# Gravitational Field Intensity

## Gravitational Field Intensity

The space surrounding a material body in which gravitational force of attraction can be experienced is called its gravitational field. 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. So if a test mass $$m$$ at a point in a gravitational field experiences a force $$\overrightarrow{F}$$ then, $$\overrightarrow{I}=\frac{\overrightarrow{F}}{m}$$

1) It is a vector quantity and is always directed towards the center of gravity of body whose gravitational field is considered.

2) Units: $$N/kg$$ (or) $$m/{{\sec }^{2}}$$

3) Dimension: $$\left[ {{M}^{0}}L{{T}^{-2}} \right]$$

4) If the field is produced by a point mass $$M$$ and the test mass $$m$$ is at a distance r from it then by Newton’s law of gravitation, $$F=\frac{GMm}{{{r}^{2}}}$$, then intensity of gravitational field.

$$I=\frac{F}{m}=\frac{GMm/{{r}^{2}}}{m}$$$$\Rightarrow I=\frac{GM}{{{r}^{2}}}$$

5) As the distance (r) of test mass from the point mass (M), increases, intensity of gravitational field decreases.

$$I=\frac{GM}{{{r}^{2}}}$$ $$\therefore \,\,\,I\,\,\propto \,\,\frac{1}{{{r}^{2}}}$$

6) Intensity of gravitational filed,$$I=0$$  when $$r=\infty$$

7) Intensity at a given point (P) due to the combined effect of different point masses can be calculated by vector sum of different intensities. $${{\overrightarrow{I}}_{net}}=\overrightarrow{{{I}_{1}}}+\overrightarrow{{{I}_{2}}}+\overrightarrow{{{I}_{3}}}+…….$$

8) Gravitational field line is a line, straight or curved such that a unit mass placed in the field of another mass would always move along this line. Field lines for an isolated mass m are radially inwards.