# Gravitational Field

## Gravitational Field

The space around an object within which its force of gravitation is experienced is termed as gravitational field.

What is Gravitational field Intensity?

The gravitational field intensity is the intensity of the gravitational field of a material body at any point in its field is defined as the force experienced by a unit mass placed at that point, provided the unit mass itself does not produce any change in the field of the body.

Assume,

M = Mass of an object around which a gravitational field occurs.

m = A test mass located in this field.

The test mass is so selected that it does not influence the gravitational field. The arrow over $$\overrightarrow{E}$$ specifies it is a vector quantity, although mass is a scalar unit.

A force $$\overrightarrow{F}$$ field is the force felt by the unit mass m. The strength $$\overrightarrow{E}$$ of the field is the force felt by the unit mass.

$$\overrightarrow{E}\,=\,\frac{\overrightarrow{F}}{m}$$, $$\overrightarrow{E}$$ is a vector quantity. It is directed towards M.

$$\overrightarrow{E}\,=\,\frac{\overrightarrow{F}}{m}\,=\,\frac{m\,\times \,\overrightarrow{a}}{m}\,=\,\overrightarrow{a}$$.

If the test mass m was free to move, it world move with acceleration towards M. So, $$\overrightarrow{a}$$ = Free acceleration.

The intensity is described as the free acceleration experienced by a trial mass at that point.

Units of Gravitational Field: If M is the mass of Earth then $$\overrightarrow{E}\,=\,\frac{m\overrightarrow{g}}{m}\,=\,\overrightarrow{g}$$.

Where,

$$\overrightarrow{g}$$ = Acceleration due to gravity.

The SI system of Gravitational Field is N/ kg (or) m/sec².