Gravitational field

Gravitational Field

               The gravitational field is the space around a body within which any other mass experience a gravitational force of attraction.

Intensity of gravitational field at a point:

                It is defined as the gravitational force acting on a unit point mass, placed at a given point, in the gravitational field of the body.

                 Consider a body of mass M which sets up the gravitational field in the space surroundings it.→

                  Now, a small test mass ‘m' is placed at a point P at a distance ‘r' from the mass M. The test mass ‘m' experience an attractive gravitational force F.

                 Then the intensity of gravitational field E at point P is given by:  E=F/m

                 The intensity of gravitational field is a vector quantity.

      The direction of E is same as that of F.

                 The magnitude of gravitational field strength at point P is :

                 .•. E= F/m = - GM/r²      .....(1)    

                 since, F= - G Mm/ r²

                 Negative sign shows that the field is directed towards the mass M , In vector form, the intensity of gravitational field can be given as :

                 E= GM/r² r^  ....... (2) 

                 Where, r^= unit vector along the line of force.

                  It's SI unit is N/kg and 

dimensions are [M°L¹T-²].