Gravitational Potential

The Gravitational Potential (V) refers to the work done per unit mass at a point in a gravitational field. Some external application force is responsible for performing this work. This work would be required to get a huge item to that particular point from a zero potential’s defined position. Usually, such a position is said to be infinity.  The symbol V is used for representing gravitational potential. Keep on reading to understand the concept of Gravitational Potential (V) in more detail. Here, we shall look at the gravitational potential (V) meaning and importance.

Gravitational Potential (V) Meaning

Gravitational Potential (V) can be described as the gravitational potential energy per unit mass that is relative to a zero potential energy’s defined position.

Suppose the gravitational potential field is because of a finite-sized item. In such a case, its definition must take place as the zero potential at a distance from this particular item. Most noteworthy, this distance is infinite. This gravitational potential shall turn out to be negative everywhere due to the fact that the gravity force is characterised by attractiveness.

An important fact to note here is that gravitational potential is quite similar to a potential that is electrostatic. In both the above-mentioned potentials, the forces that are underlying, rely on the isolation, r, of interacting items as 1/r 2. Furthermore, in both these potentials, the potential change can be described through the work performed in altering separation between the interactive items.

 The difference can be found in the force’s characteristics. The charges may either turn out to be positive or negative. Due to this, the electrostatic interaction would correspondingly have attraction or repulsion.  Most noteworthy, the gravity force always has attractiveness.

Gravitational Potential (V) Mathematical Expression

The SI unit of Gravitational Potential (V) can be expressed as:

J kg-1

Its expression in SI base units:

m2 s-2

When an object is raised via Δ h at the planet’s surface, it causes a variation in gravitational potential. The Δ h represents the height. This can be expressed as:

Δ V = gΔ h

Here, g represents the planet’s surface gravitational field. Moreover, Δ h turns out to be significantly lesser compared to the Earth’s radius.

In a more general sense, its expression is as follows:

Δ V = GM/R – GM/(R+Δ h)

This way, we get GMΔ h/R(R+Δ h)

Here, M represents the planet’s mass, while R represents its radius. As far as G is concerned, it represents the gravitational constant that is universal.

Finally, at a distance r from a mass M, the gravitational potential is as: V = -GM/r

The calculation of gravitational potential energy at height h, of an item with mass m can take place as:

 Ep =  mgh

However, this would only work when there is no change in the gravitational field strength. As such, this would not work for radial fields. So, in the case of radial fields, the expression of gravitational field strength is as:

g = -GM/r2

Using the above, the calculation of the gravitational potential energy in a radial field is as:

Ep = mGM/r

The calculation of the gravitational potential energy, in light of the above equation, is as:

Ep = mV

Gravitational Potential (V) Importance

The conversion of gravitational potential energy may take place to other forms of energy, for example, kinetic energy. In case the mass is released, work will be performed by gravitational force that would be equal to mgh on it. This way, its kinetic energy would be increased by that same amount. This is an example of Gravitational Potential (V)  and it can be understood by the work-energy theorem.

It would be more helpful to focus on just the conversion of PEg to KE without focusing on the intermediate step of work. This shortcut is useful in solving problems by making use of energy instead of explicitly using forces.

For a more precise understanding, please see the following:

 The change gravitational potential energy ΔPEg can be defined to be ΔPEg = mgh

Here, the denotation of the change in height takes place by h instead of the usual Δh.

Using Gravitational Potential (V) energy can help in the simplification of calculations. The application of the equation ΔPEg = mgh takes place for any path that experiences a modification in the height of h. As such, it is not only when the lifting of the mass takes place straight up.

This way, the calculation of mgh becomes much more practical with a simple multiplication compared to a complex path calculation of work done. As such, the idea of gravitational potential energy makes calculations easier as it can be applied in a broad manner.

Conclusion

The Gravitational Potential (V) refers to the work done per unit mass at a gravitational field’s point. Some external application force is responsible for performing this work of bringing a huge item to that particular point from a zero potential’s defined position. This position, usually, is said to be infinity. Also, J kg-1 is the SI unit of Gravitational Potential (V).