Digital Library of GLT Saraswati Bal Mandir. Gravitation is a natural phenomenon by which all physical bodies attract each other. It is most commonly experienced as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped.

1. Prepared By:
Suraj Jha – Class-XI-B
Anoop Kr. Singh – Class-XI-B

2. Early Astronomy
As far as we know, humans have always
been interested in the motions of objects in
the sky.
Not only did early humans navigate by
means of the sky, but the motions of
objects in the sky predicted the changing of
the seasons, etc.

3. Early Astronomy
There were many early attempts both
to describe and explain the motions of
stars and planets in the sky.
All were unsatisfactory, for one reason
or another.

4. The Earth-Centered Universe

A geocentric (Earth-centered) solar system is often
credited to Ptolemy, an Alexandrian Greek,
although the idea is very old.

5. Ptolemy’s Solar System
Ptolemy’s solar system could be made to fit the
observational data pretty well, but only by becoming
very complicated.

6. Copernicus’ Solar System
The Polish cleric Copernicus proposed a heliocentric
(Sun centered) solar system in the 1500’s.

7. Objections to Copernicus
How could Earth be moving at enormous speeds
when we don’t feel it?
(Copernicus didn’t know about inertia.)
Why can’t we detect Earth’s motion against the
background stars (stellar parallax)?

Copernicus’ model did
data very well.
not fit the observational

8. Galileo & Copernicus
Galileo became convinced that Copernicus was
correct by observations of the Sun, Venus, and the
moons of Jupiter using the newly-invented
telescope.
Perhaps Galileo was motivated to understand
inertia by his desire to understand and defend
Copernicus’ ideas.

9. Kepler’s Laws:
Kepler’s First Law
Kepler determined that the orbits of the planets were
not perfect circles, but ellipses, with the Sun at one
focus.
Planet
Sun

10. Kepler’s Second Law
Kepler determined that a planet moves faster when
near the Sun, and slower when far from the Sun.
Planet
Faster
Sun
Slower

11. Kepler's Third Law
T2αR3
The above equation was formulated in 1619
by the German mathematician and
astronomer Johannes Kepler (1571-1630). It
expresses the mathematical relationship of
all celestial orbits. Basically, it states that
the square of the time of one orbital period
(T2) is directly proportional to the cube of
its average orbital radius (R3).

12. Why?
Kepler’s Laws provided a complete kinematical
description of planetary motion (including the
motion of planetary satellites, like the Moon) - but
why did the planets move like that?

13. The Apple & the Moon
Isaac Newton realized that the motion of a falling
apple and the motion of the Moon were both actually
the same motion, caused by the same force - the
gravitational force.

14. Universal Gravitation
Newton’s idea was that gravity was a universal force
acting between any two objects.

15. At the Earth’s Surface
Newton knew that the gravitational force on the
apple equals the apple’s weight, mg, where g = 9.8
m/s2.
W = mg

16. Universal Gravitation
From this, Newton reasoned that the strength of the
gravitational force is not constant, in fact, the
magnitude of the force is inversely proportional to
the square of the distance between the objects.

17. Universal Gravitation
Newton concluded that the
gravitational force is:
Directly proportional to the
masses of both objects.
Inversely proportional to the
distance between the objects.

18. Law of Universal Gravitation
In symbols, Newton’s Law of Universal Gravitation
is:
Fgrav = G
Mm
r2
Where G is a constant of proportionality.
G = 6.67 x 10-11 N m2/kg2

19. An Inverse-Square Force

20. The Gravitational Field
During the 19th century, the notion of the
“field” entered physics (via Michael
Faraday).
Objects with mass create an invisible
disturbance in the space around them
that is felt by other massive objects - this is
a gravitational field.

21. The Gravitational Field
So, since the Sun is very massive, it
creates an intense gravitational field
around it, and the Earth responds to
the field. No more “action at a
distance.”

22. Gravitational Field Strength
Near the surface of the Earth, g = F/m = 9.8
N/kg = 9.8 m/s2.
In general, g = GM/r2, where M is the mass
of the object creating the field, r is the
distance from the object’s center, and G =
6.67 x10-11 Nm2/kg2.

23. Gravitational Field Inside a Planet
If you are located a distance r from the
center of a planet:
 all of the planet’s mass inside a sphere of
radius r pulls you toward the center of the
planet.
All of the planet’s mass outside a sphere
of radius r exerts no net gravitational
force on you.

24. Gravitational Field Inside a Planet
The blue-shaded part
of the planet pulls you
toward point C.
The grey-shaded part
of the planet does
not pull you at all.

25. Gravitational Field Inside a Planet
Half way to the center of the planet, g has one-half of
its surface value.
At the center of the planet, g = 0 N/kg.

26. Variation of ‘g’ Due To Altitude,
Latitude And Depth
(i)Variation of g with altitude :
 Let M be the mass of the earth and R be the radius of
the earth. Consider body of mass m is situated on the
earth's surface. Let g be the acceleration due to
gravity on the earth's surface.

