NCERT Textbook - Gravitation Class 11 Notes | EduRev

 Page 1


CHAPTER EIGHT
GRAVITATION
8.1 INTRODUCTION
Early in our lives, we become aware of the tendency of all
material objects to be attracted towards the earth.  Anything
thrown up falls down towards the earth, going uphill is lot
more tiring than going downhill, raindrops from the clouds
above fall towards the earth and  there are many other such
phenomena.  Historically it was the Italian Physicist Galileo
(1564-1642) who recognised the fact that all bodies,
irrespective of their masses, are accelerated towards the earth
with a constant acceleration.  It is said  that he made a public
demonstration of this fact.  To find the truth, he certainly did
experiments with bodies rolling down inclined planes and
arrived at a value of the acceleration due to gravity which is
close to the more accurate value obtained later.
A seemingly unrelated phenomenon, observation of stars,
planets and their motion has been the subject of attention in
many countries since the earliest of times.  Observations since
early times recognised stars which appeared in the sky with
positions unchanged year after year.  The more interesting
objects are the planets which seem to have regular motions
against the background of stars.  The earliest recorded model
for planetary motions proposed by Ptolemy about 2000 years
ago was a ‘geocentric’ model in which all celestial objects,
stars, the sun and the planets, all revolved around the earth.
The only motion that was thought to be possible for celestial
objects was motion in a circle.  Complicated schemes of motion
were put forward by Ptolemy in order to describe the observed
motion of the planets.  The planets were described as moving
in circles with the center of the circles themselves moving in
larger circles.  Similar theories were also advanced by Indian
astronomers some 400 years later.  However a more elegant
model in which the Sun was the center around which the
planets revolved – the ‘heliocentric’ model – was already
mentioned by Aryabhatta (5
th
 century A.D.) in his treatise. A
thousand years later, a Polish monk named Nicolas
8.1 Introduction
8.2 Kepler’s laws
8.3 Universal law of
gravitation
8.4 The gravitational
constant
8.5 Acceleration due to
gravity of the earth
8.6 Acceleration due to
gravity below and above
the surface of earth
8.7 Gravitational potential
energy
8.8 Escape speed
8.9 Earth satellites
8.10 Energy of an orbiting
satellite
8.11 Geostationary and polar
satellites
8.12 Weightlessness
Summary
Points to ponder
Exercises
Additional exercises
Page 2


CHAPTER EIGHT
GRAVITATION
8.1 INTRODUCTION
Early in our lives, we become aware of the tendency of all
material objects to be attracted towards the earth.  Anything
thrown up falls down towards the earth, going uphill is lot
more tiring than going downhill, raindrops from the clouds
above fall towards the earth and  there are many other such
phenomena.  Historically it was the Italian Physicist Galileo
(1564-1642) who recognised the fact that all bodies,
irrespective of their masses, are accelerated towards the earth
with a constant acceleration.  It is said  that he made a public
demonstration of this fact.  To find the truth, he certainly did
experiments with bodies rolling down inclined planes and
arrived at a value of the acceleration due to gravity which is
close to the more accurate value obtained later.
A seemingly unrelated phenomenon, observation of stars,
planets and their motion has been the subject of attention in
many countries since the earliest of times.  Observations since
early times recognised stars which appeared in the sky with
positions unchanged year after year.  The more interesting
objects are the planets which seem to have regular motions
against the background of stars.  The earliest recorded model
for planetary motions proposed by Ptolemy about 2000 years
ago was a ‘geocentric’ model in which all celestial objects,
stars, the sun and the planets, all revolved around the earth.
The only motion that was thought to be possible for celestial
objects was motion in a circle.  Complicated schemes of motion
were put forward by Ptolemy in order to describe the observed
motion of the planets.  The planets were described as moving
in circles with the center of the circles themselves moving in
larger circles.  Similar theories were also advanced by Indian
astronomers some 400 years later.  However a more elegant
model in which the Sun was the center around which the
planets revolved – the ‘heliocentric’ model – was already
mentioned by Aryabhatta (5
th
 century A.D.) in his treatise. A
thousand years later, a Polish monk named Nicolas
8.1 Introduction
8.2 Kepler’s laws
8.3 Universal law of
gravitation
8.4 The gravitational
constant
8.5 Acceleration due to
gravity of the earth
8.6 Acceleration due to
gravity below and above
the surface of earth
8.7 Gravitational potential
energy
8.8 Escape speed
8.9 Earth satellites
8.10 Energy of an orbiting
satellite
8.11 Geostationary and polar
satellites
8.12 Weightlessness
Summary
Points to ponder
Exercises
Additional exercises
184 PHYSICS
B
A
C
P
S
S'
2b
2a
Copernicus (1473-1543) proposed a definitive
model in which the planets moved in circles
around a fixed central sun.  His theory was
discredited by the church, but notable amongst
its supporters was Galileo who had to face
prosecution from the state for his beliefs.
It was around the same time as Galileo, a
nobleman called Tycho Brahe (1546-1601)
hailing from Denmark, spent his entire lifetime
recording observations of the planets with the
naked eye.  His compiled data were analysed
later by his assistant Johannes Kepler (1571-
1640). He could extract from the data three
elegant laws that now go by the name of Kepler’s
laws.  These laws were known to Newton and
enabled him to make a great scientific leap in
proposing his universal law of gravitation.
8.2  KEPLER’S LAWS
The three laws of Kepler can be stated as follows:
1.  Law of orbits : All planets move in elliptical
orbits with the Sun situated at one of the  foci
Fig. 8.1(a) An ellipse traced out by a planet around
the sun. The closest point is P and the
farthest point is A, P is called the
perihelion and A the aphelion. The
semimajor axis is half the distance AP.
Fig. 8.1(b) Drawing an ellipse. A string has its ends
fixed at F
1
 and F
2
. The tip of a pencil holds
the string taut and is moved around.
of the ellipse (Fig. 8.1a). This law was a  deviation
from the Copernican model which allowed only
circular orbits. The ellipse, of which the circle is
a special case, is a closed curve which can be
drawn very simply as follows.
Select two points F
1
 and F
2
.  Take a length
of a string and  fix its ends at F
1
 and F
2
 by pins.
With the tip of a pencil  stretch the string taut
and then draw a curve by moving the pencil
keeping the string taut throughout.(Fig. 8.1(b))
The closed curve you get is called an ellipse.
Clearly for any point T on the ellipse, the sum of
the distances from F
1
 and F
2
 is a constant.  F
1
,
F
2
 are called the focii. Join the points F
1 
and
  
F
2
and extend 
  
the line to intersect the ellipse at
points P and A as shown in Fig. 8.1(b). The
midpoint of the line PA is the centre of the ellipse
O and the length PO = AO  is called the semi-
major axis of the ellipse. For a circle, the two
focii  merge into one  and the semi-major axis
becomes the radius of the circle.
2. Law of areas : The line that joins any planet
to the sun sweeps  equal areas in equal intervals
of time (Fig. 8.2).  This law comes from the
observations that planets appear to move slower
when they are  farther from the sun than when
they are nearer.
Fig. 8.2 The planet P moves around the sun in an
elliptical orbit. The shaded area is the area
?A swept out in a small interval of time  ?t.
3. Law of periods : The square of the time period
of revolution of a planet is proportional to the
cube of the semi-major axis of the ellipse traced
out by  the planet.
The table below gives the approximate time
periods of revolution of nine planets around the
sun along with values of their semi-major axes.