Gravitation, free fall, variation in 'g' and keplers law lecture wise
1. Contents Lecture 1
Gravitational force
Universal law of Gravitation
Importance of Universal law of Gravitation
Gravitational forces between different
Objects
2. Gravitation Force
Gravitational force is one of the
fundamental forces in nature.
Every object in this Universe attracts every
other object with a certain force.
The force with which two objects attract
each other is called gravitational force.
If the masses of two bodies are small, then
the gravitational force between them is very
small.
4. According to Newton’s law of gravitation, the
force of attraction (F) between the two
objects is given as:
where G is the proportionality constant
known as the universal gravitation constant.
Universal gravitation constant ‘G’ is
numerically equal to the gravitational force of
attraction between the two bodies, each of
unit mass kept at unit distance from each
other.
The value of G is 6.67 × 10-11 Nm2kg-2 .
In CGS , G is 6.67 × 10-8 dyne cm2g-2
5. Importance of Universal law of
Gravitation
The gravitational force holds the Solar System
together.
Holding the atmosphere near the surface of
earth.
The flow of water in the rivers.
For rainfall and snowfall
Motion of the moon around earth.
Occurrence of tides
6. Gravitational forces between different Objects
Mass of earth 6 x 1024 kg
Radius of earth 6.4 x 106 m
Mass of sun 2 x 1030 kg
Mass of moon 7.36 x 1022 kg
Distance between Sun and Earth = 1.5 x 1011 m
Distance between Moon and Earth = 3.8 x 108 m
Gravitation force between Sun and Earth = 3.6 x
1022 N
Gravitation force between Moon and Earth = 2.5 x
1020 N
7. Contents Lecture 2
Free Fall
Equations of motion for a body moving
under gravity
Gravity and gravitation
Mass and weight
8. Free Fall
When an object falls from any height under
the influence of gravitational force only, it
is known as free fall. In the case of free fall
no change of direction takes place but the
magnitude of velocity changes because of
acceleration.
This acceleration acts because of the force
of gravitation and is denoted by ‘g’. This is
called acceleration due to gravity.
9. Equations of Motion for a body moving
under gravity
where ‘u’ is the initial
velocity, ‘v’ is the final
velocity after ‘t’ sec and ‘h’
is the height covered in ‘t’
sec.
g should be positive if the
acceleration due to gravity
is in the direction of
motion, and it should be
negative if it is in the
direction opposite to the
motion.
10. Gravity and Gravitation
Gravity Gravitation
The force of gravitation
exerted by a huge heavenly
body such as the earth, the
sun etc., on a smallest object
near its surface is called
force of gravity.
The force of attraction
between any two objects by
virtue of there masses is
called gravitation (or
gravitational force)
e.g. : Earth pulls an object of
mass 1kg towards it with a force
of 9.8 N.
e.g. : force of attraction between
any two objects such as books,
tables, chairs, and between two
heavenly bodies are the
examples of gravitation.
11. Mass and Weight
Mass Weight
Mass of the body is the quantity of
matter contained in it.
Weight of the body is the force with
which the body is attracted towards
the centre of earth.
It is a scalar quantity. It is a vector quantity.
Mass of the body is constant
quantity.
Weight of the body varies place to
place (with value of g)
SI unit is kilogram(kg) SI unit is newton(N)
It is measured with the help of a
common balance
Weight is measured with a spring
balance.
15. Variation of g due to shape of the earth
The shape of the earth is bulged at the equator and
flat at the poles.
This means earth has large radius at the equator than
at poles. We know that,
So, acceleration due to gravity is more at the pole than at
the equator.
16. Variation of g with the altitude (height)
Let body be at height h above the surface of the
earth as shown in fig. the distance of the body from
the centre of earth = (R+h)
So, acceleration due to gravity decreases with the height
from the surface of earth.
17. Variation in the value of g
Location
Distance from Earth's
center
(m)
Value of g
(m/s2)
Earth's surface 6.38 x 106 m 9.8
1000 km above surface 7.38 x 106 m 7.33
2000 km above surface 8.38 x 106 m 5.68
3000 km above surface 9.38 x 106 m 4.53
4000 km above surface 1.04 x 107 m 3.70
5000 km above surface 1.14 x 107 m 3.08
18. Planet Radius (m) Mass (kg) g (m/s2)
Mercury 2.43 x 106 3.2 x 1023 3.61
Venus 6.073 x 106 4.88 x1024 8.83
Mars 3.38 x 106 6.42 x 1023 3.75
Jupiter 6.98 x 107 1.901 x 1027 26.0
Saturn 5.82 x 107 5.68 x 1026 11.2
Uranus 2.35 x 107 8.68 x 1025 10.5
Neptune 2.27 x 107 1.03 x 1026 13.3
Pluto 1.15 x 106 1.2 x 1022 0.61
20. Kepler’s Law of Planetary Motion
Johannes Kepler was a
German
mathematician,
astronomer, and
astrologer. A key figure
in the 17th-century
scientific revolution,
he is best known for
his laws of planetary
motion.
21. Kepler’s First Law(law of orbits)
Each planet moves
around the sun in
an elliptical orbit
with the sun at one
of the foci of the
orbit.
22. Second law (law of areas)
The line joining the
planet sweeps out
equal areas in equal
intervals of time.
Area OP1P2 = OP3P4
A planet does not
move around the sun
with a constant
speed
23. Third law (law of periods)
Kepler’s third law, the law of periods, defines the
relationship between the orbital period of a
planet and the average radius of its orbit.
The orbital period of a planet, denoted by T, is
the time taken by the planet to make a complete
revolution around the sun along its orbit.
The average radius of the orbit of a planet is also
the mean distance of the planet from the sun.
24. The law of periods
states that the square
of orbital period T, of a
planet is proportional
to the cube of its mean
distance, R, from the
sun.
The law of periods can
be expressed as T2 α
R3.
