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5. GRAVITATION Introduction: From the observations in many natural phenomenon’s it is clear than all material objects have a natural tendency to get attracted towards the Earth. The basic cause is that every massive object in the universe experiences gravitational force. It is the force of mutual attraction between any two objects by virtue of their masses. It is always an attractive force with infinite range. It does not depend upon intervening medium. It is much weaker than other fundamental forces. Gravitational force is 10°° times weaker than strong nuclear force. Kepler’s Laws: Governing to the motion of Planet’s around the Sun there are three different Laws known as Kepler’s laws for planetary motion. 1. Law of orbit: This law states that, “All planets move in elliptical orbits around the Sun with the Sun at one of the foci of the ellipse.” Explanation: The orbit of the planet around the Sun is shown in the figure. In this S and S' are the two foci of the ellipse traced by planet so that position of the Sun is | either at S or S'. P is the closest position of the planet from the Sun is called the ‘Perihelion’ or ‘Perigee’. While A is the farthest position of the planet from the Sun and is known as ‘Aphelion’ or ‘Apogee’. PA is the major axis of which length is (2a), PO or AO are the semi-major axes = a. MN is the minor axis = 2b. MO and ON are the semi-minor axes = b. 2a 2. Law of area: This law states that, “The line that joins a planet and the Sun sweeps equal areas in equal intervals of time.” or “Areal velocity of the given planet around the Sun is always remains constant.” Explanation: Kepler observed that planets speed around the Sun is not uniform but is different at different position. At the closest point (Perigee) it is maximum ——_ E and at the farthest point (Apogee) it is minimum so that area ce swept by position vector of the planet around the Sun ina given interval of time is always remains constant as shown by shaded region in figure. * The law of area can be considered as an outcome of conservation of angular momentum, which is valid for any central force i.e. the force which is always directed along the line joining the position of the object and a fixed point usually taken to be the origin of the co-ordinate system. From the figure the area swept by the planet of mass m in given interval of time At is given by: AA = ; (# x VAt) -—— (i) As for small At, v is perpendicular to r and hence this is the area of triangle. From equation (i) we write, a - ; (7.x V) -------- (2) [RSG/XU/PHY/GRAVITATION] Page 2 Scanned with CamScanner 
