Question

How law of gravitation is derived from keplers laws?

Answer 1

1. Kepler's 1st law- The gravitation force between two objects is directly proportional to the product of their masses

For Example-If the mass of two objects be M1 and M2

Then gravitation force between them (F)∝M1×M2

2. Kepler's 2nd law of gravitation- states that the force of gravitation between two objects is also inversely proportional to the square of the distance between them.

For example-Let the objects with mass M1 and M2 are kept at a distance of r

∴Force of gravitation between them (F)∝1/r²

∴From the two relations we get

F∝(M1×M2)/r²

⇒F=(M1×M2)/r² ×G

[G is the proportionality constant of gravitation whose value is 6.674×10^{-11}

∴F=G×(M1×M2)/r²