Chapter 7: GravitationClass 11 Physics — summary, notes, extra questions & MCQ quiz

Summary

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 \(F=Gm_1m_2/r^{2}\), directed along the line joining them, where \(G=6.67\times10^{-11}\ \text{N m}^{2}\text{kg}^{-2}\) was measured by Cavendish. Acceleration due to gravity \(g=GM_E/R_E^{2}\) decreases with height as \(g(1-2h/R_E)\) and with depth as \(g(1-d/R_E)\). Gravitational potential energy of two masses is \(-Gm_1m_2/r\), taken zero at infinity. The escape speed from Earth is \(v_e=\sqrt{2gR_E}\approx11.2\ \text{km s}^{-1}\). Earth satellites obey Kepler's laws; the orbital speed is \(\sqrt{GM_E/(R_E+h)}\) and the total energy of an orbiting satellite is negative, \(-Gm M_E/2(R_E+h)\), confirming a bound orbit. A uniform spherical shell exerts no gravitational force on a mass inside it.

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