GRAVITATION CLASS 11TH

SUMMARY OF CHAPTER:-
Definition of Gravitation
Acceleration Due to Gravity
Variation Of “G” With Respect to Height And Depth
Escape Velocity
Orbital Velocity
Gravitational Potential
Time period of a Satellite
Height of Satellite
Binding Energy
Various Types of Satellite
Kepler’s Law of Planetary motion

1. Gravitation By, HIMANSHU XI A GRAVITATION MADE BY-HIMANSHU CLASS 11 TH A

2. Summary Definition for Gravitation Acceleration Due to Gravity Variation Of “G” With Respect to Height And Depth Escape Velocity Orbital Velocity Gravitational Potential Time period of a Satellite Height of Satellite Binding Energy Various Types of Satellite Kepler’s Law of Planetary motion

3. GRAVITATION Gravitation is an Natural Phenomenon by physical bodies attract each other. Newton focused on his attention on the motion of the moon about the earth. He declared that the laws of nature that operating between earth and the apple is same as the laws operating between earth and moon. He calculated the acceleration due to gravitation (on earth) to be 9.8m/s 2 . Newton predicted that a  

4. Also, F By , The third law of motion, the force on a body due to the earth must be equal to the force on the earth due to the body. Therefore, this force should also be proportional to the mass of the earth. Thus , the Force between the earth and a body is F F= G is called the universal constant of gravitation and its value is found to be 6.67x10-11 N-m2 /kg 2 .  

5. 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. Attraction Force between two bodies

6. Important Features 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.

7. Test Your Brain… ??? Consider an Elevator freely falling from North pole to South pole through the center of earth. Describe its motion?? For answer Press Enter ..

8. Acceleration due to Gravity of the earth Suppose a mass ‘m’ is situated outside the earth at a distance ‘r’ from it centre. The gravitational force on the mass is F = F=mg. mg= g= By the above equation we can say that Acceleration due to gravity is independent of mass.  

9. Test Your Brain… ??? Determine the mass of earth using the knowledge of G. G=6.6x10 11 and g=9.8 m/s 2 and r = 6.36x10 6 . For answer press enter… As we know g= . m= . m= m=5.97x10 24 Do you know ?? Cavendish was the first person the calculate the mass of earth because he was the first person to calculate value of G.  

10. Variation in Acceleration due to Gravity Consider a Body placed at the point ‘p’ above the earth surface at a distance of ‘h’. The g will be . g = at earth surface. …( i ). gh = at point m ….(ii). Dividing (ii) by ( i ). We get = = …..(iii) = = ) -2   Variation of ‘g’ with respect to altitude

11. = …(iv) Both the eq. (iii and iv) show that the ‘g’ decreases as the height increases. Eq. iii must be used in the numerical when ‘h’ is comparable to ‘r’. Eq. iv must be used in the numerical when h<<r. Variation of g with respect to the altitude.  

12. Variation in Acceleration due to Gravity Variation of ‘g’ with respect to Depth Consider a Body placed at the point ‘d’ below the earth surface at a distance of ‘d’. The g will be . g = M = Volume x Density = . g = g = . At earth surface ...( i ) gd = . At the point d …(ii) Dividing (ii) by ( i ). gd /g = G4/3 π (r-d) ρ / G4/3 π rρ gd /g = g(1-d/r). Clearly the “g” increases with increase in depth.  

13. The Variation of g with respect to Depth and Height (graph). The Variation of g with respect to height will never be zero. It will increase after certain height. The Variation of g with respect to depth will be zero when the body is placed at the center of earth.

14. Earth is not perfectly sphere. It is flattened at the poles and bulges out at equator. g = g Type equation here. . The radius at Equator is greater than the radius at pole by 21 km. Therefore Ge > Gp . The variation of g between the poles and the equator is about 0.5%.   Variation in Acceleration due to the shape of earth

15. Gravitational field 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

16. 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. F = Work down in bringing the body to point B from Point A. W = Fdx W = dx = W = GMm W = - GMm   A P R O r x B dx

17. W = - GMm [ - U = - Gravitational Potential Amount of work done in bringing a body of unit mass from infinity to the given point Gravitational Potential = -  

18. 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. Consider the earth to be a sphere of mass M and radius R with centre O.

19. Using total energy concept we can derive the equation for escape velocity. At any point the Total energy must be zero. We know that Kinetic energy = Potential energy = K.E+P.E = 0 + = v e 2 = V e = Multiply and divide by R Ve =  

20. Test Your Brain… ??? Can you tell why moon has no atmosphere ?? For answer press enter Due to the small value of g. The escape velocity in the moon is 2.38 km/s . The air molecules have thermal velocity is greater than the escape velocity and therefore air molecules escape.

21. Types of satellite

22. Satellites Satellite is an body which continuously revolves on it own around and a much larger body in a stable orbit. Natural satellites : A satellite created by nature is called natural satellite . example : moon. Artificial satellite : A man made satellite is called an artificial satellite. Example Chandrayaan . World’s Frist satellite was SPUTNIK-1.

23. Launching of a Satellite Principle for launching a satellite : Consider a high tower with its top projecting outside the earth’s atmosphere. Lets throw a body horizontally from the top of the tower with different velocities. 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.

24. Launching of a Satellite Click on the video

25. Orbital velocity Orbital velocity is the velocity required to put the satellite into its orbit around earth

26. Orbital Velocity Force of gravity on satellite F = Centripetal Force required by the satellite to keep its orbit F = In equilibrium , the centripetal force is just provided by the gravitational pull of the earth. = V o 2 = V o = simplified eq is   R R+h h Vo

27. Time period of a satellite It is the time takes by a satellite to complete one revolution around the earth. It is given by T = circumference of the orbit / orbital velocity T = T= If the earth is a sphere the density = then mass would be = volume * density = T= =  

28. Height of a satellite T= (Gm = gR 2 ) T 2 =4 ( R+h ) 3 = R+h = H = - R  

29. 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.

30. 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.

31. Uses Geostationary Satellite In communicating radio,T.V and telephone signals across 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).

32. Polar Satellite A satellite that revolves in a planar 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

33. Total Energy of a 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 U = - Kinetic energy = m . Total Energy = - E = - The negative sign shows that the satellite is bound to the earth.  

34. Binding Energy of a satellite The energy required by a satellite to leave its orbit around the earth 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.  

35. Kepler’s law of planetary motion Law of orbits (first law) : Each planet revolves around the sun in an elliptical orbit with the sun situated at the one of the two foci.

36. Kepler’s law of planetary motion 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.

37. Proof : x = 0 [ opp. Faced] = 0. Or = constant . = ( = Area) = = t = t   Kepler’s law of planetary motion   sun         planet P’

38. Kepler’s law of planetary motion = x t = x = ( x ) = [L and m are constant]  

39. Kepler’s law of planetary motion Law of periods (third law) : The square of the period of revolution of a planet around the sun is proportional to the cube of the semi major axis of the its elliptical orbit. Proof : Suppose a planet of mass m moves around the sun in a circular orbit of radius r with orbital speed v. Let M be the mass of the sun. The force of gravitation between the sun and the planet provides the necessary centripetal force. = or v 2 = . v = = =  

40. = x r 3 = constant r 3 r 3 . For better understanding please click the here .   Kepler’s law of planetary motion

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