Sir Isaac Newton developed the Universal Law of Gravitation in 1687. The gravitational force between any two objects in the universe is described by this law. In this we come to know about planetary motion, celestial mechanics, and how objects behave when subjected to gravity.
Newton’s Law of gravitational states that every particle in this universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.
Statement of the Law
According to the Universal Law of Gravitation, all particles in the universe are drawn to all other particles by a force that is inversely proportional to the square of the distance between their centers and directly proportional to the product of their masses. It can be stated mathematically as: F = G m1 m2 / r2
Where:
F is the gravitational force between two objects.
m1 and m2 are the masses of the two objects.
r is the distance between the centers of the two masses.
G is the universal gravitational constant (6.674×10−11 N \ m2 / kg2).
Key Features of the Law
1.Universal Applicability: The law is universal, it holds true for all objects in the universe, regardless of their mass, size, or distance from one another.
2. Mutual Force: There is a reciprocal gravitational pull between two things. According to Newton’s Third Law of Motion, if object A applies a force on object B, object B will respond by applying an equal and opposite force to object A.
3. Central Force: The line connecting the centers of two interacting bodies is where the gravitational force acts.
4. Action at a Distance: When there is no direct physical touch between the two bodies, gravity still works.
Importance of the Universal Law of Gravitation
1.Planetary Motion: According to Johannes Kepler, the elliptical orbits of planets around the sun are explained by Newton’s law. It offers the starting point for understanding celestial mechanics.
2. Tides: Earth’s ocean tides are a result of the moon and sun’s gravitational pull.
3. Artificial Satellites: Artificial satellites are kept in orbit by the law, which controls their motion.
4. Formation of Celestial Bodies: Because of gravitational pulls everything come together, it is essential to the development of stars, planets, and galaxies.
Derivation and Applications
1.Acceleration Due to Gravity: Near the Earth’s surface, the gravitational force simplifies to F = mg, where g is the acceleration due to gravity (9.8 m / s2).
2. Orbital Motion: By equating gravitational force with centripetal force, F = mv2 / r, the velocity and period of orbiting objects can be determined.
3. Escape Velocity: The minimum velocity required to escape Earth’s gravitational pull is derived using law.
Limitations of the Law
While the Universal Law of Gravitation is remarkably accurate for most practical purposes, it has limitations:
1. Scale: It does not account for extremely small scales, such as atomic and subatomic particles.
2. Relativistic Effects: In the presence of very strong gravitational fields or when dealing with high velocities, the predictions of General Relativity by Einstein supersede Newton’s law.
Characteristics of the gravitational force:-
Gravitational force is always attractive and directed along the line joining the particles.
It is independent of the nature of the medium surrounding the particles.
It holds good for long distances like interplanetary distance also for short distances like interatomic distances.
It is conservative force. Therefore, the work done by the gravitational force on a particle is independent of the path described by the particle.
It depends upon the initial and final positions of the particle. Therefore, no work is done by the gravity if a particle moves in closed path.
If we have collection of point masses, the force of any one of them is the vector sum of the gravitational forces exerted by the other point masses. e.g gravitational force on point mass m1 is the vector sum of the gravitational forces exerted by m2, m3, and m4.
Modern Perspectives
Einstein’s General Theory of Relativity improved our understanding of gravity by characterising it as a mass-induced curvature of space time, Newton’s law is still very useful in practical applications and is a fundamental idea for education.
Note:-
How the universe functions is provided by the Universal Law of Gravitation. It highlights the interdependence of all matter by skillfully tying together items that range in size from the tiny particles to the grand galaxies.
Every particle in the universe is drawn to 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, according to Sir Isaac Newton’s Universal Law of Gravitation.
The gravitational force F is given by:
F = G m1m2 / r2
Here, G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
The universal gravitational constant, G, has a value of 6.674×10−11 N \ m2 / kg2.
It applies universally to all objects with mass.
The gravitational force is mutual and acts along the line joining the centers of two objects.
The force decreases with the square of the distance between the objects.
The law explains:
How satellites and planets move.
• The moon and sun-induced tide phenomenon.
• The movement of man-made satellites and space travel.
• The way heavenly bodies develop and behave.