Physics

Session Gravitation

Session Opener “Planets revolve in elliptical orbits with sun at its focus”. Have you ever wondered what forces are responsible?

Session Objectives

Session Objective Newton's law of Gravity Weight & Gravitational Force Kepler's Law’s Gravitational Field Gravitational Potential Relation between field and potential Gravitational Potential Energy

Newton’s Law of Gravitation Any particle of mass m1 attracts a particle of mass m2 with a force given by: G=6.67x10-11 N.m2/kg2 Where, r is the distance between them G is Universal Gravitational Constant m1 m2 F r

Newton’s Law of Gravitation Important fact about this formula Applicable only for point masses Does not depend on the medium between the masses Not valid for nuclear distances These forces are always added vectorially

Weight & Gravitational force Earth attracts every body towards itself by virtue of which the body experience weight. The true weight of nay body is only at the earths surface at every other place it has apperant weight. Weight = mass x acceleration due to gravity. W = mg

Kepler’s Laws Kepler’s First Law: All planet move in elliptical orbits with the sun at one focus. Sun Kepler’s Second Law: A line that connects a planet to the sun sweeps out equal areas in equal time, i.e. the areal velocity of the planet is always constant

Kepler’s Laws A A’ B B’ Kepler’s Third Law: Sun A B A’ B’ Kepler’s Third Law: The square of the period of revolution of any planet is proportional to the cube of the semi-major axis of the orbit.

Gravitational Field Intensity It is defined as force experienced per unit mass acting on a test mass supposed to be placed at that point. Source point Field m (Test mass) M r [Gravitational Field]

Gravitational Potential It is defined as negative of the work done per unit mass in shifting a rest mass from some reference point to the given point. [Gravitational Potential]

Relation between Gravitational Potential

Gravitational Potential Energy Gravitational potential energy at a point is defined as the amount of work done by an external agent in bringing any body of mass (m) from infinity to that point. F(r) m U r [For a point mass] M

Expressions of potential for different bodies Gravitational potential V due to a spherical shell of mass M and radius R at a point distant r from the centre. (a) When r > R (b) When r = R V R r (c) When r < R (d) When r = 0

Expressions of potential for different bodies Gravitational potential V due to a solid sphere of radius R and mass M at a point distant r from the centre. (a) When r > R (b) When r = R (c) When r < R (d) When r = 0

Expressions of gravitational field for different bodies Gravitational field E due to a spherical shell of mass M and radius R at a point distant r from the centre. (a) When r > R (b) When r = R (c) When r < R E = 0 (d) When r = 0 r R E

Expressions of gravitational field for different bodies Gravitational field E due to a solid sphere of radius R and mass M at a point distant r from the centre. (a) When r > R (b) When r = R (c) When r < R (d) When r = 0 E = 0 E R r

Class Test

Class Exercise - 1 In order to find time, an astronaut orbiting in an earth satellite can use pendulum clock (b) spring -on trolled clock (c) any one of above (d) Neither of the two

Solution As the acceleration for a satellite continuously changes so it will give wrong time. Where this is not in case of spring-controlled clock. Hence answer is (b).

Class Exercise - 2 Which of the following graphs represent the motion of a planet moving about the sun? T is the period of revolution and r is the average distance (from centre to centre) between the sun and the planet.

Solution By statement of Kepler’s law Hence answer is (a).

Class Exercise - 3 A planet of mass M moves around the sun along an ellipse so that its minimum distance from the sun is r and maximum is R. Using Kepler’s law, find its period of revolution around the sun.

Solution According to Kepler’s law

Class Exercise - 6 If the radius of the earth were to shrink by 1%, its mass remaining the same, the acceleration due to gravity on the earth’s surface would (a) decrease (b) remain unchanged (c) increase (d) Cannot say

Solution but as R is decreased so g would increase. Hence answer is (c).

Class Exercise - 7 Two planets of radii r1 and r2 are made from the same material. The ratio of the acceleration of gravity at the surfaces of two planets is

Solution Hence answer is (a).

Thank you