Question

derive an expression for the gravitational force bewteen two bodies

Answer 1

According to the Universal Law of Gravitation, every object in this UNIVERSE attracts every other object with a Force which is directly proportional to the mass of two objects and inversely proportional to the square of distance between the two, i.e.,

$F ∝ Mm$
$F ∝ \frac{1}{ {d}^{2} }$
Now, combining both equations, we get

$F ∝ \frac{Mm}{ {d}^{2} }$
To remove the sign of proportionality, we multiply R.H.S by a constant. Here, we take the universal constant G, which has been calculated to be 6.673 × 10 ^-11 and never changes.

$F =\frac{GMm}{ {d}^{2} }$
Hence, we use the formula stated above to calculate the force of gravitation between two objects, where F is the force of gravitation, G is a universal constant, M is the mass of larger object, m is the mass of smaller object, and d² is the square of distance between the two objects.

Hope it'll help.. :-D