# Newtons law of Gravitation

The Force of attraction between two bodies is proportional to the product of their masses. And considering the equation $F=ma$. Acceleration due to gravity will be more for objects lower mass. This contradicts the established theory that objects with different masses take the same time to reach the ground if dropped from the same height. Please explain

For gravity the force is :

$$F=\frac {G M_1 M_2} {r^2}$$

But the acceleration :

$$a=\frac F {M_2} =\frac {G M_1 } {r^2}$$

and this is the same for all bodies as it depends only on the primary's mass ($M_1$).

The force of attraction between two bodies is proportional to the product of their masses.

Correct. StephenG gave the expression: $F=\frac {G M_1 M_2} {r^2}$. If the masses are greater the force is even greater.

This contradicts the established theory that objects with different masses take the same time to reach the ground if dropped from the same height. Please explain.

It's simpler than you think. Imagine you have two Earth-sized objects A and B. Object A will "fall" towards object B at 9.8m/s². In addition object B will "fall" towards object A at 9.8m/s². So their closing acceleration is 19.6m/s². It's more than 9.8m/s². The net effect is that the two objects fall together faster.

However if your two objects are apple-sized and Earth-sized, object A will "fall" towards object B at 9.8m/s², but object B experiences no measurable "fall" towards object B. An apple is just too small. It's the same if you have a melon-sized object and an Earth-sized object. It's also the same if you have a melon+apple-sized object and an Earth-sized object. You measure an acceleration of 9.8m/s². Your melon+apple needs to be very very big before you measure a closing acceleration of more than 9.8m/s².