## Unit – III B |

## The concept of Gravitational Intensity:

### Gravitational Field:

- Material particle, when placed in a space, modifies the space around it. This modified space is called gravitational field. When another particle is brought in this field, it experiences a force of gravitational attraction.
- The gravitational field is the space around a mass or assembly of masses over which it can exert gravitational forces on other masses.
- Theoretically speaking the gravitational field extends up to infinity, but actually, it becomes very weak to be measured beyond a certain distance.

### Gravitational Intensity:

- Gravitational intensity at a point in a gravitational field is represented in magnitude and direction by the force acting on unit mass placed at that point.
- It is a vector quantity, whose direction is same as that of the gravitational field.
- It is denoted by or
- Its S.I. unit is N kg
^{-1}or m s^{-2}. and c.g.s unit is dyne g^{-1}or cm^{-2}. - Its Dimensions are [M
^{0}L^{1}T^{2}]

### Expression for Gravitational Intensity:

- Let us consider a body of mass ‘m’ at a distance of ‘r’ from the centre of the earth. Let ‘M’ be the mass of the earth. By Newton’s law of gravitation, the force of gravitational attraction is given by

This is the expression for intensity at a point due to earth’s gravitational field. Where G is universal gravitational constant.

- If the test mass ‘m’ is free to move in a gravitational field, then it will move with acceleration towards the mass ‘M’ creating the field. Let the acceleration of the body be ‘a’. Then the force acting on the test mass is .

- Thus the gravitational intensity at a point in the gravitational field is equal to the free acceleration of the test mass placed at that point.
- If the body creating this gravitational field is earth, then the free acceleration of the test mass is equal to the acceleration due to gravity.
- Thus the gravitational field strength at a place is equal to the acceleration produced in a freely falling body at that place.

### Gravitational Intensity due to the Earth at Different Points:

- Inside the earth, the gravitational intensity is zero. On the surface, it is maximum, as the distance of the point from the centre of the earth increases, the gravitational intensity decreases. It is negligible (almost zero) at infinity.
- This distribution is the same for a solid sphere.