Vector Form of Universal Law of Gravitation
The action-reaction pair formed by the gravitational forces acting between the two particles is called the vector form of Newton’s law of gravitation. Consider two point mass bodies A and B of masses m₁ and m₂ placed at distance r apart as shown in the below figure:
Vector Form of Newton’s Law of Gravitation
Here,
= Unit vector from A to B
= Unit vector from B to A.
= Gravitational force exerted on body A by body B.
= Gravitational force exerted on body A by body B.
From the above figure, it can be seen that the two particles of masses are placed at a distance
Therefore, according to Newton’s law of gravitation, the force applied on m2 by m1 is
The negative sign indicates the attractive nature of the force.
Similarly, Gravitational force on m1 by m2
We know that
| r12 |2 = | r21 |2
Thus,
This implies that the above two vectors are equal and opposite to each other which says that gravitational force satisfies Newton’s third law.
Hence, this vector form of Newton’s law of gravitation signifies that the gravitational forces acting between the two particles form the action-reaction pair as shown above.
Universal Law of Gravitation
Universal Law of Gravitation or Newton’s law of Universal Gravitation as the name suggests is given by Sir Isaac Newton. This law helps us to understand the motion of very large bodies in the universe. According to this law, an attractive force always acts between two bodies that have masses. The strength of the force is directly proportional to the mass of the object and is inversely proportional to the square of the distance between them.
In this article, you are going to read about everything related to Universal Law of Gravitation including its definition, what Gravitational Law states, weight vs. Gravitational Force, etc.
Table of Content
- What is the Universal Law of Gravitation?
- Universal Gravitation Equation
- Vector Form of Universal Law of Gravitation
- Principle of Superposition of Gravitational Forces
- Newton’s Law of Gravitation from Kepler’s Law
- Weight and Gravitational Force
- Universality of Gravity
- Importance of Universal law of Gravitation
- Solved Examples
- FAQs