Gravitation ch-7 class-11 phy..pptx

gravitation

1. Gravitation class 11 physics

2. Flow of chapter Introduction of Gravitation Kepler’s Law of Planetary motion Universal law of gravitation Gravitational constant Acceleration due to gravity on earth Gravitational potential energy Escape velocity Earth satellites Energy of orbiting satellites Geostationary and polar satellite Weightlessness

3. Introduction Whenever we throw an object towards the sky, it falls back to the ground. For example: a ball comes down when thrown up; rain drops fall towards the ground. There is a force due to which all bodies are attracted towards the earth, known as gravitation. Gravitation is the force of attraction between all massive bodies in the universe. In this chapter we will take a look at gravitational force and laws governing gravitation. We will also study about planetary and satellite motion.

4. Kepler's Law of planetary motion

5. Law of orbits (first law) Each planet revolves around the sun in an elliptical sun situated at the one of the two foci. orbit with the

6. Law of areas (second law) The radius vector drawn from the sun to a planet sweeps out equal areas in equal intervals of time i.e the areal velocity ( area covered per unit time) of a planet around the sun is constant.

7. Law of periods (third law) Kepler's third law states that the square of the period is proportional to the cube of the semi-major axis of the orbital

8. Newton's universal law of gravitation Gravitational force F ,is always attractive, and it depends only on the masses involved and the distance between them. Every object in the universe attracts every other object with a force along a line joining them. The equation for Newton’s law of gravitation is: Fg is the gravitational force between m1 and m2 G is the gravitational constant

9. Evidence in support of law of gravitation The rotation of the earth around the sun or that of the moon around earth is explained on the basis of this law. The tide are formed in ocean due to the gravitational force of attraction between earth and the moon. The value of g can be used to predict the orbits and time period of an satellite.

10. Important feature of law of gravitation The Gravitation force between two masses is independent of the intervening medium. The mutual gravitational forces between two bodies are equal and opposite i.e. Gravitational Forces obey Newton’s third law of motion. The gravitational force is an conservative force. The law of gravitation holds only for point masses. The gravitational force between two point masses is a central force. Its magnitude depends only on r and has no angular dependence . The Gravitational force between two bodies is independent of the presence of other bodies.

11. Acceleration due to gravity Near the surface of Earth, the acceleration due to gravity is approximately constant. But, at large distances from the Earth, or around other planets or moons, it is varying. The acceleration due to gravity depends on the terms as the following Suppos e a mass ‘m ’ i s situated outsid e th e eart h a t a distanc e ‘ r ’ from it Centre . The gravitational force on the mass is As the height (h) is negligibly small compared to the radius of the earth we re-frame the equation as follows, f = GmM r 2 Now equating both the expressions, mg = GmM r 2 ⇒ g = GM r 2 By the above equation we can say that Acceleration due to gravity is independent on mass of object

12. Acceleration at Height from the surface of earth Let g be the value of acceleration due to gravity at the surface of earth and g' at a height h above the surface of earth.

13. Acceleration Variation with depth Let g be the value of acceleration due to gravity at the surface of earth and g' at a depth d below the surface of earth. If the earth is considered as a sphere of homogeneous composition o f densit y ρ , the n g a t an y poin t o n th e surface o f the earth is given by:

14. Gravitational field Two bodies attract each other by the gravitational force even if they are not in direct contact. This interaction is called action at a distance. It can best explained in terms of concept of field. According to the field concept. Every mass modifies the space around it . This modified space is called gravitational field When any other mass is placed in this field , it feels a gravitational force of attraction due to its interaction with the gravitational field The space surrounding a material body within which its gravitational force of attraction can be experiences a force of attraction towards the Centre of earth

15. Gravitational potential energy Amount of work done in bringing a body from infinity to the given point in the gravitational field of the other. Expression for Gravitational potential energy. W = Fdx W or k dow n i n bringin g th e bod y t o poin t B fro m Poin t A.

16. Escape velocity If we throw a ball into air , it rises to a certain height and falls back. If we throw it with a greater velocity , it will rise higher before falling down.If we throw with sufficient velocity , it will never come back .i.e. It will escape from the gravitational pull of the earth. The minimum velocity required to do so is called escape velocity. Conside r th e eart h t o b e a sphere o f mass M an d radius R with Centre O.

17. Satellites Satellit e i s a n bod y whic h continuously revolves o n i t ow n around and a much larger body in a stable orbit. Natural satellites : A satellite created by nature is called natural satellite . example : moon. Artificia l satellite : A man made satellite i s called a n artificial satellite. Example Chandrayaan . World’s Frist satellite was SPUTNIK-1.

18. Launching a satellite Principle for launching a satellite : Consider a high tower projecting outside the earth’s atmosphere. Lets throw a body horizontally from the top of the tower with different velocities. with its top As we increase the velocity of horizontal projection , the body will hit the ground at point farther and farther from the foot of the tower. At certain velocity the body will not hit the ground , but always be in a state of free fall under the influence of the gravity. Then the body will follow a stable circular orbit . And that body is called satellite.

19. Geostationary satellite A satellite which revolves around the earth in tis equatorial plane with the same angular speed and in the same direction as the earth rotates about its own axis is called a geostationary or synchronous satellite.

20. Necessary condition for geostationary satellite It should revolve in an orbit concentric and coplanar with the equatorial plane of the earth. Its sense of rotation should be same as that of the earth , i.e From west to east. Its period of revolution around the earth should be exactly same as that of the earth about its own axis , i.e 24 hours It should revolve at a height of exactly 35930 km.

21. Orbital velocity Orbital velocity is the velocity required to put the satellite into its orbit around earth Centripetal force is also important, as this is the force responsible for circular motion. For deriving a simple equation for orbital velocity, we will assume uniform circular motion. In the case of an orbiting body, the centripetal force is the gravitational force.

22. Total energy of satellite Consider a satellite of mass m moving around the earth with velocity in an orbit of a radius r. Because of the gravitation pull of the earth, the satellite has a potential energy which is given by

23. Binding energy of satellite Th e ene r gy required by a satellit e t o leav e it s orbit aroun d th e eart h and escape to infinity is called binding energy. Binding energy Because the total energy of the satellite is In order to escape into infinity , it must be supplied extra energy so that its energy E becomes zero.

24. Use of geostationary satellite I n communicating radio, T . V an d telephon e signals acros s the world. In studying the upper regions of the atmosphere. In Forecasting weather. In studying meteorites. In studying solar radiation and cosmic rays. And used in GPS (Global positioning System).

25. Polar satellite A satellite that revolves in a p ola r orbit is called a polar satellite. Eg IERS (Indian earth resources satellites) Uses of Polar satellite Polar satellites are used in weather and environment monitoring. Spying Study topography of other celestial bodies

26. Weightlessness In case of a satellite that is rotating around the earth, every part of the satellite has an acceleration which is exactly the value of earth’s acceleration due to gravity at that position. Thus in the satellite everything is in the state of free fall. Therefore , weightlessness is experienced by astronauts in satellites.