Knowing that the formula for gravitational potential is the following.
$$V = -\frac{GM}{r}.$$
We take two masses in between one point let us say T. One mass is m and another 24m. Let us say that the distance of m from T is $\frac{d}{5}$ and distnace from T to 24m is $\frac{4d}{5}$
How do we calculate the net V? Wouldn't that just be the Gravitational Potential added from both masses, since Gravitational potential is a scalar? In this case, we would calculate it like this:
$$V = -\frac{5GM}{d} -\frac{30GM}{d} = - \frac{35GM}{d}.$$
However, bearing in mind that as we move away from one source of mass to another one gets weaker as another gets stronger. Therefore, to find the net potential we should change the sign of the other gravitational potential disregarding the fact that it is a scalar and thus we would result with this answer:
$$V = -\frac{5GM}{d} +\frac{30GM}{d} = \frac{25GM}{d}.$$
Do I understand this concept correct or where is my mistake, I cannot seem to grasp why answering a question about scalar quantities you would answer with the latter answer.
