weight.
•    If lift is going down with acceleration, the apparent weight of a body is less than the true weight.
•    If the cord of the lift is broken, it falls freely. In this situation the weight of a body in the lift becomes zero. This is condition of weightlessness.
•    When going downward, if the acceleration of lift is more than acceleration due to gravity, a body in the lift goes in contact with the ceiling of the lift.

Kepler's Laws of Planetary Motion


Johannes Kepler, working with data painstakingly collected by Tycho Brahe without the aid of a telescope, developed three laws which described the motion of the planets across the sky.

1. The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus.

2. The Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal times.

3. The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.

Kepler's laws were derived for orbits around the sun, but they apply to satellite orbits as well.

Satellite

A satellite can be defined as any object, either manmade or naturally existing, which orbits around something else. For example, the moon orbits around Earth and is thus moon is said to be a satellite of earth. The Earth orbits around the sun and is thus called a satellite of the sun. Examples of naturally occurring satellites include comets, stars, asteroids, and other planets.

The orbit of a satellite is determined by the gravitational pull of the object around which the satellite circles. The thing around which a satellite circles is called the primary object. However, primary objects are also affected by their satellites, and feel some of their gravitational pull. In some cases, when two objects have a similar size and weight (mass), and a similar gravitational pull, they may be called binary systems, rather than being called a primary object and a satellite. Thus Pluto’s moon Charon, and Pluto, represent a binary system instead of a primary object and satellite, since both have similar mass.


Orbital Speed
•    The orbital speed of a satellite is free of its mass, so satellites of various masses revolving in the orbits of same radius describe same orbital speed.

•    Orbital speed of a satellite depends upon the radius of the orbit i.e. height of satellite from the surface of earth. Greater is the radius of orbit, more is the orbital speed.

•    The orbital speed of a satellite revolving near the surface of the earth is 7.9 km/sec.

Period of Revolution of a Satellite- The  time taken by a satellite to complete one revolution in its orbit is called its period of revolution.

i.e Period of Revolution = circumference of orbit / orbital speed

•    The period of revolution of a satellite depends upon the height of satellite from the surface of earth. Greater the height more will be the period of revolution.
•    Period of revolution is independent of its mass.
•    The period of revolution of a satellite revolving near the surface of earth is 84 minutes.

Geo Stationary Satellite


If a satellite revolves in equatorial plane in the direction of earth’s rotation i.e. from west to east with a period of revolution equal to time period of rotation of earth on its own axis i.e. 24 hours, then the satellite will appear stationary relative to earth. Such a satellite is called Geo- Stationary Satellite.

A geo stationary satellite revolves around the earth at a height of 36000 Km. The orbit of Geo Stationary satellite is called parking Orbit. Arthur C. Clarck was the first man to predict that a communication satellite can be stationed in the geosynchronous orbit.

Escape Velocity
Escape Velocity is the minimum velocity with which a body should be projected from the surface of earth so as it goes out of gravitational field of earth and never return to earth.

•    Escape Velocity is independent of the mass, shape and size of the body as well as its direction of projection.
•    Escape Velocity is also termed as Second Cosmic Velocity.
•    For earth, escape velocity = 11.2 Km/s
•    For moon, Escape Velocity = 2.4 m/s
•    Orbital Speed of a Satellite V0 = √g /r and Ve = √2gr; where, r = radius of earth, i.e Ve = √2V0 i.e escape velocity is twice the orbital velocity.

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