In the region of the Gravitational Field at
any point in space, a characteristic property is defined, called the Gravitational
Potential, which is defined as the gravitational interaction energy of a unit
mass, placed at that point, or alternatively defined as the work done in
bringing a unit mass from infinity to that point, against the gravitational
forces acting on it.
If at any point in space, gravitational
potential is V, then the gravitational interaction energy of a mass m placed at
this point is directly given as mV.
As gravitational forces are attractive in
nature, the gravitational potential is always a negative value. Using
gravitational potential, we can also find the work done in displacing a mass
from one point to another, by or against gravitational forces by using the
relation
Work
= mass x gravitational potential difference
To understand gravitational potential from
basics see the video below –
At any point in space, the force
experienced by a unit mass gives the gravitational field strength at that point
in space. If we wish to calculate the gravitational potential at any point, we
need to calculate the work done in bringing the unit mass from infinity to this
point, so it can be calculated by integrating the elemental work done in
displacing a unit mass by an elemental distance dx, within limits from infinity
to that given point. Using this analysis we can find the relation between g and
V in space, which will have a similar relation that exists between force and
potential energy in a conservative field. To understand the same see the video
below –
