Sir Isaac Newton, was one of the greatest scientist of the world. He made fundamental contributions not only to several branches of Physics (like optics and mechanics) but also to Astronomy and Mathematics. He formulated the laws of motion and law of Universal gravitation.
. The distance between their centers is r.
According to the statement force of attraction between two bodies is directly proportional to the product of their masses.
The gravitational force of attraction is inversely proportional to the square of the distance between the centers of the masses of the bodies. Therefore
Where 'G' is constant of proportionality known as “Universal gravitational constant” or Newtonian constant of gravitation or the Cavendish gravitational constant.
. This is very small value. ‘G’ remains constant everywhere.
We do not feel the gravitational force of attraction between objects around us due to the very small value of 'G'. But it exists everywhere in the universe.
The pull of the gravity also affect the moon. It changes the path of the Moon, which revolve the Moon around the Earth.
In other words, the Earth's gravity keeps the Moon orbiting us. It keeps changing the direction of the Moon's velocity. This means gravity makes the Moon accelerate all the time, even though its speed remains constant.
Ans: In 1666, One day Isaac Newton was sitting in his mother’s, garden where he witnessed an apple falling from a tree. The scenario helped him to explore the idea of gravity. Newton successfully discovered the cause of falling bodies. He further revealed that gravity makes the planets to revolve around the sun and it also causes the moon and satellite orbiting around the earth in a specific fashion.
every two objects attract each other with equal force but in opposite direction.
This shows that, the two forces are equal in magnitude but opposite in direction. Now, if F
as “Reaction Force”. Then by using above equation, it is concluded that:
OR
Gravitational force forms an action-reaction pair.
As we know that, above statement is in accordance with the Newton's third law of motion which states that
“To every action there is always an equal and opposite reaction”.
Hence, Newton's law of gravitation is consistent with Newton's third law of motion.
For example:
According to Newton's law of Universal gravitation the Earth pulls the Moon with its gravity and the Moon pulls the Earth with its gravity. Therefore they form an action-reaction pair, which is in accordance with Newton's third law of motion.
Q.7: Define gravitational field. Describe the Earth's gravitational field. OR Explain gravitational field as an example of field of force.
Ans:
GRAVITATIONAL FIELD:
Gravitational field can be described as:
“A gravitational field is a region in which a mass experiences a force due to gravitational attraction”.
Earth's Gravitational Field:
The earth has an attractive gravitational field around it. Any object near the Earth experience this force which is due to Earth's gravity. This field is directed towards the centre of the Earth.
Field force Of Earth's Gravitational Field:
The force of this field is strongest near the surface of the Earth and gets weaker as we move farther and farther away from the Earth. This force is called the “Field Force” because it acts on all objects whether they are in contact with Earth's surface or not. So, it is a non-contact force.
For example,
It acts on an aeroplane either it is standing on Earth's surface or flying in the sky.
Gravitational Field Strength:
A body of mass one kilogram (1 kg) on Earth experiences a force of about ten newton (10 N) due to Earth's gravitational field. This force determines the gravitational field strength which is defined as:
"Gravitational field strength ‘g’ is the gravitational force acting per unit mass."
The gravitational field strength “g” is approximately 10 Newton per kilogram or 10 Nkg
-1. The gravitational field strength “g” is different at different planets.
For example,
The gravitational field strength “g” on the surface of Moon is approximately 1.6 Newton per Kilogram 1.6 Nkg
-1.
Gravitational Field Strength Of Different Planets:Acceleration due to gravity “g” at different planets are as follows:
| Planet |
Value of g ms-2 |
|---|
| Earth | 10 |
| Moon | 1.62 |
| Venus | 8.87 |
| Mars | 3.77 |
| Jupiter | 25.95 |
| Sun | 274 |
| Mercury | 3.59 |
| Saturn | 11.08 |
| Uranus | 10.67 |
| Neptune | 14.07 |
Q.8: Define weight? What instrument is used to measure the weight of an object? OR Define weight (as the force on an object due to a gravitational field.)
Ans:
WEIGHT:
All the objects which are thrown upward in the air, fall back to the ground.
The force applied by the Earth's gravitational field, pulls the objects downward. Weight is another name for the Earth's gravitational force on the objects. Because ‘gravity’ is taken from Latin word ‘gravitas’ means ‘weight’.
