When Newton was a child, one day he saw an apple falling down from a tree. At the point of contact with tree, the apple is at rest. When it is falling it hits the earth with some velocity. Thus while it is falling, in motion is accelerated. Thus he concluded that earth attracts the apple with some force which was named it as "Gravitational Force".
The entire atmosphere of the earth including all living and non-living things bond to the earth because of this gravitational force. Without this force the moon cannot bound to the earth and similarly the earth will not be in the solar system. Without this force we cannot stand on the floor and the food we ate, the water we drink will not enter our stomach. So we can simply say that without this force life would be un imaginable.
Before Newton, Indian scholars had been using the term "Gurtvakarshan" which means attraction by massive body. Before copernicus, our ancient scripture Rigveda described that sun is the centre of the universe and holds all other planets including the earth by the force called gravitational force.
Basic forces in nature:
Any phenomenon that occurs between two bodies can be understood in terms of any one of the basic forces or a combination of basic forces. These basic forces are
1. Strong force,
2. Electromagnetic force,
3. Weak force and
4. Gravitational force
1. Strong force: This force is also called as Nuclear force and is responsible for stability of the nucleus. This force is a short range force as it acts inside the nuclear, which has dimensions of 10-15m (fermii). This force is an attractive force which acts between any pair of nucleons. A nucleon is a common term that can be used for proton as well as for a newton. This is the strongest force in the nature and is communicated by π mesons This was proposed by yukawa.
2. Electromagnetic force: Starting from atomic level to infinite range this force acts. This force is responsible for the atomic stability. This force is either attractive or repulsive depending upon the charges of interacting particles. All the forces such as air resistance, friction, elasticity... etc will fall under this category. It is communicated by "photons".
3. Weak force: In the β decay this force is necessary. Not only in β decay but also in several processes involving decay of fundamental particles this force is responsible. It is a short range force and is communicated through "weak bosons".
4. Gravitational force: This force is responsible for binding two massive particles. This is an attraction force in nature and is a long range one. It is the weakest force but it is the strongest in case of celestial bodies. All natural phenomenon can be explained in terms of this force. For example the ocean tides which occur during the new moon day and full moon day are due to moon's gravitational force. It is communicated through a particle called "graviton" which is not yet experimentally detected.
Law of Universal Gravitation
Depending upon the observations of Tyco Brahe, Kepler proposed the three laws of planetary motion. The first law states that every planet revolves round the in sun in an elliptical orbit with sun at one of in focii. Kepler did not gave any information regarding the factor which is influencing the planet for its motion. Later using his law's of motion and kepler's laws, Newton was the man to suggest that the planet to subjected to gravitational influence of sun and due to it the planet moves around sun in an elliptical orbit.
The universal gravitational law stated by Newton can be stated as follows "The attraction force between any two massive particles is directly proportional to the product of their masses and inversely proportional to square of the distance between them and acts along the line joining those bodies".
If two particles of masses m1, and m2 are separated by a distance 'r' then the attractive force between them is given by
Where G is universal gravitational constant. The value of G is 6.67 × 10-11 Nm2 / kg2
'-' ve sign indicates that the force is attractive.
Inspite of the gravitational forces between two bodies, they are of the same position which means the force with which the first body attracts the second one, the second body also attracts the first one with the same force.
One is named as action and other is named as reaction which is explained in Newton's third law. This Newton's third law is obtained from universal gravitational law.
Relation between G and g: The acceleration produced due to gravitational force is called as acceleration dueto gravity. Example is acceleration of a freely falling body.
Consider a body of mass 'm' on the surface of the planet.
If acceleration due to gravity is 'g' then the gravitational force exerted by plant on the body = weight of the body = mg → (1)
If M is the mass of the planet and 'R' is its radius then from universal law of gravitation the gravitational force between them
The acceleration due to gravity of a planet depends upon mass of planet and its radius. So all bodies which are falling freely from the some height will move with same acceleration irrespective of their masses which was proved by Galilee.
This 'g' varies with planet while 'G' is a universal Constant.
Variation of 'g'
As the force exerted by earth depends upon altitude (height), depth, latitude and shape of the earth so 'g' also depends upon these factors.
i. Variation of 'g' with altitude
Altitude means height from the surface of the earth.
Consider a stone of mass 'm' at a height 'h' from the surface of earth, whose massis 'M' and radius 'R'.
The force exerted by the earth on the stone = mgh → (1)
Where gh is the acceleration due to gravity at height 'h'.
From universal gravitational law. We have 
As distance between centre of earth and stone is R + h.
neglecting higher powers of x
So clearly we can say that as 'h' increases 'g' decreases.
Don't think that g becomes zero at h = 
ii. Variation of 'g' with depth
Consider a stone of mass 'm' placed at a depth 'd' from the surface of planet of mass 'm' and Radius 'R'.
It gd is the acceleration due to gravity at a depth 'd' is gd then gravitational fore exerted by earth on stone is = weight = mgd ------> (1)
The mass of earth inside the circle of depth 'd' i.e. of radius (R- d) only contribute for the newton's universal law of gravitation.
