Formulas from NCERT Class 9 Chapter 10 Gravitation:
Gravitation, also known as gravity, is the force that attracts two bodies towards each other. It is one of the four fundamental forces of nature and plays a crucial role in our understanding of the universe. Gravitation is responsible for holding the planets in their orbits around the sun, for keeping the moon in orbit around the Earth, and for determining the shape and structure of galaxies.
Newton’s law of gravitation: F = G * (m1 * m2) / d^2
where F is the force of attraction between two bodies, G is the gravitational constant, m1 and m2 are the masses of the two bodies, and d is the distance between their centers.
Gravitational field intensity: g = G * M / r^2
where g is the gravitational field intensity at a distance r from the center of a planet or celestial body of mass M, and G is the gravitational constant.
Gravitational potential energy: U = – G * (m1 * m2) / r
where U is the gravitational potential energy of two bodies of masses m1 and m2 separated by a distance r, and G is the gravitational constant.
Escape velocity: v = sqrt(2GM/r)
where v is the escape velocity required by an object to escape the gravitational field of a planet or celestial body of mass M and radius r, and G is the gravitational constant.
Gravitational potential: V = – G * M / r
where V is the gravitational potential at a distance r from the center of a planet or celestial body of mass M, and G is the gravitational constant.
Weight of an object: W = mg
where W is the weight of an object, m is its mass, and g is the acceleration due to gravity.
Inertial mass: F = ma
where F is the force acting on an object, m is its inertial mass, and a is its acceleration.
Gravitational force between a point mass and a spherical shell of mass: F = (G * m1 * m2 * r) / R^3
where F is the gravitational force between a point mass m1 and a spherical shell of mass m2 and radius R, and r is the distance between the point mass and the center of the shell.
Kepler’s third law: T^2 = (4π^2 * r^3) / (GM)
where T is the period of revolution of a planet around the sun, r is the average distance between the planet and the sun, G is the gravitational constant, and M is the mass of the sun.
Gravitational potential energy of an object near the surface of the Earth: U = mgh
where U is the gravitational potential energy of an object of mass m at a height h above the surface of the Earth, and g is the acceleration due to gravity.
In this article, we have covered the basic concepts of gravitation, including the inverse square law of gravitation, acceleration due to gravity, and Kepler’s laws of planetary motion. We hope that this guide has been helpful in understanding the fundamental principles that govern this important force. With this knowledge, you will be able to apply the formulas and equations to solve problems in the field of gravitation.