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GRAVITATION KEPLER'S LAWS * Every planet revolves in the time in an elipical orbit ot the sun and lined at time of one. P * The areal velocity of Ae the time period of the ] ollipsites of the S " 20 square of area, is the planal at of the seight, planet sund <—— 2a ——> TP «a? * The square of the time period of the revolution of planet is directly relolving the cube of semei semi major sines of the elilistical solution /'t = a® T?« a? ¢ The constant lance of planet * The Gravitpendent of alamient forces * The square velocity like vector in a point mass is the vector sum of the gravitational forces (t) VARIATION OF g DUE TO ALTITUDE GM h = g (Re+h)* VARIATION OF 9 DUE TO DEPTH == ga 9(1- 2) ~~ ------- ESCAPE SPEED © The minimum grafron peclifically in a nit protection of earth e It is crotsum of earth in projection s that just is inaces smaller froon about 5 Ve = [26M = [2gR =./8nGpR’ : j26x8 - = | 81GPR* Ve Re 3 NEWTON'S LAW OF GRAVITATION ¢ The Gravitational force (F) between bodies is directly intopential productional of masses of masses pncierance between them c Gm,m2 Fa - SMe y* ¢ Characteristics of Gravitational medium ¢ It is independent and considentral force ¢ It is intenenite distance between them ACCELERATION DUE TO GRAVITY (9) 9 = an * For a body falling freely eeely gravity and M—+ Gm/R, ‘Ther T is low * Acceleration of boly body acceleration due to qmm/R? ° Escape bodly gravitational constant ¢ M—is mas of density flasomng average times smaller earth GRAVITATIONAL POTENTIAL ENERGY * The work done in bringing a from infinity to a point in Seiebing a oni is gravitational potential system U =- Gm,m2 * For two point mass system Y= - Gmum2 Y EARTH'S SATELLITE ° Orbital Speed of Satellite ° Energy Speed of T= 2% ° Time Period of Satellite ° Kinetic energy K = © Potential energy U= ee ° Total energy (EK) = S™ ° Binding energy (BE = -E) ° Binding energy (BE = -E) 8. TYPES OF SATELLITES @ Polar Satellite @ | Geostationary Satellite * Revolves in polar orbit around | * Time period is 24h. the earth | * Height is approximately 35800 km. a is approximately 500-800 et A angular speed. an ‘| * Time period is nearly sense of rotation a a # Used in. military spyin 4, weather| * eg for satellite communication, jorecasting, meteorology etc. * INSAT is group of Geostationary satellites sent up by India. N ee Polar i Orbit Geostationary ? ) XQ J L wv ‘ — : ‘ ‘ ‘ | / ‘ s I *. - * ‘ ¢ s ‘ - * H * al . ‘ , Tos ae” e WW o * Cee ee . WEIGHTLESSNESS | An Astronaut experiences weightlessness in a space | satellite. This is not because the gravitational force is small at that location in space. It is because both the astronaut and every part of satellite has an acceleration towards the center of the earth which is exactly the value of earth's acceleration due to gravity. at that position. we 
