# Gravitational potential between two massive particles....

• R. E. Nettleton
In summary, particles are sources of gravitational fields and the gravitational potential energy between two bodies is given by U = -GMm/r. As two particles with mass but no repulsion due to charge approach each other, their gravitational potential energy increases and at r = 0, it becomes infinite. This would theoretically lead to an increase in mass according to E=mc2, but this is not possible as infinitely massive particles are implausible. In the classical model, the decrease in gravitational potential energy is compensated by an increase in kinetic energy, keeping the total energy of the system constant. However, this model cannot accurately describe the effects of gravity on particles on a quantum level.
R. E. Nettleton
If my understanding is correct, all particles are sources of gravitational fields (albeit minor ones), and the gravitational potential energy between two bodies is given by:
U = -GMm/r

So, if we have two Z bosons (or any other bosons with mass but no repulsion due to charge) which are traveling toward one another and pass through the same space, their gravitational potential energies would increase as the distance between them approaches 0 -- and at 0, the value would be infinite. In accordance with E=mc2, this would result in an increase of mass, tending to infinity.

However, infinitely massive particles seems implausible. Which part of this is incorrect?

Are you asking "Is the classical gravitational potential at r = 0 infinite?"?

The answer is yes. But it's also true that quantum mechanically you cannot reach a stationary state with r = 0.

Are you asking "Is the classical gravitational potential at r = 0 infinite?"?

The answer is yes. But it's also true that quantum mechanically you cannot reach a stationary state with r = 0.
Thanks. Does this increase in gravitational potential lead to a temporary increase in mass?

R. E. Nettleton said:
If my understanding is correct, all particles are sources of gravitational fields (albeit minor ones), and the gravitational potential energy between two bodies is given by:
U = -GMm/r

So, if we have two Z bosons (or any other bosons with mass but no repulsion due to charge) which are traveling toward one another and pass through the same space, their gravitational potential energies would increase as the distance between them approaches 0 -- and at 0, the value would be infinite. In accordance with E=mc2, this would result in an increase of mass, tending to infinity.

However, infinitely massive particles seems implausible. Which part of this is incorrect?

The GPE decreases as the particles get closer. In the classical model, this is compensated for by an increase in kinetic energy. The total energy of the system remains constant.

stoomart
R. E. Nettleton said:
Does this increase in gravitational potential lead to a temporary increase in mass?

Your mixing Newtonian and relativistic mechanics here. The only thing that will make is a mess.

## 1. What is gravitational potential?

Gravitational potential is the measure of the potential energy that a particle has due to its position in a gravitational field. It is directly related to the force of gravity between two objects.

## 2. How is gravitational potential calculated?

The gravitational potential between two massive particles can be calculated using the formula: V = -(GMm)/r, where G is the gravitational constant, M and m are the masses of the two particles, and r is the distance between them.

## 3. How does distance affect gravitational potential?

The gravitational potential between two particles is inversely proportional to the distance between them. This means that as the distance increases, the gravitational potential decreases.

## 4. Can gravitational potential be negative?

Yes, gravitational potential can be negative. This indicates that the particles are attracting each other and the potential energy is decreasing as they move closer together.

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

Gravitational potential is the potential energy per unit mass of a particle in a gravitational field, while gravitational potential energy is the total potential energy of a system of particles due to their positions in a gravitational field. In other words, gravitational potential energy is the sum of the individual gravitational potentials of each particle in the system.

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