Gravitation Formulas & Definitions: In this post we will provide all the important definitions and formulas of CBSE Class 11 Physics Chapter Gravitation. This will help you to memorise and revise your chapter quickly and easily.
Newton’s Law of Gravitation
\( F = \frac{G m_1 m_2}{r^2} \) where \( G \) is the universal gravitational constant.
\( G = 6.67 \times 10^{-11} \, \text{Nm}^2 \text{kg}^{-2} \)
Acceleration due to Gravity
\( g = \frac{GM}{R^2} \) where \( M \) is the mass of the Earth and \( R \) is the radius of the Earth.
Gravitational Potential Energy
\( PE = -\frac{G m M}{(R + h)} \)
Gravitational Potential
\( V = -\frac{GM}{(R + h)} \)
Kepler’s Law of Planetary Motion
Law of Orbits: Each planet revolves around the Sun in an elliptical orbit with the Sun at one of the foci of the elliptical orbit.
Law of Areas: The straight line joining the Sun and the planet sweeps out equal areas in equal intervals of time.
Law of Periods: The squares of the periods of the planets are proportional to the cubes of their mean distance from the Sun, i.e., \( T^2 \propto R^3 \).
Escape Velocity
Escape velocity is the minimum velocity with which a body must be projected in order that it may escape Earth’s gravitational pull. Its magnitude is \( v_e = \sqrt{2gR} \).
Satellites
Orbital Velocity: The velocity which is imparted to an artificial satellite a few hundred kilometers above the Earth’s surface so that it may start orbiting the Earth is \( v_0 = \sqrt{gR} \).
Periodic Time: \( T = 2\pi \sqrt{\frac{(R + h)^3}{gR^2}} \)
Variation of g
With altitude: \( g_h = g \left( 1 – \frac{2h}{R} \right) \)
With depth: \( g_d = g \left( 1 – \frac{d}{R} \right) \)
With latitude: \( g_\ell = g – 0.034 \cos^2 \phi \)