# Definition:Gravitational Field

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## Definition

Every body which has mass influences every other body which has mass, according to Newton's Law of Universal Gravitation.

Thus any body can be considered as being surrounded by a field given rise to by its mass, called a **gravitational field**.

Its value $\mathbf g$ at any point is given by:

- $\mathbf g = \dfrac {G M} {d^3} \mathbf d$

where:

- $G$ is the universal gravitational constant;
- $M$ is the mass of the body;
- $\mathbf d$ is the displacement vector from the point to the center of gravity of the body, whose magnitude is $d$.

## Sources

- 1951: B. Hague:
*An Introduction to Vector Analysis*(5th ed.) ... (previous) ... (next): Chapter $\text {V}$: Further Applications of the Operator $\nabla$: $9$. The Vector Field $\map \grad {k / r}$