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Revision Notes: Gravitation
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Page 1
Physics
Gravitation
The universe's constituents are galaxies, stars, planets, comets, asteroids, and
meteoroids. The force which keeps them bound together is called gravitational force.
Gravitation is a natural phenomenon by which material objects attract one another.
In 1687 A.D., English Physicist Sir Isaac Newton published Principia Mathematica,
which explains the inverse-square law of gravitation.
Newton’s law of gravitation:
? According to Newton's law of gravitation, “Everybody in the universe
attracts every other body with a force which is directly proportional to
the product of their masses and inversely proportional to the square of
the distance between them”. The directions of this force are along the line
joining the two bodies.
? The magnitude of gravitational force acting between two bodies of masses
1
m
and
2
m placed distance apart is
12
12 21 2
Gm m
FF
r
??
Where
12 21
FF ??
? It is a universal law.
? Universal Gravitational constant G is a scalar quantity. Its value is the same
throughout the universe and is independent of the nature and size of the bodies
as well as the nature of the medium between the bodies.
? The value of G in SI system is
11 2 2
6.67 10 Nm kg
??
? and in CGS system is
8 2 2
6.67 10 dynecm g
??
? .
Page 2
Physics
Gravitation
The universe's constituents are galaxies, stars, planets, comets, asteroids, and
meteoroids. The force which keeps them bound together is called gravitational force.
Gravitation is a natural phenomenon by which material objects attract one another.
In 1687 A.D., English Physicist Sir Isaac Newton published Principia Mathematica,
which explains the inverse-square law of gravitation.
Newton’s law of gravitation:
? According to Newton's law of gravitation, “Everybody in the universe
attracts every other body with a force which is directly proportional to
the product of their masses and inversely proportional to the square of
the distance between them”. The directions of this force are along the line
joining the two bodies.
? The magnitude of gravitational force acting between two bodies of masses
1
m
and
2
m placed distance apart is
12
12 21 2
Gm m
FF
r
??
Where
12 21
FF ??
? It is a universal law.
? Universal Gravitational constant G is a scalar quantity. Its value is the same
throughout the universe and is independent of the nature and size of the bodies
as well as the nature of the medium between the bodies.
? The value of G in SI system is
11 2 2
6.67 10 Nm kg
??
? and in CGS system is
8 2 2
6.67 10 dynecm g
??
? .
o The dimensional formula for G is
1 3 2
M L T
??
??
??
.
o The value of the universal gravitational constant G was determined
experimentally by English scientist Henry Cavendish in 1798.
Image: Newton’s law of gravitation
o Newton’s law of gravitation in vector form is,
12
2
ˆ .
Gm m
Fr
r
??
-ve sign shows that gravitational force is always attractive.
Characteristics of Gravitational Force:
The characteristics of gravitational force are as follows:
1. It is always attractive in nature
2. It obeys the inverse square law.
3. It is independent of the nature of the intervening medium.
4. It is independent of the presence or absence of other bodies.
5. It is independent of nature and the size of the bodies, till their masses remain
the same and the distance between their centres is fixed.
Principle of superposition of gravitation:
Page 3
Physics
Gravitation
The universe's constituents are galaxies, stars, planets, comets, asteroids, and
meteoroids. The force which keeps them bound together is called gravitational force.
Gravitation is a natural phenomenon by which material objects attract one another.
In 1687 A.D., English Physicist Sir Isaac Newton published Principia Mathematica,
which explains the inverse-square law of gravitation.
Newton’s law of gravitation:
? According to Newton's law of gravitation, “Everybody in the universe
attracts every other body with a force which is directly proportional to
the product of their masses and inversely proportional to the square of
the distance between them”. The directions of this force are along the line
joining the two bodies.
? The magnitude of gravitational force acting between two bodies of masses
1
m
and
2
m placed distance apart is
12
12 21 2
Gm m
FF
r
??
Where
12 21
FF ??
? It is a universal law.
? Universal Gravitational constant G is a scalar quantity. Its value is the same
throughout the universe and is independent of the nature and size of the bodies
as well as the nature of the medium between the bodies.
? The value of G in SI system is
11 2 2
6.67 10 Nm kg
??
? and in CGS system is
8 2 2
6.67 10 dynecm g
??
