Gravitation - Everything you need to know

                        GRAVITATION

Historical Introduction:- 

    The motion of celestial bodies such as the moon,the earth ,the planets etc., has been a subject of great interest for a long time . Famous Indian astronomer and mathematician, Aryabhat,studied these motions in great detail, most likely in the 5th century A.D. ,and wrote his conclusions in his book "Aryabhatiya". He established that the earth revolves about its own axis. 

                 About a thousand years after Aryabhatt, the brilliant combination of Tycho Brahe (1546-1601) and Johannes Kepler (1546-1630) studied the planetary motion in great detail. [which will discuss latter as "Kepler Laws"]

    The year 1665 was very fruitful for Issac Newton (aged 23) . In this year he performed brilliant theoretical  and experimental tasks mainly in the field of mechanics and optics. The saying goes that Newton was sitting under an apple tree when an apple fell down from tree on the earth. This sparked the idea that the earth attracts all bodies towards its centre. He declared that the laws of nature are same for earthly and celestial bodies.

Mathematical Equations:
      Newton guessed that the acceleration of a body towards the eqrth is inversely proportional to the square of the disrance of the body from centre of earth.
                           
                                a= 1/r2

Also , the force is mass times accelertion  {i.e. F=m.a} so it is proportional to the mass of the body.
                           F< Mm/ r2
            or,              F= GMm/r2       .......(1)

                                               where G= Grqvitational constant
                                                               = 6.67 ×(10)-11  Nm2/kg2           (measured through Cavandish method)
  
                            Above eq.(1) is known as universal law of gravitation 
    

Difference b/w Gravity & Gravitation

             Note:- Gravity is a special case of gravitation when one of the mass in a system is "earth".

   Value of 'g' :- If a body falls feeeely then it excutes a free falling motion and the body comes near the Earth's surface. The velocity of the body increases and the acceleration produced is called "acceleration due to gravity".......i.e. "g"
                                  g=9.8 m/s2      (for earth).{at lattitude of 45' and at a sea-level the std. value of g}

      Note:>>       F =  GM.m /R2  = mg       {M= mass of                                                                                          earth/planet
                               => g=   GM/ R2                  m= mass of obj.
                                                                            R= radius of                                                                                                  planet}
                   >>     g= max.(at poles of earth)
                              = min.(at equator)

Variarion of 'g'
   
Cause of Gravitation:-                                         
According to quantum studies, all substances is in nature is made up of atoms and atoms consists of about more than 35 sub atomic particles.In that, "Graviton" is also one particle which causes a field of attraction, called " Gravitation". 
                                                      

All sub atomic particle including "Graviton"

      What is Gravitational field:-                                                                        

 Some other pictures related with Gravity- effects and others :-

             Modifications:-
There is some indication that the force between two masses is not aa described above.
                    The deviation from the simple law F=GMm/R2  is being taken as an indication of the existence of a fifth interection besides gravitational, electromagnetic, nuclear and . It has been reported (Physics Rev. lett. Jan. 6, 1986) that the force between two masses may be better represented as:-

For r>>200m 

F=   G"(m1m2 / r2 )

The value of G for small distance is about 1% lesss than the value of G for large distances.

Notes:-

R of earth = 6400km (aprox.)

M of earth =6× (10)24 kgs.

g for mercury= 3.61 m/s2

g for jupitor= 26 m/s2

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