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GRAVITATION CONCEPTS Kepler's law of planetry motion
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GRAVITATION CONCEPTS Kepler's law of planetry motion
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K.V. Lumding; K.V. Karimganj; K.V. LangjingGRAVITATION
CONCEPTS
Kepler's law of planetry motion
(a) Kepler's first law (law of orbit): Every planet revolves around the sun in an
elliptical orbit with the sun is situated at one focus of the ellipse.
(b) Kepler's second law (law of area): The radius vector drawn from the sun to a
planet sweeps out equal areas in equal intervals of time , i.e., the areal velocity of
the planet around the sun is constant.
(c) Kepler's third law (law of period): The square of the time period of revolution of a
planet around the sun is directly proportional to the cube of semimajor axis of the
elliptical orbit of the planet around the sun.
Gravitation is the name given to the force of attraction acting between any two
bodies of the universe.
Newton's law of gravitation: It states that gravitational force of attraction acting
between two point mass bodies of the universe is directly proportional to the
product of their masses and is inversely proportional to the square of the
distance between them, i.e., F=Gm1m2/r2, where G is the universal
gravitational constant.
Gravitational constant (G): It is equal to the force of attraction acting between
two bodies each of unit mass, whose centres are placed unit distance apart.
Value of G is constant throughout the universe. It is a scalar quantity. The
dimensional formula G =[M-1L3T-2]. In SI unit, the value of G =6.67X10-
11
Nm2kg-2.
Gravity: It is the force of attraction exerted by earth towards its centre on a
body lying on or near the surface of earth. Gravity is the measure of weight of
the body. The weight of a body of mass m=mass X acceleration due to
gravity=mg. The unit of weight of a body will be the same as those of force.
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,K.V. Lumding; K.V. Karimganj; K.V. Langjing
Acceleration due to gravity (g): It is defined as the acceleration set up in a
body while falling freely under the effect of gravity alone. It is vector quantity.
The value of g changes with height, depth, rotation of earth the value of g is
zero at the centre of the earth. The value of g on the surface of earth is 9.8
ms-2. The acceleration due to gravity (g) is related with gravitational constant
(G) by the relaion, g=GM/R2 where M and R are the mass and radius of the
earth.
Variation of acceleration due to gravity:
(a) Effect of altitude, g’=Gr2/(R+h)2 and g’=g(1-2h/R)
The first is valid when h is comparable with R and the second relation
is valid when h<<R.
The value of g decreases with increase in h.
(b) Effect of depth g’=g(1-d/R)
The acceleration due to gravity decreases with increase in depth d and
becomes zero at the center of earth.
(c) Effect of rotation of earth: g’=g-R ω2
The acceleration due to gravity on equator decreases on account of
rotation of earth and increase with the increase in latitude of a place.
Gravitational field: It is the space around a material body in
which its gravitational pull can be experienced by other bodies.
The strength of gravitational field at a point is the measure of
gravitational intensity at that point. The intensity of gravitational
field of a body at a point in the field is defined as the force
experienced by a body of unit mass placed at that point
provided the presence of unit mass does not disturb the original
gravitational field. The intensity of gravitational field at a point
distance r from the center of the body of mass M is given by
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, K.V. Lumding; K.V. Karimganj; K.V. Langjing
E=GM/r2=acceleration due to gravity.
Gravitational potential: The gravitational potential at a point in
a gravitational field is defined as the amount of work done in
bringing a body of unit mass from infinity to that point without
acceleration. Gravitational potential at a point, V=work
done(W)/test mass(m0)= -GM/r. V= = -
Gravitational intensity (I) is related to gravitational potential (V)
at a point by the relation, E= -dV/dr
Gravitational potential energy of a body, at a point in
the gravitational field of another body is defined as the
amount of work done in bringing the given body from
infinity to that point without acceleration.
Gravitational potential energy U=gravitational potential X
mass of body =- X m.
Inertial mass of a body is defined as the force required
to produce unit acceleration in the body.
Gravitational mass of a body is defined as the
gravitational pull experienced by the body in a
gravitational field of unit intensity.
Inertial mass of a body is identical to the gravitational
mass of that body. The main difference is that the
gravitational mass of a body is affected by the presence
of other bodies near it. Whereas the inertial mass of a
body remains unaffected by the presence of other bodies
near it.
Satellite: A satellite is a body which is revolving
continuously in an orbit around a comparatively much
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