? .
o The dimensional formula for G is
1 3 2
M L T
??
??
??
.
o The value of the universal gravitational constant G was determined
experimentally by English scientist Henry Cavendish in 1798.
Image: Newton’s law of gravitation
o Newton’s law of gravitation in vector form is,
12
2
ˆ .
Gm m
Fr
r
??
-ve sign shows that gravitational force is always attractive.
Characteristics of Gravitational Force:
The characteristics of gravitational force are as follows:
1. It is always attractive in nature
2. It obeys the inverse square law.
3. It is independent of the nature of the intervening medium.
4. It is independent of the presence or absence of other bodies.
5. It is independent of nature and the size of the bodies, till their masses remain
the same and the distance between their centres is fixed.
Principle of superposition of gravitation:
It states that the resultant gravitational force F acting on a particle due to the number
of other particles is equal to the vector sum of the gravitational forces exerted by
individual particles on the given particle.
i.e.,
01 02 03 0 0
1
......
n
ni
i
F F F F F F
?
? ? ? ? ? ?
?
Where
01 02 03 0
, , ,...,
n
F F F F are the gravitational forces on a particle of mass
0
m due to
particles of masses
12
, ,....,
n
m m m respectively.
Gravity:
? It is defined as the force of attraction exerted by the earth towards its centre
on a body lying on or near the surface of the earth.
? It is merely a special case of gravitation and is also called earth's gravitational
pull.
? It is the measure of weight of the body.
? The weight of the body = mass(m) × acceleration due to gravity (g) = mg.
Acceleration due to Gravity:
? Acceleration produced in a body due to the force of gravity is called
acceleration due to gravity. It is denoted by symbol ‘g’ and mathematically it
is given by
2
e
GM
g
r
?
Where
e
M
the mass of the earth and r is is the distance of the body from the
centre of the earth
? If the body is on the surface of the earth i.e.
e
rR ? (radius of the earth), then
2
e
e
GM
g
R
?
Page 4
Physics
Gravitation
The universe's constituents are galaxies, stars, planets, comets, asteroids, and
meteoroids. The force which keeps them bound together is called gravitational force.
Gravitation is a natural phenomenon by which material objects attract one another.
In 1687 A.D., English Physicist Sir Isaac Newton published Principia Mathematica,
which explains the inverse-square law of gravitation.
Newton’s law of gravitation:
? According to Newton's law of gravitation, “Everybody in the universe
attracts every other body with a force which is directly proportional to
the product of their masses and inversely proportional to the square of
the distance between them”. The directions of this force are along the line
joining the two bodies.
? The magnitude of gravitational force acting between two bodies of masses
1
m
and
2
m placed distance apart is
12
12 21 2
Gm m
FF
r
??
Where
12 21
FF ??
? It is a universal law.
? Universal Gravitational constant G is a scalar quantity. Its value is the same
throughout the universe and is independent of the nature and size of the bodies
as well as the nature of the medium between the bodies.
? The value of G in SI system is
11 2 2
6.67 10 Nm kg
??
? and in CGS system is
8 2 2
6.67 10 dynecm g
??
? .
o The dimensional formula for G is
1 3 2
M L T
??
??
??
.
o The value of the universal gravitational constant G was determined
experimentally by English scientist Henry Cavendish in 1798.
Image: Newton’s law of gravitation
o Newton’s law of gravitation in vector form is,
12
2
ˆ .
Gm m
Fr
r
??
-ve sign shows that gravitational force is always attractive.
Characteristics of Gravitational Force:
The characteristics of gravitational force are as follows:
1. It is always attractive in nature
2. It obeys the inverse square law.
3. It is independent of the nature of the intervening medium.
4. It is independent of the presence or absence of other bodies.
5. It is independent of nature and the size of the bodies, till their masses remain
the same and the distance between their centres is fixed.
Principle of superposition of gravitation:
It states that the resultant gravitational force F acting on a particle due to the number
of other particles is equal to the vector sum of the gravitational forces exerted by
individual particles on the given particle.
i.e.,
01 02 03 0 0
1
......
n
ni
i
F F F F F F
?
? ? ? ? ? ?
?
Where
01 02 03 0
, , ,...,
n
F F F F are the gravitational forces on a particle of mass
0
m due to
particles of masses
12
, ,....,
n
m m m respectively.
