Physics – Gravitation: Additional Questions

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Concepts:

Newton’s Law of Gravitation in Vector Form:

Difference Between Universal Gravitation Constant (G) and Acceleration Due to Gravity (g):

  • Universal gravitation constant ‘G’ is a scalar quantity while acceleration due to gravity ‘g’ is a vector quantity.
  • Universal gravitation constant ‘G’ is universal constant, while acceleration due to gravity ‘g’ changes from place to place and from planet to planet.
  • Dimensions of Universal gravitation constant ‘G ‘are [M-1L3 T-2], while dimensions of acceleration due to gravity ‘g’ are [M0L1 T-2].

Relation Between  g and gh:

Difference Between Gravitation and Gravitational Force:

  • Gravitation is a natural phenomenon by which material objects attracts towards one another.
  • Gravitational force is the force of attraction which keeps two bodies in universe bonded together.

Variation in acceleration due to gravity due to Shape of the Earth:

  • The acceleration due to gravity on the surface of the earth is given by



  • We can see that the acceleration due to gravity at a place is inversely proportional to the square of the distance of the point from the centre of the earth. Now, the earth is not perfectly spherical. It is flattened at the poles and elongated on the equatorial region. The radius of the equatorial region is approximately 21 km more than that at the poles. Hence acceleration due to gravity is maximum at the poles and minimum at the equator. As we move from the equator to the poles the distance of the point on the surface of the earth from the centre of the earth decreases. Hence the acceleration due to gravity increases

Weight of a Body:

  • A weight of a body is the force with which body is attracted towards the centre of the earth (planet).
  • Its unit is newton (N) and dimensions are the same as that of the force [M1L1 T-2]
  • Mathematically the weight of a body on the surface of the Earth (Planet) is given by

F = mg

Where m = mass of the body and

g = acceleration due to gravity on the surface of the earth

Derivation of Expression for Critical Velocity of Satellite Orbiting Very Close to the Earth’s Surface in terms of Density of the Earth:

The critical velocity of a satellite orbiting very close  to the earth’s surface is given by



  • This is the expression for the critical velocity of a satellite orbiting very close to the earth’s surface in terms of density of the material of the earth/planet:

Characteristics

Characteristics of Gravitational Force:

  • The gravitational force between two bodies forms the action-reaction pair. The gravitational force between two masses is always that of attraction. If the first body attracts the second body with force F (direction of force from the second body to the first body), then the second body attracts the first body with equal force F  (direction of force from the first body to the second body).
  • The gravitational force between two masses is always acting along the line joining the centre of the two masses.
  • The gravitational force between two masses is independent of the medium between the two masses.
  • The gravitational force between two bodies does not depend upon the presence or the absence of other bodies.
  • Gravitational force is a conservative force because the work done by the gravitational force is independent of the path between initial and final position.

Characteristics of Acceleration Due to Gravity:

  • The acceleration due to gravity is on account of the gravitational force acting on the body.
  • Average acceleration due to gravity on the surface is different for different planets.
  • At given place, the value of acceleration due to gravity is the same for all bodies irrespective of their masses.
  • The acceleration due to gravity changes from place to place. i.e. it changes with the change in latitude or altitude or depth.
  • Acceleration due to gravity decreases with the increase in latitude, decreases with the increase in altitude, and decreases with increase in the depth.
  • The acceleration due to gravity at a small height ‘h’ from the surface of the earth is the same as the acceleration due to gravity at the depth, ‘d = 2h’ below the surface of the earth. It means that the value of acceleration due to gravity at a small height from the surface of the earth decreases faster than the value of the acceleration due to gravity at the depth below the surface of the earth.

Factors Affecting:

Factors Affecting the Gravitational Force Between Two Bodies:

  • The gravitational force of attraction between two bodies is directly proportional to the product of masses. If the distance between two masses is constant, then increase in mass of one of the two or of both increases the gravitational force of attraction between the two bodies.
  • The gravitational force of attraction between two bodies is inversely proportional to the square distance between the two bodies. If the masses are kept constant, then the increase in distance between the two bodies decreases the gravitational force of attraction between the two bodies.
  • The gravitational force between two masses is independent of the medium between the two masses.
  • The gravitational force between two bodies does not depend upon the presence or the absence of other bodies.

Factors Affecting Critical Velocity of Satellite:

  • Critical Velocity of a satellite is given by

  • Critical velocity of the satellite is directly proportional to the square root of mass (M) of the planet (earth) around which the satellite is orbiting.
  • Critical velocity of the satellite is inversely proportional to the square root of the radius of its orbit.
  • The equation does not contain the term, ‘m’ which shows that the critical velocity is independent of the mass of the satellite.

Factors Affecting Period of Satellite:

  • Period of a satellite is given by

  • The square of the time period of the satellite is directly proportional to the cube of the radius of orbit (r) of the satellite
  • The equation does not contain the term, ‘m’ which shows that the critical velocity is independent of the mass of the satellite.

Factors Affecting Escape Velocity:

  • The escape velocity of a body on the surface of the planet is given by

Gravity

  • The escape velocity of a body is directly proportional to the square root of mass (M) of the planet (earth) around which the satellite is orbiting.
  • The escape velocity of a body is inversely proportional to the square root of the radius of the Planet
  • The equation does not contain the term, ‘m’ which shows that the critical velocity is independent of the mass of the satellite.
  • The escape velocity of a body is independent of direction of projection.

Scientific Reasons:

The universality of Newton’s Law of Gravitation:

  • Newton’s law of gravitation is also called as the universal law of gravitation because
  • It is applicable to all material bodies irrespective of their sizes. It is applicable to very minute particles like atoms, electrons at the same time it is applicable to heavenly bodies like planets, stars etc.
  • The law is applicable to all material bodies irrespective of the distance between them. It is applicable to interatomic distances at the same time it is applicable to stellar distances i.e. the distance between stars.

A Satellite is Placed Outside Earth’s Atmosphere:

  • The satellite orbiting very close to the earth’s surface has an orbital speed of about 8 km/s. As the height of the satellite from the surface of the earth increases its orbital velocity decreases.
  • If the satellite is placed in the atmosphere, due to the high velocity of satellite and friction between the atmosphere and the satellite, large heat will be produced and the satellite will get burnt.
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