If total mass of earth is M and its radius is 'R' then the density of earth
If the mass of earth inside a circle of radius (R - d) is m' then density
As density of earth is constant i.e. P = P'.
So gravitational force between stone and earth's element of mass m' by universal law of gravitation
Thus we can say that as depth increases g decreases.
At centre of earth i.e. d = R we have gd = g [1 - 
] = 0
So at centre of earth acceleration due to gravity is zero and so weight of the body at that place will be zero.
Hence from the above two cases we can conclude that g is maximum on the surface of the earth.
iii. Variation of 'g' with latitude
Latitude is the angular distance on globe.
Consider an object of mass 'm' at a latitude 'Φ'
If g is the acceleration due to that gravity at that place then the object will be
attracted by earth with a force Fg' = mgΦ
If 'g' the acceleration due to gravity on surface then the gravitational force Fg' = mg.
The resultant force = F = Fg - Fg' (... Both are in same directions)
As earth rotates, particle also rotates
When 'r' is the radius of the circle on which particle is moving, R is the radius of earth.
Then r = R cos ϕ.
The centrifugal force acting on the particle due to earth's rotation is
Fc = mrω2 Where ω is angular velocity of earth.
The component of this force is E cos ϕ which will be balanced by the resultant force.
Then mg - mg' = Fc cos ϕ
⇒ mg - mg' = mrw2 cos ϕ
⇒ g' = g - rω2 cos ϕ
= g - R cos θ ω2 cos ϕ (... r = R cos ϕ)
= g - ω2R cos2 ϕ
At equator ϕ = 0° ⇒ gϕ = g [1 - 
] Which shows that g is minimum.
At poles ϕ = 90° ⇒ gϕ = g Which shows that g is maximum
iv. Variation of 'g' with shape
Earth is not a perfect sphere. It is an ellipsoid. So the equatorial radius is greater than polar radius. As 
. So 'g' is minimum at equator while maximum at poles.
Characteristics of gravitational force
* Gravitational forces between two bodies form a action and reaction pair
* As it depends upon the distance between the two bodies, hence it is a central force
* It is a conservative force i.e. work done by it does not depend upon the path followed
* It does not depend upon the medium in which the bodies are separated.
* Gravitational force between two bodies is independent of the presence of other bodies.
Limitations of Newton's third law
* It is not applicable when velocity of a body is in comparison with velocity of light.
* It is not applicable when the gravitational fields are very strong.
* It is not applicable for large distances. Gravitational field
The region around a massive body where it exerts gravitational force on another body when placed in that region is called as gravitational field.
Simply we can say that it is a region where gravitational force acts.
Gravitational force acting on a body of unit mass is called as gravitational field strength which is denoted by E. If Fg is the gravitational force acting on a body of mass 'm' then gravitational field strength is given by
So gravitational field strength 'E' is equal to acceleration due to gravity 'g' in both magnitude and direction by both are separate physical quantities.
Frame of reference: Consider a pen on the table is the room. When a question ''where is the pen?'' is asked the answer will be "It is on the table." So pen's position is indicated with reference to the table. So table is necessary for determining the position of pen. To determine the position of pen in space we need a set of reference lines which constitute the co-ordinate system. With respect to this co-ordinate system we can specify the position of a point or a body in space. This co-ordinate system is called as frame of reference. Generally we use cartesian co-ordinate system as frame of reference.
There are two types of frames of references. They are
1. Inertial frame of reference
2. Non-inertial frame of reference.
1. Inertial frame of reference: Aframe of reference in which Newton's laws hold good is called as inertial frame of reference. A frame of reference which is at rest or of moving with uniform velocity can be considered as an inertial frame of reference.
2. Non-inertial frame of reference: Aframe of reference in which Newton's laws do not hold good is called Non-inertial frame of reference. A frame which is linearly accelerated or rotating with respect to an inertial frame of reference is an non-inertial frame of reference.
Now a question arises whether a frame fixed on earth is inertial or non-inertial frame. A frame fixed on earth is inertial for an observer on earth as with respect to earth he is in rest. When the observer is in the space i.e. for example say on moon the frame fixed on earth is non-inertial as it is an accelerated frame because of its rotational motion.
Inertial Mass
Mass is defined as the quantity of matter contained in it.
The property that measures in resistance to applied force is called as Inertial mass.
From Newton's laws if "Fo" is the applied force on body which produces an acceleration "a" then it's inertial mass
This inertial mass is a measure of its inertia. The mass which in used in Newton's laws is called as inertial mass.
Gravitational mass
The property responsible for exertion of gravitational force on a body is called as gravitational mass.
If 'g' is the acceleration due to gravity and with the weight of a body then the gravitational mass of a body is mg = 
.
It is a measure of gravitational force on gravitational field.
It is not possible to measure inertial mass directly because number of forces act on it and some of these forces cannot be measured easily while we can measure directly and accurately the gravitational mass.
The food grains such as Rice, pulses, vegetables etc.
Which we buy daily will be measured in gravitational mass only.