Gravity:
? It is defined as the force of attraction exerted by the earth towards its centre
on a body lying on or near the surface of the earth.
? It is merely a special case of gravitation and is also called earth's gravitational
pull.
? It is the measure of weight of the body.
? The weight of the body = mass(m) × acceleration due to gravity (g) = mg.
Acceleration due to Gravity:
? Acceleration produced in a body due to the force of gravity is called
acceleration due to gravity. It is denoted by symbol ‘g’ and mathematically it
is given by
2
e
GM
g
r
?
Where
e
M
the mass of the earth and r is is the distance of the body from the
centre of the earth
? If the body is on the surface of the earth i.e.
e
rR ? (radius of the earth), then
2
e
e
GM
g
R
?
? It is also defined as the acceleration produced in the body while falling freely
under the effect of gravity alone.
? It is a vector quantity. Its SI unit is
2
ms
?
and its dimensional formula is
02
M LT
?
??
??
.
? The value of g on the surface of earth is taken to be
2
9.8ms
?
.
? The value of g varies with altitude, depth, shape, and the rotation of earth.
? The acceleration due to gravity (g) is related with gravitational constant (G)
by the relation
3
22
4
4
3
3
e
e
e
ee
GR
GM
g GR
RR
??
?? ? ? ?
Where
e
M is the mass of the earth,
e
R is the radius of the earth and ? in the
uniform density of the material of the earth.
? The acceleration value due to gravity is independent of the body's shape, size,
mass etc. of the body but depends upon mass and radius of the earth or planet
due to which there is a gravity pull.
F ma ?
2
GMm
ma
r
?
Then, cancelling m on both sides
2
GM
ag
r
??
Page 5
Physics
Gravitation
The universe's constituents are galaxies, stars, planets, comets, asteroids, and
meteoroids. The force which keeps them bound together is called gravitational force.
Gravitation is a natural phenomenon by which material objects attract one another.
In 1687 A.D., English Physicist Sir Isaac Newton published Principia Mathematica,
which explains the inverse-square law of gravitation.
Newton’s law of gravitation:
? According to Newton's law of gravitation, “Everybody in the universe
attracts every other body with a force which is directly proportional to
the product of their masses and inversely proportional to the square of
the distance between them”. The directions of this force are along the line
joining the two bodies.
? The magnitude of gravitational force acting between two bodies of masses
1
m
and
2
m placed distance apart is
12
12 21 2
Gm m
FF
r
??
Where
12 21
FF ??
? It is a universal law.
? Universal Gravitational constant G is a scalar quantity. Its value is the same
throughout the universe and is independent of the nature and size of the bodies
as well as the nature of the medium between the bodies.
? The value of G in SI system is
11 2 2
6.67 10 Nm kg
??
? and in CGS system is
8 2 2
6.67 10 dynecm g
??
? .
o The dimensional formula for G is
1 3 2
M L T
??
??
??
.
o The value of the universal gravitational constant G was determined
experimentally by English scientist Henry Cavendish in 1798.
Image: Newton’s law of gravitation
o Newton’s law of gravitation in vector form is,
12
2
ˆ .
Gm m
Fr
r
??
-ve sign shows that gravitational force is always attractive.
Characteristics of Gravitational Force:
The characteristics of gravitational force are as follows:
1. It is always attractive in nature
2. It obeys the inverse square law.
3. It is independent of the nature of the intervening medium.
4. It is independent of the presence or absence of other bodies.
5. It is independent of nature and the size of the bodies, till their masses remain
the same and the distance between their centres is fixed.
Principle of superposition of gravitation:
It states that the resultant gravitational force F acting on a particle due to the number
of other particles is equal to the vector sum of the gravitational forces exerted by
individual particles on the given particle.
i.e.,
01 02 03 0 0
1
......
n
ni
i
F F F F F F
?
? ? ? ? ? ?
?
Where
01 02 03 0
, , ,...,
n
F F F F are the gravitational forces on a particle of mass
0
m due to
particles of masses
12
, ,....,
n
m m m respectively.
Gravity:
? It is defined as the force of attraction exerted by the earth towards its centre
on a body lying on or near the surface of the earth.
