From Ancient
times many scientists had shown great interest towards the sky. Most of the scientist
studied the motion of celestial bodies.
One of the most
influential Greek astronomers and geographers of his time, "Ptolemy" propounded the
geocentric theory in a form that prevailed for 1400 years. He made
astronomical
observations from Alexandria in Egypt during the year. AD 127-41. In fact the
first observation
which can date exactly was made by Ptolemy on 26 march 127. While last was made on 2nd feb 141.
The Almagest is
the earliest of Ptolemy work and gives in detail the mathematical theory
of motions. Of
sun, moon and planets. Ptolemy made his most original contribution by presenting
details for the motion of each of the planets. The almagest was not super
seeded until a century
after copernicus presented his heliocentric theory.
Ptolemy first of
all justifies his descriptions of the universe based on earth - centred system. It is a
view of the world based on fixed earth around which the sphere of the fixed stars rotates every day, this
carrying with it the sphere of the sun, moon and planets.
Nicolas Copernicus:
In 16th century AD nicolas copernicus, a polish monk was born on 19th feb 1473 and the died
on may 24, 1543
Copernicus summerised his heliocentric theory. According to this theory, the earth and
other planets moved in perfect circles around the sun located at the centre of these circles. The earth and other planets would also rotate about their own axes while orbiting around the sum in circular orbits of different radii.
Johannes Kepler (1571-1630) was a German mathematician, astronomer and astrologer and key figure in the 17th century scientific revolution. He was assistant to astronomer Tycho Brache. He learned both the ptolemic system and copernican system of planetary motion. He believed Copernicus at that time. He defended heliocentrism form both theoretical and theological perspective, maintaining that the sun was the principal source of motive power in the Universe.
Issac Newton:
The English physicist Issac newton (1642-1727) introduced the term "Gravity" after he saw
an apple falling on to the ground in his garden. "Gravity" is the force of attraction exerted by
the earth on an object. The moon orbits around the earth because of gravity too. Newton
later proposed that gravity too. Newton later proposed that gravity was fast a particular case
of gravitation. Every mass in the universe attracts every other mass. This is the idea of
Newton's law of Gravitation.
Newton derived the relation in such a way that F is proportional to 'm'. because the force on a body is directly proportional to its mass by Newton's 2nd law of motion F=ma. When the earth exerts a force on the falling body, by the Newton's 3rd law of motion. The falling body exerts an equal and opposite force on the earth. Therefore the gravitational force F is proportion to both the masses of falling body and the earth, i.e., m1 and m2. The inverse
square relationship 1/r2, was justified by observing motion of the moon. Newton also observed that it is not only the earth which attracts other objects, but every object in the universe attracts every other objects and he termed such a general force as ''gravitational force". One law is known as the Universal law of gravitation".
According to this law, the gravitational force of attraction between any two objects is
i) Directly proportional to the product of their masses.
ii) Inversely proportional to the square of the distance between them.
If the masses of any two objects are 'm1' and m2 and the separation between them is r
then the gravitation at force of attraction between them is
F alpha m1m2 ..................... (1)
F alpha 1/r2 ..................... (2)
Where 'G' is proportionality constant and known as ''Universal Gravitational Constant".
"Every body 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 distance between them. The force acts along the line joining the two bodies".
The Universal Gravitational Constant 'G':
We know that F = Gm1m2/r2
Units of G:
- In SI system units of 'F' is Newton (N)
- Units of Distance (r) is meter (m)
- Units of mass (m) is kilogram (kg)
If the masses of any two objects are 'm1' and m2 and the separation between them is r
then the gravitation at force of attraction between them is
F alpha m1m2 ..................... (1)
F alpha 1/r2 ..................... (2)
Where 'G' is proportionality constant and known as ''Universal Gravitational Constant".
"Every body 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 distance between them. The force acts along the line joining the two bodies".
The Universal Gravitational Constant 'G':
We know that F = Gm1m2/r2
Units of G:
- In SI system units of 'F' is Newton (N)
- Units of Distance (r) is meter (m)
- Units of mass (m) is kilogram (kg)
The numerical value of 'G' is experimentally found to be 6.67 × 10–11 Nm2Kg –2
Acceleration due to gravity:
Galileo proved, (from leaning tower of pisa experiment) that objects of different masses and sizes, when dropped simultaneously from the same height, would reach the ground at same time.
In other words when an object is dropped from some height, it experiences uniform acceleration by the gravitational pull of the earth and this acceleration does not depend on the mass of the body.
The uniform acceleration produced in a freely falling body due to the gravitational pull of the earth is known as acceleration due to gravity and denoted by letter 'g' is given by the equation g = GM/r2
In other words when an object is dropped from some height, it experiences uniform acceleration by the gravitational pull of the earth and this acceleration does not depend on the mass of the body.
The uniform acceleration produced in a freely falling body due to the gravitational pull of the earth is known as acceleration due to gravity and denoted by letter 'g' is given by the equation g = GM/r2
where G =Universal Gravitational Constant (6.67 × 10–11 Nm2/kg2)
M =Mass of the Earth
r =Radius of Earth
from the equation (5) Value of g is g = 9.8 ms–2
Variation of 'g' value: At a given place on the earth 'g' is constant. However, it varies due
to the fact that the earth is not a perfect sphere and its radius 'r' is not the same at all places
on its surface. Due to flattering of the earth at the poles, 'r' is minimum and hence 'g' is
maximum at the poles. Since 'r' is maximum at the equator, the value of 'g' becomes
minimum at the equator. The value of 'g' decreases as we move upwards from the surface.
As we go deep in to the earth (mine), the value of 'g' decreases.