Therefore weight can be defined as:
"The weight of an object is the measurement of gravitational force acting on the object."
OR
"Weight of an object is the gravitational pull of Earth acting on it."
Weight 'W' of an object of mass 'm', in a gravitational field of strength 'g' is given by the relation:
W = mg .......... (i)
Unit Of Weight:
Like other forces, weight is a vector quantity and is also measured in Newton's (N).
Instrument Use To Measure Weight:
Spring balance:
is used to measure weight of an object.
An object of mass 1 kg has a weight of 9.8 N near the surface of Earth. The objects with larger masses may have larger weights. Our weight vary slightly from place to place, because Earth's gravitational field strength varies at different places. The weight of the object changes as it moves away from the Earth. The weight of the object is different at different planets.
For example:
We will have less weight at Moon because Moon's gravitational field is weaker than Earth.
Q.9: What is "Atwood machine"?Ans:
ATWOOD MACHINE:British scientist George Atwood (1746-1807) used two masses suspended from a fixed pulley, to study the motion and measure the value of ‘g’. This is named as “Atwood Machine”.
Q.10: By using Newton's Law of Gravitation, find the mass of the earth?
Ans:
MASS OF THE EARTH:
Mass of Earth can not be measured directly by placing it on any weighing scale. But it can be measured by an indirect method. This method utilizes the Newton's law of universal gravitation.
Let us consider a small ball is placed on the surface of Earth.
-
m ⟶ Mass of the ball.
-
ME ⟶ Mass of Earth.
-
G ⟶ Universal gravitational constant.
-
Rg ⟶ Radius of earth; which is also the distance between the ball and centre of earth.
Then according to Newton's law of universal gravitation, the gravitational force F of the Earth acts on the ball is:
Whereas the force with which Earth attracts the ball towards its centre is equal to the weight of the ball.
Therefore,
F = W = mg ............. (ii)
Comparing equation (i) and (ii); we get:
Numerical values of the constants at right hand side of equation (iii) are:
g = 10 Nkg-1
RE = 6.38 x 106m
G = 6.673 x 10-11Nm2kg-2
Substituting these values in equation (iii), we get:
ME = 6.0 x 1024kg.
Thus, mass of Earth is 6.0 x 10
24kg.
Q.11: What are satellites? Define its types?
Ans:
SATELLITES:
A satellite is an object that revolves around a planet. Satellites are of two types:
-
Natural satellites
-
Artificial satellites
1. Natural satellites:
The planet which revolves around another planet naturally is called “Natural Satellite”.
E.g: Moon is a natural satellite because it revolves around the Earth naturally.
2. Artificial Satellites:
The object which are sent into space by scientists to revolve around the Earth or other planets are called “Artificial Satellite”.
E.g. Sputnik-1, Meteosat, Explorer-1 are amongst the artificial satellites.
Sputnik-1 was the first artificial satellite which was sent into space by Soviet Union (Russia) on 4th October 1957.
Q.12: What are the uses of artificial satellite? OR Write down any four uses of artificial satellite.
Ans:
USES OF ARTIFICIAL SATELLITE:
Artificial satellites are used for different purposes like:
-
For communication.
-
For making star maps.
-
For making maps of planetary surfaces.
-
For collecting information about weather.
-
For taking pictures of planets, etc.
Artificial satellites carry instruments, passengers or both to perform different experiments in space.
Q.13: What do you know about the orbits of artificial satellite?
Ans:
ORBITS OF ARTIFICIAL SATELLITE:
Artificial satellites have been launched into different orbits around the Earth. There are different types of orbits like:
-
For communication.
-
Low- Earth orbit.
-
Medium- Earth orbit.
-
Geostationary orbit.
-
Elliptic orbit.
CHARACTERS OF ORBITS:
These orbits are characterized on the basis of different parameters like,
-
Their distance from the Earth,
-
Their time period around the Earth etc.
Q.14: Describe communication satellite and geostationary orbit?
Ans:
COMMUNICATION SATELLITE:
An artificial satellite which completes its one revolution around the Earth in 24 hours is used for communication purpose. As it is used for communication purpose, therefore it is known as “Communication Satellite”.
