# Question #f2f58

Oct 7, 2014

The best way to think about this problem is through Newton's third law, which states that, "for every action, there is an equal and opposite reaction." This means that forces come in pairs; whenever a force is exerted from Body A onto Body B, Body B exerts a force onto Body A equal in magnitude but opposite in direction to first force. The same is true for gravity. When the earth exerts a force ${F}_{g}$ downwards on an apple, the apple exerts an equal force ${F}_{g}$ on the earth, but in an upwards direction.

The reason that we don't observe the effect of ${F}_{g}$ from the apple on the earth is due to Newton's second law, which can be summarized by the following equation,

$a = \frac{\text{F}}{m}$

where $a$ is acceleration of the body, $F$ is the net force applied to the body and $m$ is the mass of the body. From the equation, and also from your own intuition, for a given force, the observed change in acceleration will depend on how large (i.e. massive) the body in question is. Applying a force of $10 N$ on a large boulder will result in far less acceleration than applying the same $10 N$ force on a pebble.

So to answer your question directly, it is never possible to "nullify" the effect of gravity between two objects. Whenever an object has mass, it will apply a force on any other object of mass (through something called a gravitational field ).

If you had two bodies with equal mass, they would still exert a force on each other, but just like in the case of an apple falling to the ground, the forces wouldn't cancel out. Both bodies would simply be attracted to each other.

To visualize this, suppose there was an apple falling towards earth from outer space. Intuitively, it will continue to fall until it collides with the earth's surface. Also, as we mentioned above, the earth will be attracted to the apple and will accelerate towards it by the slightest amount. Now imagine that apple grows larger and larger until it is the same size and mass as the earth. It will still be attracted to the earth, and the earth will still be attracted to the "apple". All that will change is the magnitudes.