Universal Law of Gravitation
In addition to Newton's famous three laws of motion, Sir Isaac Newton in 1687 proposed a law about the force of attraction between the two objects in the universe which is known as Newton’s law of gravitation or universal law of gravitation.
According to this law, every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is along the line joining the centres of two objects.
Let two objects A and B of masses m_{1} and m_{2} lie at a distance d from each other as shown in the figure.
Let the force of attraction between two objects be F ( = F_{12} = F_{21}). According to the universal law of gravitation, the force between two objects is directly proportional to the product of their masses. That is,
F ∝ m_{1}.m_{2} ................... (1)
And the force between two objects is inversely proportional to the square of the distance between them, that is,
F ∝ (1/d^{2}) ................... (2)
Now from equations (1) and (2), we get
F ∝ (m_{1}.m_{2})/ d^{2}
F = G.m_{1}.m_{2}/ d^{2} ................... (3)
Where G is the constant of proportionality and is called the universal gravitation constant.
SI Unit of G: Nm^{2} / kg^{−2}
Importance of Universal Law of Gravitation
1. This law is applicable to every object in the universe.
2. This law explains the cause of the revolution of the moon around the earth and the revolution of planets around the sun.
3. This law explains the cause of neap and tide due to the moon and the sun.
Note That:
1. The value of universal gravitational constant G is 6.67 x 10^{-11} N-m^{2} Kg^{-2}.
2. The value of G does not depend on the medium between two bodies.
3. The value of G is same throughout the universe and hence the name.
4. Universal gravitational constant G is different from acceleration due to gravity g. Therefore correct symbol must be used accordingly.
5. If two bodies of mass 1 kg each are separated by 1 m from each other, then, G = F. Therefore, universal gravitational constant G is numerically equal to the force of gravitation which exists between two bodies of unit masses kept at a unit distance from each other.
Properties of Gravitational Force
1. Gravitational force is the weakest force in nature. If two bodies of mass 1 kg each are separated by 1 m from each other, then, F = G = 6.67 x 10^{-11} N.
2. It is an attractive force (Unlike electrostatic and magnetic force; which are both attractive and repulsive).
3. It is a mutual force (the first body attracts the second body and the second body attracts the first body with equal force).
4. It is a central force (It acts along the line joining the centres of the bodies).
5. It is mass and distance dependent.
6. It obeys inverse square law.
7. It is a long-range force (It decreases with distance as per inverse square law and becomes zero only at infinite distance – like electrostatic and magnetic force).
8. It does not depend on the medium between the interacting bodies (There is no gravitational shielding).
Newton’s 3^{rd} law of motion and Newton’s law of gravitation
According to Newton’s third law of motion, “Every object exerts equal and opposite force on other object but in the opposite direction.” According to Newton’s law of gravitation, “Every mass in the universe attracts every other mass.” In case of freely falling stone and the earth, stone is attracted towards earth means earth attracts the stone but according to Newton’s third law of motion, the stone should also attract the earth and really it is true that stone also attracts the earth with the same force F = m × a but due to very less mass of the stone, the acceleration (a) in its velocity is 9.8 m/s^{2} and acceleration (a) of the earth towards stone is 1.65 × 10^{-24} m/s^{2} which is negligible and we cannot feel it.