GEOSTATIONARY ORBIT:
A communication satellite completes its one revolution around the Earth in 24 hours. As Earth also completes its one rotation about its axis in 24 hours, therefore the communication satellite appears to be stationary with respect to Earth. The orbit of communication satellite is therefore called “Geostationary orbit”. The height of a geostationary satellite is about 42,300 km from the surface of the Earth. Its velocity with respect to Earth is zero.
Q.15: Define orbit?
Ans:
ORBIT:
The curved path along which a natural or artificial satellite revolves around a planet is called an “orbit”;. Rockets are used to put satellites into orbits in space.
Q.16: Discuss the importance of Newton's law of gravitation in understanding the motion of satellites? OR Derive the expression for the velocity and time period of a satellite that orbiting around the Esarth?
Ans:
Importance Of Newton’s Law of Gravitation in the motion of satellite:
The Newton's law of gravitation has an important role in the motion of satellite in its orbit, because the gravitational pull of Earth on the satellite provides the centripetal force needed to keep a satellite in orbit around some planet.
Expression For The Velocity That A Satellite Possess When Orbiting Around The Earth:
Let us consider the motion of a satellite which is revolving around the Earth:
-
m ⟶ Mass of the satellite.
-
M ⟶ Mass of Earth.
-
R ⟶ Radius of Earth
-
h ⟶ Height (altitude) of satellite from the surface of Earth.
-
r = R + h ⟶ Radius of orbit.
Then, as we already discussed:
This gives the velocity that a satellite must possess when orbiting around Earth in an orbit of radius (r = R+h).
This shows that, the speed of the satellite is independent of its mass. Hence every satellite whether it is very massive (large) or very light (small) has the same speed in the same orbit.
Expression For The Time Period Of A Satellite Orbiting Around The Earth:
The time required for a satellite to complete one revolution around the Earth in its orbit is called its time period “T”. The time period of a satellite can be calculated as:
Equations (iv) gives the expression for the time period of a satellite orbiting around the Earth. Thus, Newton's law of gravitation helps to describe the motion of a satellite in an orbit around the Earth.
Q.17: Describe the motion of artificial satellite around the Earth.
Ans:
Motion of Artificial Satellite around the Earth:
The satellites are put into their orbits around the Earth by rockets. When a satellite is put into orbit, its speed is selected carefully and correctly. If speed is not chosen correctly then the satellite may fall back to Earth or its path may take it further into orbit. During the motion of a satellite in the orbit the gravitation pull of Earth on it is always directed towards the centre of Earth.
Newton used the following example to explain how gravity makes the orbiting possible.
Let us imagine a cannonball launched from a high mountain, three paths the ball can follow are:
| Path A |
Path B |
Path C |
|---|
| The canon ball is launched at a slow speed. | The canon ball is launched at a medium speed. | The canon ball is launched at a high speed. |
| The canon ball will fall back to Earth. | The canon ball will fall back to Earth. | The canon ball will not fall back to Earth instead it orbits around the Earth. |
Above example shows that, for an artificial satellite to orbit the Earth and to retrace its path it requires certain orbital velocity.
Q.18: Define orbital velocity? Derive an expression for the orbital velocity of an artificial satellite?
Ans:
ORBITAL VELOCITY:
The orbital velocity is defined as:
"The velocity required to keep the satellite into its orbit is called “Orbital Velocity”.
Expression for the orbital velocity of an artificial satellite:
The gravitational pull of Earth on a satellite provides the necessary centripetal force for orbital motion. Since this force is equal to the weight of satellite,
‘WS = mg’, therefore
FC = WS ........ (i)
and, WS = mgh
where,
-
m ⟶ Mass of the satellite.
-
gh ⟶ Acceleration due to gravity at height ‘h’ from the surface of Earth.
The centripetal force ‘F
C ’ on the satellite is:
If satellite is orbiting very close to the surface of Earth
then: h << R
In this case orbital radius may be considered equal to radius of Earth.
Therefore, R + h = R
Also gh = g
and v = vc
Where,
-
vc ⟶ Critical velocity
-
g ⟶ Acceleration due to gravity on the surface of Earth.
In terms of above factors equation (ii) becomes:
vc = √ gR ........ (iii)
This is known as
“Critical velocity”.
It is defined as:
"The constant horizontal velocity required to put the satellite into a stable circular orbit around the Earth."
