Definition:Gravitational Field

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 $d$.

Also see

• Results about gravitational fields can be found here.

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 $\map \grad {k / r}$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): gravitation
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): gravitational field
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): gravitation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): gravitational field