If I have a big ball of 20,000,000kg and another of 100g, does it mean that the big ball will pull the small ball towards it?
Answer
The magnitude of the force for both balls is $F = G \frac{M m}{r^2}$. Here $M$ is the mass of the big and $m$ the mass of the small ball, both assumed to be point masses. As you can see the force is the same on both balls.
So $F_{Big} = F_{small}$. This leads with $F = m\cdot a $ to $m a_{small} = M a_{big}$ or in a much nicer way:
$$\frac{a_{small}}{a_{big}} = \frac M m = 200,000,000$$
As you can see both balls will move, but the smaller ball has a much bigger acceleartion. With this you can assume that the big ball stays at rest and only the small ball is moving.
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