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.