Newton’s law of gravitation

Newton’s Law of Gravitation states that every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
The mathematical expression for gravitational force is F = G (m₁m₂ / r²), where G is the gravitational constant, m₁ and m₂ are the masses, and r is the distance between the centers of the masses.
The gravitational constant (G) has a value of approximately 6.674 × 10⁻¹¹ N·m²/kg² in SI units.
Gravitational force is a central force, meaning it acts along the line joining the centers of two objects.
Gravitational force is a mutual force, meaning both masses experience the same magnitude of force but in opposite directions.
It is a universal force that applies to all objects with mass, regardless of size or composition.
Gravitational force is always attractive in nature, pulling objects toward each other.
The force decreases rapidly with an increase in distance, as it is inversely proportional to the square of the distance.
The concept of gravitation is crucial for understanding the motion of planets, moons, and stars.
Gravitational force is much weaker than electromagnetic, nuclear strong, and nuclear weak forces at the microscopic level.
In the absence of external forces, gravitational force is responsible for the formation of orbits in celestial systems.
The value of G is constant throughout the universe and does not depend on the nature of the interacting masses.
The weight of an object on the Earth is the gravitational force exerted on it by the Earth.
Weight is given by W = mg, where m is mass and g is the acceleration due to gravity.
The acceleration due to gravity (g) near the Earth's surface is approximately 9.8 m/s².
The value of g decreases with altitude and depth inside the Earth.
Gravitational force keeps the planets in orbit around the Sun and the moons in orbit around their planets.
The concept of gravitational force is essential for understanding phenomena like tides and satellite motion.
Newton’s law of gravitation explains why objects fall toward the Earth with a constant acceleration.
Gravitation is responsible for the structure and formation of galaxies and large-scale cosmic structures.
In a two-body system, the objects orbit around their common center of mass.
The gravitational force between two objects is independent of the presence of other bodies.
Gravitational interactions are described by Newtonian mechanics for most practical purposes, but extreme cases require Einstein’s General Relativity.
The concept of a gravitational field is used to describe the influence a mass exerts on its surroundings.
The strength of the gravitational field at a point is given by g = Gm / r², where m is the mass of the object creating the field.
For a spherically symmetric mass, the gravitational force acts as if all the mass is concentrated at its center.
The inverse-square law nature of gravity explains the weakening of the force with increasing distance.
Newton’s law of gravitation provides the foundation for calculating the escape velocity of celestial bodies.
Escape velocity is the minimum velocity required to escape a planet’s gravitational field and is given by vₑ = √(2GM / R), where M is the mass and R is the radius of the planet.
Gravitational potential energy is defined as U = -G(m₁m₂ / r), where U is the potential energy.
The negative sign in gravitational potential energy indicates that work must be done to separate the masses.
The gravitational binding energy is the energy required to disassemble a celestial body into individual particles.
Newton’s law of gravitation was instrumental in explaining the Kepler’s laws of planetary motion.
Gravitational force decreases as we move away from the Earth, affecting the motion of satellites and space probes.
The weightlessness experienced by astronauts in orbit is due to free fall under gravity.
Newton’s law of gravitation successfully describes interactions between most macroscopic objects.
It fails to explain phenomena involving high speeds or intense gravitational fields, where General Relativity is required.
Gravitational force is responsible for the collapse of stars into black holes when nuclear fusion ceases.
Artificial satellites use the principles of gravitation to maintain stable orbits around the Earth.
Geostationary satellites remain stationary relative to a point on Earth by orbiting at a specific altitude and speed.
Newton’s law of gravitation helped confirm the existence of Neptune through perturbations in Uranus’s orbit.
The gravitational influence of the Moon and Sun causes ocean tides on Earth.
Newton’s gravitational theory was later expanded upon by Einstein’s General Theory of Relativity to account for spacetime curvature.
Understanding gravitation is essential for predicting and analyzing planetary orbits, space missions, and stellar dynamics.