Newton’s Law of Gravitation

Newton’s law of gravitation was put forward by Sir Issac Newton in 1687. It stated that any particle of matter in the universe attracts the other with force varying with a direct proportionality between the product of the masses and inverse proportionality between the square of the distance between them. 

Kepler used it to formulate the ‘Kepler’s laws of planetary motion’ in the 17th century.

It is formulated as F=Gm1.m2/ R2

 where F stands for attractive force, G stands for gravitational constant, m1 and m2 stands for masses, and R stands the distance between the two bodies. 

The value of G stays constant = 6.67 x 10-11 N-m² kg-2.

The Gravitational constant (G): It stays the same irrespective of the nature and the size of the body, and it also doesn’t depend on the texture of the medium between the two bodies. The dimensional formula for G is [M-1L3T-2]. 

Gravitation and the Formulation of Its Law

We all are familiar with the story of an apple falling on Newton’s head and pushing him into a deep and dense web of thoughts. The result of that incident and Newton’s constant working on it was the ‘Newton’s law of Gravitation.’ In simple words, we can say that gravitation is a force of attraction between two bodies of the same or different masses respectively. 

Gravitation is one of the 4 types of interactions found in nature. The fundamental interactions in Physics are the interactions of the forces, which cannot be reduced to a more basic interaction. Mathematically speaking, all of the interactions are called ‘fields.’ 

Types of interactions are:

• The gravitational force.
• The electromagnetic force.
• The strong nuclear or hadronic force.
• The weak nuclear force.

Gravitation and Newton’s law of gravitation doesn’t hold much importance for small objects with a negligible mass. They are chiefly used in studying interactions of large objects, i.e., planets.

There are some important points to be kept in mind while calculating the Gravitational forces between two bodies. If you are trying to calculate the F between two objects (usually spherical or circular), here are certain things you need to keep in mind:

• We have to assume that the entire mass is concentrated at the body’s centre. We must also assume that the mass has been uniformly distributed. 
• We must keep in mind that the gravitational field strength at a point is the force per unit mass experienced by a small point mass at that point. A point mass is a nonzero mass with an infinitesimal volume and linear dimensions. 
• The calculation of the resultant gravitational strength of the field because of the two bodies being taken into consideration would be restricted to points along the straight line which joins the bodies. 

Exceptions to the Case

Newton’s law of gravitation works fine with the bodies of high masses and the bodies kept at small and large distances. But, it loses efficiency and fails to be applied when the distance between the objects is less than 10-9 m. 10-9 m is the order of molecular distances. 

Remember that you would not be able to apply Newton’s law of gravitation in such a case, making it a glaring exception. 

Derivation of the Gravitational Force Formula From the Universal Law of Gravitation 

Assume that Fg is the magnitude of the gravitational force of attraction between the 2 objects taken into consideration. 

Let the mass of the first body be m1 and the mass of the second body be m2. Let r be the distance between the two bodies, m1 and m2. Mind that the distance has to be measured from the centre of one object to the centre of the other object. Also, we must assume that the objects are spherical in shape. 

We have read in this article before that:

Fg ∞ m1.m2

And

Fg ∞ 1/r2

Thus, we can conclude that:

Fg ∞ m1.m2/ r2

This is the final equation in which Fg is the force of gravitation between the two bodies being considered. M1 and m2 are the respective masses of the two spherical bodies, and r2 is the square of the distance between the two spherical bodies. 

We see from this derivation that the product of the masses shares a relation of direct proportionality with the magnitude of the force of attraction between the two spherical bodies. We also see that the square of the distance between the two bodies shares an inverse proportionality with the magnitude of the force of attraction between the two spherical bodies. 

We can sum up the universal law of gravitation by the given gravitational force formula:

Fg = (G.m1.m2)/r2, where G is a constant (The universal gravitational constant). 

Importance of Newton’s Law of Gravitation

Newton’s law of gravitation is one of the most important laws in physics, which became the basis of the formulation of many more laws. 

• The motion of satellites (moon for earth) has been properly explained with the help of Newton’s law of gravitation. Besides just earth, it has explained why the satellites revolve around other planets.
• It helps us calculate the value of g on earth, etc.

Conclusion

Newton’s law of gravitation has a special corner in the subject of physics as it is one of the most important laws ever formulated in the history of time. Besides explaining the motion of planets around the sun and the satellites around the planet, it has helped in various physical and mathematical problems. It has given a valid and thorough explanation of why the objects that exist on earth are bound to its surface the way they are. It also paved the way for Kepler’s ‘laws of planetary motion,’ thus, explaining the phenomenon of the rotation of various planets around the sun. It explains why every object thrown at the sky comes back to the earth.