Q.Two bodies of masses $m$ and $4m$ are placed at a distance $r$. Calculate the gravitational potential at a point on the line joining them where the gravitational field is zero.

Definition. The gravitational field at a point is the gravitational force that a unit mass would experience if placed there. For a source mass $m$, the field at distance $r$ is

a vector quantity (unit: N/kg, equivalent to $\text{m s}^{-2}$) that always points toward the source mass and depends only on that source -- not on whatever test mass might later be placed there. If a real mass $m'$ is placed in this field, the force it experiences is $\vec{F}=m'\vec{E}$, and combined with Newton's second law this shows the field numerically equals the acceleration a free test mass would feel there, $\vec{a}=\vec{E}$.

Why the field concept exists at all. Gravity acts across empty space with nothing physically touching the two masses. The field is the bookkeeping tool that turns this "action at a distance" into a definite value attached to every point in space, independent of whether anything is actually there to feel it. …