gravitation class 11 neet jee notes CBSE ncrt purly

                          gravitation 

• Kepler's laws are discovered first, 
• its first law was about the law of orbits:- all the planets have their own elliptical orbits in which they revolve around the sun.
• law of areas:- the line that joins any planet to the sun sweeps equal areas in equal intervals of time .theeta = s/r.
• law of periods:- the square of the period of the revolution of a planet is proportional to the cube of the semi-major axis of the ellipse traced out by the planet.
• Newton discovered gravitation by the apple, the universal law of gravitation that led to an explanation of terrestrial gravitation as well as of Kepler's laws. 
• a=v2/Rm=4pi2Rm/T2.
• the value of Am much smaller than the value of acceleration due to gravity g on the surface of the earth, arising also due to tot the earth's gravitational attraction.
• the gravitational law provided by newton was the body attracts every other body in the universe with the force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
• mathematical principles of natural philosophy.
• point masses whereas we deal with the extended objects which have infinite size, if we have a collection of point masses, the force on any one of them is the vector sum of the gravitational forces exerted by the other point masses. 
• F= Gm1.m2 / r2 .
• gravitational constant was discovered by henry cavendish and has the value = 6.67 into 10 -11 Nm2/ kg2
• so .the two special cases:- the force of attraction between a hollow spherical shell of uniform density and a point mass situated outside is just as if the entire mass of the shell is concentrated at the centre of the shell. ,   qualitatively, this can be understood as follow:-  gravitational forces caused by the various regions of the shell have components along the line joining the point mass to the centre as well as along the direction perpendicular to this line. the components perpendicular to this line cancel out when summing over all regions of the shell leaving only the resultant force along the line joining the point to the centre. 
• the next case is the force of attraction due to the hollow spherical she;; of uniform density, on a  point mass situated inside it, is 0. various regions of the spherical shell attract the point masses inside it in various directions. these forces cancel each other completely.
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