PPT: Gravitation

 Page 1


CAN YOU RECALL?
• When released from certain height why do 
objects tend to fall vertically downwards?
When released from certain height it falls vertically 
downward because of Earth's gravitational force.
• What is the shape of the orbits of planets?
All orbits are elliptical, which means they are an ellipse, 
similar to an oval. 
• What are Kepler ’ s laws?
First Law: Planetary orbits are elliptical with the sun at 
a focus. 
Second Law: The radius vector from the sun to a planet 
sweeps equal areas in equal times. 
Third Law: The ratio of the square of the period of 
revolution and the cube of the ellipse semimajor axis is 
the same for all planets.
Page 2


CAN YOU RECALL?
• When released from certain height why do 
objects tend to fall vertically downwards?
When released from certain height it falls vertically 
downward because of Earth's gravitational force.
• What is the shape of the orbits of planets?
All orbits are elliptical, which means they are an ellipse, 
similar to an oval. 
• What are Kepler ’ s laws?
First Law: Planetary orbits are elliptical with the sun at 
a focus. 
Second Law: The radius vector from the sun to a planet 
sweeps equal areas in equal times. 
Third Law: The ratio of the square of the period of 
revolution and the cube of the ellipse semimajor axis is 
the same for all planets.
Introduction
• All material objects have a natural tendency to get attracted towards the 
Earth. 
• In many natural phenomena like coconut falling from trees, raindrops 
falling from the clouds, etc., the same tendency is observed. 
• All bodies are attracted towards the Earth with constant acceleration. This 
fact was recognized  by Italian physicist Galileo. 
• Every massive object in the universe 
experiences gravitational force. It is the force 
of mutual attraction between any two 
objects by virtue of their masses. It is always 
an attractive force with infinite range. It does 
not depend upon intervening medium. It is 
much weaker than other fundamental forces.
Page 3


CAN YOU RECALL?
• When released from certain height why do 
objects tend to fall vertically downwards?
When released from certain height it falls vertically 
downward because of Earth's gravitational force.
• What is the shape of the orbits of planets?
All orbits are elliptical, which means they are an ellipse, 
similar to an oval. 
• What are Kepler ’ s laws?
First Law: Planetary orbits are elliptical with the sun at 
a focus. 
Second Law: The radius vector from the sun to a planet 
sweeps equal areas in equal times. 
Third Law: The ratio of the square of the period of 
revolution and the cube of the ellipse semimajor axis is 
the same for all planets.
Introduction
• All material objects have a natural tendency to get attracted towards the 
Earth. 
• In many natural phenomena like coconut falling from trees, raindrops 
falling from the clouds, etc., the same tendency is observed. 
• All bodies are attracted towards the Earth with constant acceleration. This 
fact was recognized  by Italian physicist Galileo. 
• Every massive object in the universe 
experiences gravitational force. It is the force 
of mutual attraction between any two 
objects by virtue of their masses. It is always 
an attractive force with infinite range. It does 
not depend upon intervening medium. It is 
much weaker than other fundamental forces.
Kepler’s Laws
• Kepler’s laws of planetary motion describe the orbits of the planets 
around the Sun. 
1. Law of orbit 
• All planets move in elliptical orbits around the Sun with the Sun at one of 
the foci of the ellipse.
• Here, S and S’ are the foci of the ellipse the Sun 
being at S. 
• P is the closest point along the orbit from S and is, 
called ‘Perihelion’. 
• A is the farthest point from S and is, called 
‘Aphelion’. 
• PA is the major axis = 2a. 
• PO and AO are the semimajor axes = a. 
• MN is the minor axis =2b. 
• MO and ON are the semiminor axes = b
Fig.: An ellipse traced by a planet 
with the Sun at the focus.
Page 4


