Gravitational Potential Confused Plz Help

[balboa]

It is said that total workdone in bringing the body from infinity to one point is gravitational potential. But what is that infinity. I mean is it far away from earth or any unknown point from the ground

[factor-fiction]

It's an infinite distance away.

[Teddio]

This is a hypothetical case.
In practice the gravitational fields of the other planets, Sun, stars and galaxies must be taken into account.
If only one body is considered, and all others ignored, the point at infinity is where the surface of the potential well becomes horizontal, or where the gravitational field strength becomes zero.
Since the gravitational force has infinite range, a point at infinity is used in the definition of gravitational potential.
If the Sun were the only object in the Universe the gravitational potential (the energy per unit mass) would, to all intents and purposes, be the same at 1 million light years distance and at 10 million light years distance.
Why does V have a negative sign in front of it ?

[vascop]

This is a theoretical concept. The potential of a particle of unit mass in the gravitational field of another particle of mass m is
V=-Gm/r where G is the gravitational constant and r is the distance between the particles. You can see that as r gets bigger and bigger V gets smaller and smaller and in the limit as r tends to infinity V tends to 0.
The particle of mass m could be the earth.

[jim360]

Gravitational potential -- indeed all potential energy -- can only be defined in terms of a reference point. It's convenient to take that point to be "infinity", because then the potential becomes just V = -Gm/r where R is the distance away from the body. But infinity here is just a sort of "really far away", as the model that gives V=-GM/r is a vastly simplified picture that will never be realised in practice -- as it relies on there being only two objects in the Universe.

[vascop]

V is negative for attractive forces and positive for repulsive forces.
The force is the derivative of V with respect to distance. In this case
Force=dV/dr=Gm/r^2 which is the force between the unit mass and m due to gravity.

[Teddio]

Balboa, was your question answered to any degree of satisfaction ?