Newton's Law of Gravitation is a fundamental principle in physics that quantifies the force of gravity between two objects. It was formulated by Sir Isaac Newton in 1687 and is considered one of the most important discoveries in the field of physics. This law mathematically describes the gravitational force exerted by one object on another and provides a foundation for understanding the motion of celestial bodies, the behavior of objects on Earth, and various other phenomena related to gravity.

Law Statement:
The law of gravitation states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, it can be represented as:

F = (G * m1 * m2) / r^2

where:
- F is the gravitational force between the two objects,
- G is the gravitational constant (approximately 6.67430 x 10^-11 Nm^2/kg^2),
- m1 and m2 are the masses of the two objects, and
- r is the distance between their centers.

Key Points:
1. Universal Nature: The law of gravitation applies to all objects in the universe, regardless of their size or composition.
2. Inverse Square Law: The gravitational force decreases as the distance between objects increases. If the distance is doubled, the force becomes one-fourth.
3. Proportional to Mass: The force of gravity is directly proportional to the product of the masses of the two objects. If either mass is increased, the force of attraction will also increase.
4. Non-Directional Force: Gravity acts along the line joining the centers of the two objects and has no preferred direction.
5. Applicability: Newton's law of gravitation is applicable to a wide range of scenarios, from everyday objects on Earth to the motion of planets, moons, and stars in space.

Significance:
Newton's law of gravitation revolutionized the understanding of gravity and provided a mathematical framework to predict and explain the motion of objects under its influence. This law helped explain the orbits of planets around the sun, the tides on Earth, and the motion of celestial bodies in the universe. Additionally, it laid the foundation for further advancements in physics, including Albert Einstein's theory of general relativity. Understanding and applying this law is crucial in fields such as astrophysics, aerospace engineering, and celestial mechanics.