# Difference between the Gravitational Potential Energy and Gravitational Potential

• Last Updated : 24 May, 2022

Potential energy is defined as the energy stored in a body due to its physical properties like the mass of the object or the position of the object. It is the force that a body could potentially develop when it is put into motion. There are different forms of potential energy, such as elastic potential energy, gravitational potential energy, electric (electromagnetic) potential energy, and nuclear potential energy. The potential energy of an object is directly proportional to the mass, height, or vertical position of the object.

### What is Gravitational Potential?

Gravitational potential at any point is defined as the work done in moving a unit mass from infinity to that point against the gravitational field. It determines the direction of motion of a body in the gravitational field of another body. Gravitational Potential is equal to the potential energy of the unit mass kept at that point.

Formula of Gravitational Potential:

The Gravitational Potential is,

V = – GM/r

where,

• G = Gravitational constant = 6.67×10-11 Nm2 /kg2
• M= mass of the larger body around which there is a gravitational field.
• r = distance between bodies.

### What is Gravitational Potential Energy?

Gravitational Potential Energy is defined as the energy stored in an object that is held in a vertical position due to the force of gravity working on it to pull it down. The amount of gravitational potential energy depends on the mass and height of an object.

Formula of Gravitational Potential Energy:

The Formula of Gravitational Potential Energy is,

U = mgh

where,

• m = mass of the object (kg)
• g = acceleration due to gravity = 9.8 m/s2
• h = height  (m)

Difference between Gravitational Potential and Gravitational Potential Energy:

### Sample Questions

Question 1: What is the gravitational potential of the sun with respect to the earth. The mass of the sun is 1.99×1030 kgs. The distance between the sun and earth is 150×106 km?

Answer:

Given that,

Mass of sun M = 1.99×1030kg.

Distance r = 150×106 km.

Gravitational Potential V = – GM/r

V = (-6.67×10-11×1.99×1030)/ (150×106)

= 8.85×108 J/kg.

Therefore, the gravitational potential of sun with respect to earth is 8.85×108 J/kg.

Question 2: What is the Gravitational Potential of an object with of mass 2×1024 kg with respect to another object. It is at a distance of 1400 km.

Answer:

Given that,

Mass of object M = 2×1024 kg.

Distance r = 1400 km.

Gravitational Potential V = – GM/r

(-6.67×10-11×2× 1024) / (1400×1000)

V = 9.52×107 J/kg.

Therefore, the gravitational potential required is 9.52×107 J/kg.

Question 3: Where is gravitational potential minimum. What is it minimum value?

Answer:

Gravitational potential is minimum at the centre of the earth, r > 0 at centre of the earth, the above friction goes undefined. The minimum value of gravitational potential is not defined.

Question 4: What is the Gravitational Potential Energy of a body at a distance of 3r from the center of the earth.

Answer:

Given that,

Distance r = 3r

We know that, gravitational potential energy at distance r is

U = -GMm/r

Gravitational Potential Energy at distance 3r is

= – GMm/3r

= U/3

Therefore, gravitational potential energy at distance 3r is U/3.

Question 5: The Gravitational Potential Energy of a body at a distance of 2r from the earth is U. Find the gravitational force at that point.

Answer:

Given that,

Gravitational Potential Energy = U

distance r = 2r

We know that, gravitational potential energy at distance r is

U = GMm/r

Formula of gravitational force F = GMm/r2

F = GMm/(2r)2

= GMm/4r2

= GMm/(4r)r

= U/4r

Therefore, the gravitational force at distance 2r is U/4r.

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