It is also known as orbital speed or proper speed.
If
g = 10 ms-2
R = 6.38 106 m
Then equation (iii) becomes.
vc = √ gR = √ 10 ms-2 x 6.38 106 m
vc = √ 7.99 x 103 ms-1
vc = 8.0 kms-1
It should be noted that as the satellite get closer to the Earth, the gravitational pull of the Earth on it gets stronger.
So, the satellites in order to stay in an orbit closer to Earth needs to travel faster as compare to those satellites in the farther orbits.
Q.19: How would the value of "g" and "G" be affected, if the mass of the earth becomes four times!
Ans
: (i) For "g":
As g = GMe / Re2
It means that "g" is directly proportional to the mass of the earth if the mass of the earth decrease, the value of "g" will also decreases. If the mass of the earth increases the value of "g" will also increases. If the mass of the earth becomes four times the value of "g", g will also become four times. It means "g" will increase four times.'
(ii) For "G":
"G" is a universal gravitational constant it remains the same through out the universe. If the mass of the earth becomes four times the value of "G" will not change. It will remain the same as it is a constant. Its value is 6.673 x 10
-11 Nm
2Kg
-2.
Point to Ponder
Does the whole solar system works in a push and pull network?
Ans: Gravity keeps things together. It is a force that attracts matter towards it. Anything with mass creates gravity, but the amount of gravity is proportional to the amount of mass. Therefore, Jupiter has a stronger gravitational pull than Mercury. Distance also affects the strength of the gravitational force. Therefore, the Earth has a stronger pull on us than Jupiter does, even though Jupiter is as big as over 1,300 Earths. While we are familiar with gravity's impact on us and Earth, this force also has many effects on the entire solar system, too.
Creates Orbit:
One of the most noticeable effects of gravity in the solar system is the orbit of the planets. The sun could hold 1.3 million Earths so its mass has a strong gravitational pull. When a planet tries to go past the sun at a high rate of speed, gravity grabs the planet and pulls it towards the sun. Likewise. the planet's gravity is trying to pull the sun towards it but can't because of the vast difference in mass. The planet keeps moving but is always caught up in the push-pull forces caused by the interaction of these gravitational forces. As a result, the planet begins orbiting the sun The same phenomenon causes the moon to orbit around the Earth except for the Earth's gravitational force, not the sun's that keeps it moving around us.
Tidal Heating:
Just as the moon orbits the Earth, other planets have moons of their own. The push-pull relationship between the gravitational forces of the planets and their moons causes an effect known as tidal bulges. On Earth, we see these bulges as high and low tides because they occur over oceans. But on planets or moons without water, tidal bulges can occur over land. In some cases, the bulge created by gravity will be pulled back and forth because the orbit vanes in its distance from the primary source of gravity. The pulling causes friction and is known as tidal heating. On lo, one of Jupiter's moons, the tidal heating has caused volcanic activity. This heating may also be responsible for volcanic activity on Saturn's Enceladus and liquid water underground on Jupiter's Europa.
Creating Stars:
Giant molecular clouds made up of gas and dust slowly collapse because of the inward pull of their gravity. When these clouds collapse, they form lots of smaller areas of gas and dust that will eventually collapse as well. When these fragments collapse, they form stars. Because the fragments from the original GMC stay in the same general area, their collapse causes stars to form clusters.
Formation of Planets:
When a star is born, all of the dust and gas not needed in its formation ends up trapped in the orbit of the star. The dust particles have more mass than the gas so they can begin to concentrate in certain areas where they come in contact with other dust grains. These grains are pulled together by their own gravitational forces and kept in orbit by the gravity of the star. As the collection of grains becomes bigger, other forces also begin to act upon it until a planet forms over a very long period of time.
Destruction Cause:
Because many things in the solar system are held together thanks to the gravitational pull among its components, strong external gravitational forces could pull those components apart thus destroying the object. This happens with moons sometimes. For example, Neptune's Tnton is being pulled closer and closer to the planet as it orbits. When the moon gets too close, perhaps in 100 million to 1 billion years, the planet's gravity will pull the moon apart. This effect might also explain the origin of the debris that makes up the rings found around all of the large planets: Jupiter, Saturn, and Uranus.
