Question

derivation of universal law of gravitation

Answer 1

Universal law of gravitation:  The universal law of gravitation states that every object in the universe attracts every other object with a force called the gravitational force. The force acting between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
 
Say FG is the force of gravitational attraction between any two objects,

m1 is the mass of one object,

m2 is the mass of a second object,

d is the distance between the centers of the two objects. (Objects are assumed to be spherical.)

Now as said in the Law of Gravitation:

FG ∞ m1.m2

and

        FG ∞  1/d2

So,   FG ∞ m1.m2/ d2

        FG = (G.m1.m2)/ d2

G is a constant which is discussed in the next section.
This equation gives us the expression of the gravitational force.

Answer 2

Ok take any two objects of mass m1 and m2

let the force of attraction between them is F

and the distance between them is r

So F   \alpha M1

    F   \alpha M2

    F   \alpha 1/R²

 

  We can write these equations as F  \alpha M1*M2/R²

Removing the proportionality symbol and placing G as constant we get

 F=G M1*M2/R²

Thus the universal law of gravitation can be derived