27. From this equation it is obvious that acceleration
due to gravity goes on decreasing as altitude of
body from the earth's surface increases.

29. (ii) Variation of g due to depth :
Let M be the mass "of the earth and R be the radius of the
earth. The acceleration due to gravity on the surface of the
earth is given by,

30. Consider the earth as sphere of uniform density.

31. Consider a point P at the depth d below the
surface of the earth where the acceleration due
to gravity be gA. Distance of point P from centre
of the earth is (R-d).
The acceleration due to gravity at point P due to
sphere of radius (R-d) is

32. This is the expression for acceleration due to gravity at depth
d below the earth surface. From this expression, it is clear that
acceleration due to gravity decreases with depth.
Note At the centre of the earth, d = R Therefore gd = 0
Thus, if the body of mass m is taken to the centre of the earth,
its weight will be equal to zero but mass of the body will not
be zero.
The above consideration shows that the value of g is
maximum at the surface of the earth and it goes on decreasing
(i)
with increase in depth below the earth's surface.
(ii)
with increase in the height above the earth's surface.

33. Escape Velocity:
The velocity needed for an object to
completely escape the gravity of a large
body such as moon, planet, or star
If an object gains
enough orbital
energy, it may
escape (change
from a bound to
unbound orbit).

34. Escape velocity
For object to escape gravity must have:
Ek≥Ep
2
½m v ≥ mgh
Or for Earth, h = R
vesc ≥ √2 g R ≥ √ 2 G M/R
 independent of mass of object

35. Escape velocity from Earth ≈ 11 km/s from sea
level
(about 40,000 km/hr)
 Escape and orbital velocities don’t depend
on the mass of the cannonball.

36. Orbital Velocity and Altitude
 A rocket must accelerate to at least 25,039 mph (40,320 kph) to completely
escape Earth's gravity and fly off into space.
 Earth's escape velocity is much greater than what's required to place an Earth
satellite in orbit. With satellites, the object is not to escape Earth's gravity, but
to balance it. Orbital velocity is the velocity needed to achieve balance
between gravity's pull on the satellite and the inertia of the satellite's motion
-- the satellite's tendency to keep going. This is approximately 17,000 mph
(27,359 kph) at an altitude of 150 miles (242 kilometers). Without gravity, the
satellite's inertia would carry it off into space. Even with gravity, if the
intended satellite goes too fast, it will eventually fly away. On the other hand,
if the satellite goes too slowly, gravity will pull it back to Earth. At the correct
orbital velocity, gravity exactly balances the satellite's inertia, pulling down
toward Earth's center just enough to keep the path of the satellite curving like
Earth's curved surface, rather than flying off in a straight line.

38. Satellites
Satellites can be classified by their functions. Satellites are launched into
space to do a specific job. The type of satellite that is launched to
monitor cloud patterns for a weather station will be different than a
satellite launched to send television signals across Canada. The satellite
must be designed specifically to fulfill its function.
Below are the names of nine different types of satellites. There are also
nine pictures of satellites. Each picture is an example of one type of
satellite.
Main Types Of Satellites and their examples:
Astronomy satellites - Hubble Space
Telescope
Atmospheric Studies satellites – Polar
 Communications satellites - Anik E

39. Black Holes
When a very massive star gets old and runs
out of fusionable material, gravitational
forces may cause it to collapse to a
mathematical point - a singularity. All
normal matter is crushed out of existence.
This is a black hole.

40. Black Hole Gravitational Force

41. How Black Hole Looks Like

42. Black Hole Gravitational Force
The black hole’s gravity is the same as the
original star’s at distances greater than the
star’s original radius.
Black hole’s don’t magically “suck things
in.”
The black hole’s gravity is intense because
you can get really, really close to it!

43. THE BLACK HOLE

44. Earth’s Tides
There are 2 high tides and 2 low tides per day.
The tides follow the Moon.

45. Why Two Tides?
Tides are caused by the stretching of a planet.
Stretching is caused by a difference in forces on
the two sides of an object.
Since gravitational force depends on distance,
there is more gravitational force on the side of
Earth closest to the Moon and less gravitational
force on the side of Earth farther from the Moon.

46. How does gravity cause tides?
• The Moon’s gravity pulls harder on near side of
Earth than on far side.
• The difference in the Moon’s gravitational pull
stretches Earth.

47. Why the Moon?
The Sun’s gravitational pull on Earth
is much larger than the Moon’s
gravitational pull on Earth. So why do
the tides follow the Moon and not the
Sun?

48. Why the Moon?
Since the Sun is much farther from Earth than the
Moon, the difference in distance across Earth is
much less significant for the Sun than the Moon,
therefore the difference in gravitational force on
the two sides of Earth is less for the Sun than for
the Moon (even though the Sun’s force on Earth is
more).
The Sun does have a small effect on Earth’s tides,
but the major effect is due to the Moon.

49. T
K
N
A
H
U
O
Y