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In 1686, Newton stated that every single particle of matter attracts every other particle in the universe. This attractive universal force is called ‘gravitation’. Newton’s gravitational law was that the force of attraction between any two particles of material is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. It acts along the line joining the two particles.
Newton’s Law of Gravitation
Suppose two particles of masses m₁ and m₂ are situated at a distance of r apart. If the force of attraction acting between them is F, then according to Newton’s Law of gravitation, we have:
F=G(m1 m2)/r2
The constant of proportionality G is called the ‘gravitational constant’. The value of G is the same for every pair of particles in this universe. Hence G is also termed as ‘universal constant’.
Newton’s law of gravitation is applicable to the point masses. However, this law is also for large objects. But in that case, the distance between the bodies should be much larger than the mass of them.
Vector Form of Newton’s Law of Gravitation
We are considering two point-masses, m1 and m2; the distance between m1 and m2 is r. Let r12 be a unit vector directed from mass m1 to mass m2, and r21 a unit vector directed from m2 to m1. Then, the gravitational force vector F12 exerted on m1 by m2 is given in magnitude and direction by the vector relation.
F12 = -G (m2 m1 )/r2 r12
The minus sign indicates that F12 points opposite F21; the gravitational force is attractive, m₁ experiencing a force directed towards m₂.
The force exerted on m₂ by m₁ is similarly
F21 = -G (m2 m1)/r2 r21
Because r21=-r12,
Thus we can conclude:
F12 = – F21
Characteristics of Gravitational Forces:
(i) Gravitational Forces are always forces of attraction,
(ii) Every force is formed as an action-reaction pair, that means, the forces exerted by two bodies on each other are equal in magnitude but opposite in direction,
(iii) Gravitational Forces are central forces. They always act along the line that joins the centres of two bodies,
(iv) Gravitational Forces are entirely independent of the presence of other bodies and the properties of the intervening medium.
Gravity
Newton’s law of gravitation defines gravitation as the force of attraction between two bodies. Among these two bodies, if one body is earth, then the gravitational force is called gravity. Therefore gravity can be defined as the force by which earth attracts a body towards its centre. Gravity is a particular case of gravitation. Due to gravity, the bodies were thrown upwards and fell back on the earth’s surface.
Acceleration Due to Gravity: When a body is dropped freely from a height, it falls towards the earth due to the effect of gravity, and the velocity of its fall continuously increases. The acceleration developed in such a motion is called ‘acceleration due to gravity’. Thus, the acceleration due to gravity can be defined as the rate of the increased velocity of a body falling freely towards the earth. It is denoted by ‘g’. It does not depend upon the body’s shape, size, mass, etc. If m is the mass of a body, then the force of gravity acting on it is mg (body weight). Therefore, the acceleration due to gravity is equal in magnitude to the force exerted by the earth on a body of unit mass. The unit of acceleration due to gravity is ms-2 or N kg-¹.
The universal constant G is different from g. The constant G has the dimensions [M-1L3T-2] and is a scalar; g has the dimensions [LT-2] and is a vector and is neither universal nor constant.
Conclusion
The universal law of gravitation proved a lot of hypothetical beliefs practically.
For example, the law of gravitation explains the motion of planets around the sun, the motion of the moon and artificial satellites around the earth. It also helps to evaluate how these motions affect the earth and its climates, such as the phenomena of rainfall, snowfall, and flow of water in rivers on the earth.
