NCERT Books Free Download for Class 11 Physics Chapter 8 – Gravitation

The Chapter on Gravitation deals with laws like Kepler’s Laws, such as Law of orbits, Law of areas and Law of periods, Newton’s Universal Law of Gravitation, Central Forces and  acceleration due to gravity of the earth. 

Kepler’s Laws

The Law of Orbits by Johannes Kepler states that all planets move in elliptical orbits with the Sun situated at one of the foci of the ellipse. This was different from the earlier theory by Copernicus that the planets move around in circles around a fixed sun. 

The Law of Areas by Kepler states that the line joining any planet to the sun sweeps equal areas in equal intervals of time. This explains the fact that planets appear to move slower when they are farther from the sun than when they are nearer.

The Law of Periods States that the square of time period of revolution of a planet is proportional to the cube of the semi-major axis of the ellipse traced out by the planet. This law is a consequence of conservation of angular momentum which is valid for any central force on the planet acting along the vector joining the Sun and the planet.   

Universal Law of Gravitation

Newton’s law of gravitation, states that everybody in the universe attracts every other body with a force varying directly as the product of the masses and inversely as the square of the distance between them. The force F on a point mass m2 due to another point mass m1 has the magnitude | F | = G m1 m2/ r2 where G is the universal gravitational constant. The currently accepted value of G after experiment of Henry Cavendish is,

                                 G=6.67x1011 N m2/kg2 

Acceleration Due to Gravity of The Earth 

Acceleration due to gravity of the earth is the acceleration gained by an object due to gravitational force of the earth. It has both magnitude and direction. It is represented by g and its SI unit is m/s2. The standard value of g on the surface of the earth at sea level is 9.8 m/s2.

The acceleration experienced by a mass at point P under the earth surface is, 

g=F/m = GME / R2E where F is force, RE is the radius of the earth, ME the mass of the earth and G universal gravitational constant.  

The chapter also explains the acceleration due to gravity below and above the surface of the earth. In addition, the chapter deals with gravitational potential energy and the work required to be done to lift a point mass from the surface of the earth to another point vertically above the point at a height h.

W12=Force x displacement =mg (h2-h1)

The value of acceleration due to gravity ‘g’ is affected by

• Altitude above the earth’s surface.

• Depth below the earth’s surface.

• The shape of the earth.

• Rotational motion of the earth.

Importance of Newton’s Law of Gravitation

The gravitational force of the earth ties the terrestrial objects to the earth. This law explains the attractive force between any two objects having a mass. The formation of tides in the ocean is due to the force of attraction between the moon and ocean water.