# Gravitational Field

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

### Gravitational Field Strength or Intensity:

The gravitational field intensity at a point is described as the force experienced by a unit mass located at that point.

### Intensity of the field felt by a test mass:

Let M be the mass of an object around which a gravitational field occurs. Let m be 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 forceÂ $\overrightarrow{F}$ field is the force felt by the unit mass m. The strengthÂ $\overrightarrow{E}$ of the field is the force felt by the unit mass.

$\Rightarrow \overrightarrow{E} = \frac {\overrightarrow{F}}{m}$

$\overrightarrow{E}$ is a ventor quantity. It is directed towards M.

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

If the test mass m were free to move, it would move with acceleration towards M. Therefore, $\overrightarrow{a}$ is the free acceleration.

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

### Units OfÂ Gravitational field: The units in the

• The C.G.S. system is dyne gm-1Â or cms-2
• SI system is Nkg-1Â or ms-2

If M is the mass of the Earth, then $\vec{E}=\frac{m\vec{g}}{m}=\vec{g}$ , acceleration due to gravity.

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#### Practise This Question

In order to cover a certain distance in a shorter time span, the object should have greater _________.