Gravitation — Class 11 Physics

This chapter develops the universal law of gravitation from Kepler's laws of planetary motion: planets move in elliptical orbits with the Sun at a focus (law of orbits); the line joining a planet to the Sun sweeps equal areas in equal times (law of areas, a consequence of conservation of angular momentum); and the square of the orbital period is proportional to the cube of the semi-major axis (law of periods). Newton's universal law states that every body attracts every other with a force , directed along the line joining them, where was measured by Cavendish. Acceleration due to gravity decreases with height as and with depth as . Gravitational potential energy of two masses is , taken zero at infinity. The escape speed from Earth is . Earth satellites obey Kepler's laws; the orbital speed is and the total energy of an orbiting satellite is negative, , confirming a bound orbit. A uniform spherical shell exerts no gravitational force on a mass inside it.