What is the Gravitation force?
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Gravitation
Gravitation Every body attracts other body by a force
called force of gravitation,
Newton’s law oi Gravitation • The force of gravitational
attraction between two point bodies is directly proportional
to the of their masses and inversely proportional to
the square of the distance between them,
Consider two point bodies of masses and placed
at a distance r. The force of gravitational attraction between
Them F=Gm1m2/r2
Here G is constant called universal gravitational
constant. The value of G is 6.67 10-11 Nm2/kg2.
Gravity • The gravitational force ofearth is called gravity
i.e. gravity is the force by which earth pulls a towards
its
“Ihe acceleration produced in a body due to force of
gravity is called acceleration due to gravity (denoted as g)
and its value is 9.8 m/s2.
Acceleration due to gravity is independent of shape
size and mass of the body.
If a man can jump with a velcrity v from the surface of
earth/ planet. height attained by the man is v2/2g The
Value of g on moon is less than that on earth, Hence on
rtux»n, a man can jump higher than earth
Variation in (weight mg) :
1. Value of g decreases with height or depth from earth’s
surface.
2. g is maximum at poles.
3. g is minimum at equator.
4. 8 decreases due to rotation of earth.
5. g decreasۥs if angular speed of earth increases and
increases if angular speed of earth decreases.
If angular speed of earth becomes 17 tirnes its present
value, a body on the equator becomes weightless,
Weight of a body in a lift
1. If lift is s tationary or moving with uniform S}yed (either
upward or down ward), the apparent weight Of a
is equal to its true wright.
2. If lift is going up with acceleration. the apparent weight
of a body is more than the true weight.
3. If lift is going down with acceleration. thc apparent
weight of a body is less than the true weighe
4. If the cord of the lift is broken, it falls fleely. In this
situation the weight of a body in the hit becomes zero.
This is the situation of weightlessness.
5. While going down, if acceleration of lift is more
than acceleration due to gravity, a body in lift
in contact of the ceiling of lift.
Kepler’s Laws of planetary motion
l. All planets move around the sun in elliptical orbits. with
the sun tæing at rest at one fcx•us of the orbit.
2 The vxsition vector of the planet with sun at the origin
sweeps out equal area in equal time i.e. the areal
of planet around the sun always remainsconstant.
A consequence of this law is that the of
planet increases when the planet is closer to the Sun
and decreases when the planet is far away from sun.
Speed of a planet is maximum when it is at perigee
and minimum when it is at apogee.
3. The square of the period of revolution of a planet
around the sun is directly proportional to the cube of
mean distance of planet from the sun.
If T is period of revolution and r is the mean distance
of planet from sun then T2« r’.
Clearly distant planets have larger of
revolution. The time period of nearest planet Mercury
is 88 days where as time pericxi of farthest planet Pluto
is 247.7 years.
Satellite : Satellites are natural or artificial
revolving around a planet under its gravitational attraction.
Moon is a natural satellite while INSAT-IB is an artificial
satellite of earth
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.
2. Orbitals speed of a satelite depends upon the radius of orbit
(height of satellite from the suri.ce earth). Greate the
radius of orbiL lesser will be the orbital speed
The orbital speed of a gtellite revolving near the surface of earth is 7.9km/sec.
Period of Revolution of a satellite Time taken by
satellite to complete one revolution •n its orbit is called
period of revolution.
circumference of o
i.e. period of revolution =circumference of orbit/orbital speed
1. Period of revolution of a satellite depends
height of satellite from tkw surface of earth. Greater
height more Will be the period of revolution,
2. Period 01 revolution ot a satellite is independent of its
mass,
The period of revolution of satellite revolving near
surface of earth is 1 hour 24 minute (84 minute)
Geostationary Satellite If a satellite revolves in
equatorial plane in the direction of earth’s rotati«-l i.
from west to east with a of revolution equal to
period of rotation of earth on its own axis i.e. 24 hours, then
the satellite will ap•Bar stationary relative to earth. Such
a satellite is called Gee-stationary satellite. Such a satellite
revolves around the earth at a height oi 3€YX) kn.
oi Geo-stationary satellite is called parking orbit. Arthur C,
Clarck was first to predict that a communication satellite
be stationed in the geosynchronous orbit.
Escape velocity : Escape velocity is that minimum
velocity with which a should be projected irom the
surface of earth so as it (Alt oi gravitational field Ofearth
and never return to earth.
velcxity• is indelændent of the mass, shape and
size of the body and its direction of projectiorv
Escape is also called second cosmic velxity,
For earth, escape vel«ity 11.2 km/ s.
For moon. escape velocity 2.4 km / 5.
Orbital velæity of a satellite and
velocity ve where R Radius Of earth,
Ve i.e. escape velocity is times the orbital
velocity.
Therefore if the orbital velocity of a satellite is increa.Q
to times (increased by 41%), the satellite will leave
orbit and escape.