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Newton's Law of Universal
particle of matter in the universe attracts every other particle with a
force which is directly proportional to the product of their masses and
is inversely proportional to the square of the distance between them.
Where F is the magnitude of the force acting between two
bodies of masses m1 and m2, separated by a
\ F =
G is called the
universal gravitational constant.
Gravitational Constant (G)
Universal Gravitational Constant
Magnitude of G: 6.673 × 10- 11 Nm2
SI Unit of G: Newton - metre2
Dimensions of G: [M- 1 L- 3 T - 2]
between G and g
due to earth's gravity at the surface of the earth = g
The gravitational force of attraction between the earth and
a body of mass m on the surface of the earth is given by
Where M is the mass of the earth and R is the radius of the
But weight of the body = gravitational force
\ mg =
\ g =
between G and g'
At a height h above the surface of the earth,
acceleration due to earth's gravity = g'.
corresponding equations are,
(R + h)2
and F' = mg'
\ mg' =
\ g' =
between g and g'
From (1) and (2)
\ g' = g
(R + h)
Conclusion: From (3), as height 'h' above the surface of the earth
increases, acceleration due to earth's gravity decreases.
of a Satellite
of Satellite: A lighter body which revolves around a heavier body due to
the gravitational influence of the heavier body is called its satellite.
Why is it necessary to have at least a two stage rocket to
launch a satellite?
Velocity or Critical Velocity (proper speed) of a Satellite (Vc)
horizontal velocity with which a satellite should be projected from a
point above the earth's surface, so that it orbits in a circular path
around the earth is called the orbital velocity or critical velocity (Vc)
of the satellite.
Definition: The minimum velocity with which a body
should be projected from the surface of the earth so that it escapes the
gravitational field of the earth is called the escape velocity of the
Projection of a Satellite at Height h above the Surface of the Earth
Case : I
V < Vc
V ® Velocity of
Vc ® Critical
The satellite will fall back to the earth.
Case : II
V = Vc
The satellite moves in a circular path and performs UCM around
Case : III
Ve > V > Vc
Ve ® Escape
Here, the satellite will revolve in an elliptical orbit around the
Case : IV
V ³ Ve
The satellite will escape from the gravitational field of
of projection in a horizontal direction
Vc - Critical
Ve - Escape