? It is merely a special case of gravitation and is also called earth's gravitational
pull.
? It is the measure of weight of the body.
? The weight of the body = mass(m) × acceleration due to gravity (g) = mg.
Acceleration due to Gravity:
? Acceleration produced in a body due to the force of gravity is called
acceleration due to gravity. It is denoted by symbol ‘g’ and mathematically it
is given by
2
e
GM
g
r
?
Where
e
M
the mass of the earth and r is is the distance of the body from the
centre of the earth
? If the body is on the surface of the earth i.e.
e
rR ? (radius of the earth), then
2
e
e
GM
g
R
?
? It is also defined as the acceleration produced in the body while falling freely
under the effect of gravity alone.
? It is a vector quantity. Its SI unit is
2
ms
?
and its dimensional formula is
02
M LT
?
??
??
.
? The value of g on the surface of earth is taken to be
2
9.8ms
?
.
? The value of g varies with altitude, depth, shape, and the rotation of earth.
? The acceleration due to gravity (g) is related with gravitational constant (G)
by the relation
3
22
4
4
3
3
e
e
e
ee
GR
GM
g GR
RR
??
?? ? ? ?
Where
e
M is the mass of the earth,
e
R is the radius of the earth and ? in the
uniform density of the material of the earth.
? The acceleration value due to gravity is independent of the body's shape, size,
mass etc. of the body but depends upon mass and radius of the earth or planet
due to which there is a gravity pull.
F ma ?
2
GMm
ma
r
?
Then, cancelling m on both sides
2
GM
ag
r
??
Image: Acceleration due to gravity formula
Variation of Acceleration due to Gravity:
? Due to altitude (h): The acceleration due to gravity at height h above the
earth’s surface is given by
? ?
2
2
1
e
h
e
e
GM h
gg
R
Rh
?
??
? ? ?
??
?
??
2
e
e
GM
g
R
??
??
??
??
For
e
hR ??
2
1
h
e
h
gg
R
??
? ? ?
??
??
When we move above the earth’s surface, the acceleration value due to gravity
decreases.
Read MoreFAQs on Revision Notes: Gravitation
| 1. What is the difference between gravitational force and gravitational field strength? |  |
Ans. Gravitational force is the actual attractive pull between two masses measured in newtons, while gravitational field strength is the force per unit mass at a point in space measured in N/kg. Field strength tells you how strongly gravity affects any object placed there, regardless of the object's mass. Both follow Newton's law of universal gravitation but describe different aspects of gravitational interaction.
| 2. Why does gravitational potential energy become negative, and what does that actually mean? | |
Ans. Gravitational potential energy is negative because the reference point is taken at infinity where potential energy is zero. As objects move closer together, they lose energy and fall into an energy well, creating negative values. This negative sign simply indicates that work must be done against gravity to separate the masses back to infinity, not that the energy is "missing"-it's a mathematical convention that makes calculations consistent.
| 3. How do you calculate escape velocity, and why is it the same for all objects on Earth? | |
Ans. Escape velocity depends only on the planet's mass and radius, not on the escaping object's mass. Using the formula v = √(2GM/R), where G is gravitational constant, M is planetary mass, and R is radius, the object's mass cancels out mathematically. This means a feather and a spacecraft need identical velocities to escape Earth's gravitational pull, making escape velocity a planetary property rather than an object-specific one.
| 4. What's the relationship between orbital velocity and escape velocity for satellites? | |
Ans. Orbital velocity is the speed needed to maintain a circular orbit around a celestial body, while escape velocity is the minimum speed to break free from gravitational attraction entirely. Escape velocity equals √2 times the orbital velocity at any given orbital radius. A satellite at orbital velocity stays bound; increase it by a factor of √2, and it escapes into space-this precise mathematical relationship governs all orbital mechanics.
| 5. How does gravitational potential vary with distance, and why can't you feel the difference in everyday life? | |
Ans. Gravitational potential decreases with distance following V = -GM/r, becoming less negative as you move away from a mass. The potential difference between ground level and rooftop is incredibly tiny because Earth's radius is enormous compared to building heights. This minimal variation explains why gravitational acceleration remains approximately 9.8 m/s² in daily experiences, though it technically decreases with altitude following inverse-square law principles.
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