Gravitational Field

Definition. The gravitational field intensity (or simply the gravitational field) $\vec{E}_1$ at a point that is a distance $r$ from a mass $m_1$ is defined as the gravitational force experienced by a unit mass placed at that point:

Because $\vec{E}_1$ is built by dividing out $m_2$, it depends only on the source mass $m_1$ (and the position), never on whatever test mass happens to be placed there -- the field exists at every point in space around $m_1$ whether or not anything is actually there to feel it.

Relation to acceleration. If an actual mass $m$ is placed in this field, the force it feels is $\vec{F}=m\vec{E}$ (Eq. 6.17); combined with Newton's second law $\vec{F}=m\vec{a}$, this immediately gives

So numerically and directionally the gravitational field equals the acceleration a free test mass would experience there -- but conceptually they are different things: $\vec{E}$ is a property of the source mass $m_1$, while $\vec{a}$ is the effect experienced by whatever test mass is placed in that field.

Key properties.

• $\vec{E}$ is a vector quantity, always pointing toward the source mass.
• Its magnitude falls off as $1/r^2$: it is strongest closest to the source and weakens steadily with distance (Figure 6.10). …