CAN YOU RECALL?
• When released from certain height why do 
objects tend to fall vertically downwards?
When released from certain height it falls vertically 
downward because of Earth's gravitational force.
• What is the shape of the orbits of planets?
All orbits are elliptical, which means they are an ellipse, 
similar to an oval. 
• What are Kepler ’ s laws?
First Law: Planetary orbits are elliptical with the sun at 
a focus. 
Second Law: The radius vector from the sun to a planet 
sweeps equal areas in equal times. 
Third Law: The ratio of the square of the period of 
revolution and the cube of the ellipse semimajor axis is 
the same for all planets.
Introduction
• All material objects have a natural tendency to get attracted towards the 
Earth. 
• In many natural phenomena like coconut falling from trees, raindrops 
falling from the clouds, etc., the same tendency is observed. 
• All bodies are attracted towards the Earth with constant acceleration. This 
fact was recognized  by Italian physicist Galileo. 
• Every massive object in the universe 
experiences gravitational force. It is the force 
of mutual attraction between any two 
objects by virtue of their masses. It is always 
an attractive force with infinite range. It does 
not depend upon intervening medium. It is 
much weaker than other fundamental forces.
Kepler’s Laws
• Kepler’s laws of planetary motion describe the orbits of the planets 
around the Sun. 
1. Law of orbit 
• All planets move in elliptical orbits around the Sun with the Sun at one of 
the foci of the ellipse.
• Here, S and S’ are the foci of the ellipse the Sun 
being at S. 
• P is the closest point along the orbit from S and is, 
called ‘Perihelion’. 
• A is the farthest point from S and is, called 
‘Aphelion’. 
• PA is the major axis = 2a. 
• PO and AO are the semimajor axes = a. 
• MN is the minor axis =2b. 
• MO and ON are the semiminor axes = b
Fig.: An ellipse traced by a planet 
with the Sun at the focus.
Kepler’s Laws
2. Law of areas
• The line that joins a planet and the Sun sweeps equal areas in equal 
intervals of time.
• Kepler observed that planets do not move around the Sun with uniform speed. They 
move faster when they are nearer to the Sun while they move slower when they are 
farther from the Sun. This is explained by this law. 
Fig.: The orbit of a planet P 
moving around the Sun.
The area swept by the planet of mass m in given 
interval ??? is ??? =
1
2
 ?? × ?? ??? ??? ??? =
1
2
( ?? × ?? )
 ?? =?? ?? ??? ??? =
1
2
 ?? ×
?? ?? ??? = ?? × ?? ??? ??? =
?? 2??
=????????????????
Page 5


CAN YOU RECALL?
• When released from certain height why do 
objects tend to fall vertically downwards?
When released from certain height it falls vertically 
downward because of Earth's gravitational force.
• What is the shape of the orbits of planets?
All orbits are elliptical, which means they are an ellipse, 
similar to an oval. 
• What are Kepler ’ s laws?
First Law: Planetary orbits are elliptical with the sun at 
a focus. 
Second Law: The radius vector from the sun to a planet 
sweeps equal areas in equal times. 
Third Law: The ratio of the square of the period of 
revolution and the cube of the ellipse semimajor axis is 
the same for all planets.
Introduction
• All material objects have a natural tendency to get attracted towards the 
Earth. 
• In many natural phenomena like coconut falling from trees, raindrops 
falling from the clouds, etc., the same tendency is observed. 
• All bodies are attracted towards the Earth with constant acceleration. This 
fact was recognized  by Italian physicist Galileo. 
• Every massive object in the universe 
experiences gravitational force. It is the force 
of mutual attraction between any two 
objects by virtue of their masses. It is always 
an attractive force with infinite range. It does 
not depend upon intervening medium. It is 
much weaker than other fundamental forces.
Kepler’s Laws
• Kepler’s laws of planetary motion describe the orbits of the planets 
around the Sun. 
1. Law of orbit 
• All planets move in elliptical orbits around the Sun with the Sun at one of 
the foci of the ellipse.
• Here, S and S’ are the foci of the ellipse the Sun 
being at S. 
• P is the closest point along the orbit from S and is, 
called ‘Perihelion’. 
• A is the farthest point from S and is, called 
‘Aphelion’. 
• PA is the major axis = 2a. 
• PO and AO are the semimajor axes = a. 
• MN is the minor axis =2b. 
• MO and ON are the semiminor axes = b
Fig.: An ellipse traced by a planet 
with the Sun at the focus.
Kepler’s Laws
2. Law of areas
• The line that joins a planet and the Sun sweeps equal areas in equal 
intervals of time.
• Kepler observed that planets do not move around the Sun with uniform speed. They 
move faster when they are nearer to the Sun while they move slower when they are 
farther from the Sun. This is explained by this law. 
Fig.: The orbit of a planet P 
moving around the Sun.
The area swept by the planet of mass m in given 
interval ??? is ??? =
1
2
 ?? × ?? ??? ??? ??? =
1
2
( ?? × ?? )
 ?? =?? ?? ??? ??? =
1
2
 ?? ×
?? ?? ??? = ?? × ?? ??? ??? =
?? 2??
=???????????????? Kepler’s Laws
3. Law of periods
• The square of the time period of revolution of a planet around the Sun is 
proportional to the cube of the semimajor axis of the ellipse traced by the 
planet.
• If r is length of semimajor axis then, this law states that
?? 2
? ?? 3
Or 
?? 2
?? 3
=???????????????? • Kepler’s laws were based on regular 
observations of the motion of planets.
• Kepler did not know why the planets obey 
these laws,. i.e. he had not derived these 
laws.