# difference between gravitational potential and gravitational potential energy

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## What is the difference between gravitational potential energy and gravitation potential ? Derive an expression for gravitational potential energy.

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## What is the difference between gravitational potential energy and gravitation potential ? Derive an expression for gravitational potential energy.

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Updated on : 2022-09-05

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## What is the difference between gravitational potential and gravitational potential energy?

Answer (1 of 27): As you stated, potential is that which possesses the ability to do work. Its unit is the Joule (pronounced “djool”) per kilogram. In the strictest sense however, potential is a mathematical description of a directional phenomena like force in electrostatics or gravity as you hav...

What is the difference between gravitational potential and gravitational potential energy?

Sort Sarang Nath

M.S. Computational Mechanics. Author has 674 answers and 2M answer views2y

The potential energy can be defined as the amount of work that was done to raise the body from the ground to the current height in which the body is currently present in. In a different sense, this is the amount of work that the body will do before it goes back to the ground level (the position of maximum stability) if displaced from the current height. Thus, it is possible to relate the potential energy with work.

Gravitational potential at a point is the amount of work done in moving a unit mass from that point to infinity (where the effect of gravitational field cannot be felt) against the e

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Wong Ian

First Year Psychology Degree, HELP University6y

The gravitational potential is a scalar field that affects all objects with mass. The gravitational potential energy is the potential energy of a specific object in this field, so in other words, it depends on mass. It's like potential is always there, and the energy is a single number attached to a certain object which represents how much the objects experiences the field.

E.g. A bowling ball and ping pong ball are at rest on pedestals 1m of the floor surface. They both have the same gravitational potential, but because the bowling ball has a larger mass, it has more gravitational potential e

Jorge Castro

Licentiate in Physics, University of PortoAuthor has 106 answers and 140.6K answer views5y

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What is the difference between gravitational potential and gravitational potential energy?

Originally Answered: What is the differences between gravitional potential and gravitional potential energy?

An Hamiltonian is often given by the sum of a kinetic energy and a potential function (of coordinates). So, they are both energies. Thus, the gravitational potential represents a gravitational energy. In particular, the difference in gravitational potential between any two points in space, is the work (energy) required to move a unit test mass between said points against the gravitational force. And that energy does not depend on the path taken between such points, which is why it is possible do describe gravitational energy by such a potential function of position coordinates.

Đŕiśhti Đsəñà 6y

GPE is amount of work done (obtained) on bringing a mass from infinity to a pt in gravitational field . GP is amount of work one on bringing a UNiT mass from infinity to a pt in gravitational field .

So, in GPE m isn't equal to 1 & and in GP it is equal to 1.

Gravitation potential is always due to a point mass.

Both of GPE & GP are negative because work is not done but is obtained.

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## Difference between the Gravitational Potential Energy and Gravitational Potential

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## Difference between the Gravitational Potential Energy and Gravitational Potential

Last Updated : 24 May, 2022

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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:**

**Gravitational Potential**

**Gravitational Potential Energy**

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. 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.

The Formula for gravitational potential is, V = -GM/r. The Formula for gravitational potential energy is, U = mgh.

The unit of gravitational potential is Joules/kg. The unit of gravitational potential energy is Joules.

It is represented by V. It is represented by U.

It is always negative. It is always positive.

It is maximum at infinity. It is zero at infinity.

It is minimum at the center of the earth. It is minimum at the surface of the object.

The dimensional formula of gravitational potential is, [M0L2T-2]. The dimensional formula of gravitational potential energy is, [M1L2T-2]

**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.**

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