It has been experimentally observed that the ratio of inertial mass and gravitational mass of a body is one i.e.
In other words gravitational mass and inertial mass of a body are equal i.e. mi = mg.
Principle of Equivalence
This was proposed by Einstein. The fact that inertial mass and gravitational mass of a body are equal is a consequence of principle of equivalence.
According to this principle "A uniformly accelerated frame in the absence of gravitational effect is completely equivalent to a homogeneous gravitational field".
This is the starting point of "General theory of relativity" proposed by Einstein.
According to Einstein, the gravitational force as experienced locally while standing on a massive body (such as earth) is actually the same as a pseudo - force (imaginary force) experienced by an observer in a non-inertial frame.
Thus being at rest on the surface of earth in equivalent to being inside a space ship that in being accelerated.
Orbital velocity
Let a stone be projected with same initial velocity. The stone goes upto same height and falls at some distance on the ground from the point of projection. This distance is called as Range. When you increase the initial velocity then the range also increase. As the earth is round when the initial velocity reaches a particular value the stone will not fall on the earth but it starts rotating round the earth in a circular orbit. The velocity required for a body to move around the earth in a circular orbit is called as orbital velocity which is denoted by vo.
Let a stone of mass "m" is revolving around a planet of mass "M" and radius "R" at a height "h" from the surface of the planet. Let its horizontal speed be vo.
For the stone to move in the circular orbit the necessary centripetal force is provided by gravitational force i.e.
R + h is called as orbital radius.
Orbital velocity does not depend on the mass of the body but depends upon the
* Mass of the planet "M"
* Radius of the planet "R" and
* Its height from the surface of the planet "h"
Escape velocity
In our epic "The Mahabharatha" there is a story. The entire epic was written in a dialogue manner between sage vysampayana and Janamejaya, the grand grandson of Pandavas. while Listening the Kurukshetra was the king said that the history of his forefathers was an imaginary one but not real. Then the sage asked the king what was the reason for obtaining that conclusion. Then the king replied that during the kurukshetra was, regarding Bhima it was written that Bhima killed an elephant and he thrown away the elephant upwards in such away that it did not return back to the earth. Due to this the king said that this was impossible and the story is simply a trash.Then the sage using his "Tapo Power" mode the elephant that was killed by Bhima to fall on the earth. Then the king realised his mistake. Thus according to Vysya, the author of Mahabharatha, Bhima is vested with a huge power such that he can easily throw an elephant out of the earth's gravitational field.
So from this story we can conclude that a body moves away from earth's gravitational influence in such away that it never returns back. The minimum velocity required for a body to escape from a planets gravitational influence is called as Escape velocity which is denoted by ve.
Consider an object of mass 'm' at rest on the surface of planet of mass 'M' and radius 'R'.
The gravitational potential on the surface of the planet is 
Let us suppose the object is brought from infinity to the surface. Then the amount of work done in this process is stored as gravitational potential energy.
Gravitational potential energy = 
"-ve" sign indicates that the body is bound to the planet. While we impart a minimum speed ve to the body then it becomes free and moves away from the planet into space.
The Kinetic energy of the body 
As the body is free so total energy of the body = 0
Thus escape velocity also depends on the mass of the planet 'M' and its radius 'R' but not on the mass of the body.
Molecules in the atmosphere always move with a certain velocity which depend upon their nature and temperature of surroundings. At ordinary temperature, the r.m.s. velocity of hydrogen molecules is around 2 km / sec, for oxygen molecules, nitrogen, carbon dioxide and water vapour it is around 0.5 to 1 km / sec. As these velocities are much lesser than escape velocity of the earth (11.2 km / sec), so we can find all these in the earth is atmosphere. On moon surface the r.m.s. velocity of oxygen and nitrogen molecules is about 2.38 km / sec and escape velocity of moon is 2.38 km / sec.
This results on escape of these molecules from the moon's surface. Hence the moon's atmosphere is filled with vacuum. Similarly this is the same case for all other planets. Hence the earth is the only living planet.
Relation between orbital velocity and escape velocity
So escape velocity is 
times of the orbital velocity.
Geostationary Satellites
When a satellite moves around the earth such that it appears at rest for an observer on earth then it is called on Geostationary satellite. This will be possible only if the time taken for one revolution of satellite around the earth is equal to rotational time period of earth. Thus a satellite whose revolusional time period is 24 Hrs and moves from west to east in equatorial plane is called as Geostationary satellite.
From the 19th century India had been launching many geostationary satellites in space by ISRO.
Geostationary satellites have the following uses.
* Weather forecasting regarding rains, cyclones etc.
* Identifying natural resources and minerals in the earth.
* Transmission of T.V. programmes to distant places.
* Communication through cell phones between different places of earth and
* Studying the upper layers of atmosphere.
The Geostationary satellite are launched at a height of 35,600 km approximately from earth's surface while its distance from centre of earth is around 42,000 km which is called as radius of the parking orbit.
Orbital velocity of this satellite is nearly 3.08 km / sec and relative velocity of this satellite with respect to earth is zero.