Gravity meters: The instrument used to measure small changes in the value of 'g' at a given
location is known as gravity meters. The Boldien gravity meter and Gulf gravity meters are
two examples of gravity meter.
Mass and weight: The mass of a body is the quantity of matter contained in it. Mass is
independent of external factors like position and surroundings. Thus the mass of a given
body will be same at all place of earth or any where in the University.
The weight of a body is the force with which it is attracted by the earth towards its centre and is equal to the product of its mass and acceleration due to gravity.
Thus w = mg, where 'm' is mass of body and 'g' is the acceleration due to gravity.
Since the value of 'g' changes from place to place, the weight of a given body differs from one place to another. For example: The acceleration due to gravity on moon is 1/6th of the acceleration due to gravity on earth, hence the weight of the body on moon is 1/6th of its
weight on earth.
- The earth is stationary and is at the centre of the universe, with the sun, the moon, planets and stars revolving the earth.
2. What is Heliocentric theory?
- All the planets revolve in a perfect circle with the stationary sun at the centre of these circles.
3. What is acceleration due to gravity?
A- 1.The Uniform acceleration produced in a freely falling body due to gravitational pull of the earth is called acceleration due to gravity.
2. It is denoted by (g)
4. Define the mass of a body?
- The total quantity of matter contained in a body is defined as its mass.
5. Define the weight of a body.
- The weight of a body is the force with which it is pulled by the earth towards its centre.
6. State Hooke's law?
- According to Hooke's law "Stress is directly proportional to strain when a body is in elastic limit''.
7. Calculate the gravitational force on a stone of mass 10kg?
- Acceleration due to gravity (g) = 9.8m/sec2
mass of the stone, m=10kg
The gravitational force on the stone,
F = mg = 10 × 9.8 = 98 newton.
8. Define 1 kg wt?
A- The gravitational force acting on a body of mass 1kg is called 1kg wt
M =Mass of the Earth
r =Radius of Earth
from the equation (5) Value of g is g = 9.8 ms–2
Variation of 'g' value: At a given place on the earth 'g' is constant. However, it varies due
to the fact that the earth is not a perfect sphere and its radius 'r' is not the same at all places
on its surface. Due to flattering of the earth at the poles, 'r' is minimum and hence 'g' is
maximum at the poles. Since 'r' is maximum at the equator, the value of 'g' becomes
minimum at the equator. The value of 'g' decreases as we move upwards from the surface.
As we go deep in to the earth (mine), the value of 'g' decreases.
Gravity meters: The instrument used to measure small changes in the value of 'g' at a given
location is known as gravity meters. The Boldien gravity meter and Gulf gravity meters are
two examples of gravity meter.
Mass and weight: The mass of a body is the quantity of matter contained in it. Mass is
independent of external factors like position and surroundings. Thus the mass of a given
body will be same at all place of earth or any where in the University.
The weight of a body is the force with which it is attracted by the earth towards its centre and is equal to the product of its mass and acceleration due to gravity.
Thus w = mg, where 'm' is mass of body and 'g' is the acceleration due to gravity.
Since the value of 'g' changes from place to place, the weight of a given body differs from one place to another. For example: The acceleration due to gravity on moon is 1/6th of the acceleration due to gravity on earth, hence the weight of the body on moon is 1/6th of its
weight on earth.
Very Short Answer Questions
1. What is Geocentric theory?- The earth is stationary and is at the centre of the universe, with the sun, the moon, planets and stars revolving the earth.
2. What is Heliocentric theory?
- All the planets revolve in a perfect circle with the stationary sun at the centre of these circles.
3. What is acceleration due to gravity?
A- 1.The Uniform acceleration produced in a freely falling body due to gravitational pull of the earth is called acceleration due to gravity.
2. It is denoted by (g)
4. Define the mass of a body?
- The total quantity of matter contained in a body is defined as its mass.
5. Define the weight of a body.
- The weight of a body is the force with which it is pulled by the earth towards its centre.
6. State Hooke's law?
- According to Hooke's law "Stress is directly proportional to strain when a body is in elastic limit''.
7. Calculate the gravitational force on a stone of mass 10kg?
- Acceleration due to gravity (g) = 9.8m/sec2
mass of the stone, m=10kg
The gravitational force on the stone,
F = mg = 10 × 9.8 = 98 newton.
8. Define 1 kg wt?
A- The gravitational force acting on a body of mass 1kg is called 1kg wt
SHORT
ANSWER QUESTION
1. State the Universal law of gravitation? and calculate the gravitational force of
stone of mass. 10kg.
- Newton's Universal law of gravitation states ''that every body 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"
Problem: We know that F = mg
= F = 10 × 9.8 = 98 N
2. What are the various factors that effect on the value of acceleration due to gravity (g)?
- The various factors that influence the value of 'g' are
1. Shape of the earth
a) At poles
b) At equator
2. Height (Altitude)
3. Depth
4. Local Conditions
3. Why is the weight of a body not the same at poles and equator?
- The weight of a body W=mg. So it depends on acceleration due to gravity. It is directly proportional to acceleration due to gravity. As the acceleration due to gravity is not same at the poles and equator, the weight of a body is also not the same at the poles and the Equator.
4. Why does the weight of a body differs from one place to another place?
- The weight of a body w=mg. It means the weight of a body is directly proportional acceleration due to gravity. As the value of acceleration due to gravity 'g' changes from place to place, the weight of a body also changes from place to place.
5. What is gravity meter? Give examples?
1. The value of g at a given location is slightly affected by geological deposits concentration of massive concrete building and topography of the region
2. So,a sensitive instrument is used to measure such small changes in the value of g at a given location.
3. This instrument is called gravity meter.
4. Examples: Gulf gravity meter and Boliden gravity meter.
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