Question

mathematicly prove the law of gravity​

Answer 1

Answer:

Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

refer to the attachment also

Answer 2

$\huge \underline{ \underline{ \bf \purple{Solution :}}}$

$\longrightarrow\sf F \propto M \times m \\ \\ \longrightarrow\sf F \propto \dfrac{1}{ {d}^{2} } \: \: \: \: \: \: \: \: \:$

Combine ( i ) and ( ii )

$\longrightarrow\sf F\propto\frac{M \times m}{ {d}^{2} } \: \: \: \: \: \: \\ \\ \longrightarrow \boxed{ \sf F = G \frac{M \times m}{ {d}^{2} }}$

G is the gravitational constant