### gravitational field

(gravitational force as distributed over a space)

A **gravitational field** is the tendency at each point in space
to force things in a particular direction. Mathematically,
it is a vector field, a function on the three dimensions of
space yielding a vector in the direction of the force with
a magnitude consisting of the amount of force applied to
an object at that point per unit mass of the object.
Or equivalently, by Newton's law F=MA, the vector matches the
direction and degree of acceleration of an object at that point.
This field is the gradient of the gravitational potential,
the force being toward the lowest potential, which is
typically represented by negative numbers, the nearer the
object(s), the more negative.
A region of space that has such low gravitational potential,
such as the space surrounding and object, is termed
a **gravitational well**.

In a universe with a single point-size massive object, the field
would be spherically symmetric around it, the magnitudes adhering
to an inverse square law, and the direction of the object.
With two or more, there are places between where the forces
balance each other, but from a great distance from them all, the
magnitude of the field vector would approximate that of a single
point with the sum of their masses.

General relativity (GR) complicates this picture: the above can be referred to as
a **classical gravitational field** or **Newtonian gravitational field**.
The measurement precision to distinguish the differences imposed
by GR is high except in circumstances extreme compared to what we
experience on Earth.

(*gravity,physics*)
**Further reading:**

https://en.wikipedia.org/wiki/Gravitational_field

**Referenced by pages:**

Brunt-Väisälä frequency

electric field (E)

field

field lines

gravitational instability (GI)

GRAIL

gravimetry

gravitational potential energy

gravitational potential (Φ)

gravity sounding

Jeans equations

Love number

mathematical field

multipole expansion

physical field

Poisson's equation

RT instability

Schrödinger-Poisson equation

standard gravitational parameter (μ)

time dilation

Index