Gravitation
Gravitation: Every body
attracts other body by a force called force of gravitation.
Newton's Law of Gravitation: The force of
gravitational attraction between two point of bodies is directly proportional
to their mass and inversely proportional to the squire of the distance between
them.
Consider
two point bodies of masses m1 and m2 are placed at a
distance r, The force of gravitational attraction between them,
,
Here G is constant called universal
gravitational constant.
Assuming SI units, F is measured in newtons (N), m1 and m2 in kilograms (kg), r in meters (m), and the constant G is approximately equal to 6.674×10−11 N m2 kg−2
where:- F is the force between the masses,
- G is the gravitational constant,
- m1 is the first mass,
- m2 is the second mass, and
- r is the distance between the centers of the masses.
Gravity: The gravitational force of the earth is
called gravity. i.e. gravity is a force by which earth pulls a body
towards its center.
The acceleration
produced in a body due to force of gravity is called acceleration due to
gravity (g) and its value is 9.8 m/s2.
► Acceleration due to gravity is independent of shape, size
and mass of the body.
Variation in g:
(i)
Value of g decrease with height or depth from earth’s
surface.
(ii)
g is maximum at poles.
(iii)
g is minimum at equator.
(iv)
g decrease as angular speed of earth increases and g
increases as angular speed of earth decreases i.e. g is inversely proportional
to angular speed of earth
g
α angular speed of earth.
► If the angular speed of the
earth becomes 17 times its present value, the body present on the equator
weightless.
Weight of a body in a lift:
(i)
If lift is stationary or moving with uniform speed
(either upward or downward), the apparent weight of body is equal to its true
weight.
(ii)
If lift is going upward then apparent weight of a
body is more than the true weight.
(iii)
If lift is going downward then apparent weight of a
body is less than the true weight.
(iv)
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 the
situation of weightlessness.
(v)
While going down, if the acceleration of the lift
is more than the acceleration due to gravity, a body in the lift goes in the
contact of the ceiling of lift.
Kepler’s Laws of
planetary motion:
(i)
All planets move around the sun in elliptical orbits,
with the sun being at rest at one focus of the orbit.
(ii)
The position vector of the planet with sun at the
origin sweeps out equal area in equal time i.e. the areal velocity of planet
around the sun always remains constant.
A
consequence of this law is that the speed of planet increases when the planet
is closer to the sun and decreases when the planet is far away from the sun. Speed
of a planet is maximum when it is at perigee and minimum when it is at apogee.
(iii)
The squire of the period of revolution of a planet
around the sun is directly proportional to the cube of mean distance of the
planet from the sun.
If
T is period of revolution and r is the mean distance of planet from the sun,
then T2 α r3.
Clearly
distant planets have larger period of revolution. The time period of nearest
planet Mercury is 88 days, where as time period of farthest planet Pluto is
247.7 years.
Satellite: Satellites
are natural or artificial bodies revolving around a planet under its
gravitational attraction. Moon is natural satellite where as INSAT-1B is an
artificial satellite.
Orbital speed of a
satellite:
(i)
Orbital speed of a satellite is independent of its
mass. Hence satellites of different masses revolving in the orbit of same
radius have same orbital speed.
(ii)
Orbital speed of a satellite depends upon the radius of
orbit (Height of the orbit from the surface of the earth). Greater the radius
of orbit lesser will be the orbital speed.
► The orbital speed of satellite revolving near the surface
of earth is 7.9 km/sec.
Periodic revolution of a satellite:
Time taken by a satellite to complete on revolution in its orbit is called its
period of revolution.
i.e. period of revolution = circumference of orbit / orbital
speed
(i)
Period of revolution of a satellite depends upon the
height of satellite from the surface of the earth. Greater the heights more
will be the period of revolution.
(ii)
Period of revolution of a satellite is independent of
its mass.
► The period of revolution of satellite near the surface of
the earth is 1 hour 24 minute (84 minute).
Geo-Stationary
Satellite: If a satellite revolves
in a equatorial plane in the direction of the earth 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 satellite will appear stationary relative to
earth. Such a satellite is called Geo-Stationary Satellite. Such a satellite
revolves around the earth at a height of 36000 km. The orbit of Geo-Stationary
satellite is called parking orbit. Arther C. Clarck was the first to predict
that a communication satellite can be stationed in the geosynchronous orbit.
Escape Velocity: Escape velocity is that minimum velocity with
which a body should be projected from the surface of the earth so as it goes
out of the gravitational field of the earth and never returns to the earth.
► Escape velocity is independent of mass, shape and size of
the body and its direction of projection.
► Escape velocity is also called second cosmic velocity.
► For earth escape velocity = 11.2 km/sec.
For moon escape
velocity = 2.4 km/sec.
► Orbital speed of satellite V0 = √gR and escape
velocity Ve= √2gR
Where R is the radius of earth i.e. Ve= √2 V0
i.e escape velocity is √2 times the orbital velocity.
Therefore if orbital velocity of a satellite is increased √2
times (increased by 41%), then the satellite will leave the orbit and escape
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