# Neutron Stars and unbinding energy

• Minihoudini
In summary: OUNT OF ENERGY REQUIRED TO UNBIND TWO NEUTRON STARSIn summary, the gravitational binding energy of an object held together by gravity alone is the energy needed to pull all of its material apart to infinity. To unbind two neutron stars, one must smash them together at a velocity that would provide enough kinetic energy to overcome the gravitational forces holding them together. This energy can be approximated by equating the kinetic energy of the stars at collision to the total gravitational binding energy of the system. However, this assumption does not take into account other inter-atomic forces. The gravitational binding energy of two neutron stars is approximately 3GM^2/5r.
Minihoudini

## Homework Statement

The Gravitational binding energy of an object consisting of loose material, held together by gravity alone, is the amount of energy required to pull all of the material apart, to infinity. the gravitational binding energy Ug is roughly given by GM^2/R. how fast do you have to smash two neutron stars to get sufficient energy to unbind them?

## Homework Equations

I honestly don't know where to start. I believe my teacher is asking for the velocity and then get the energy? also what formula should I use?

## The Attempt at a Solution

im thinking we use Ug=Gm^2/R and use Ug= -GMm/r and have r= Tv/2pi

The energy needed to overcome the gravitational forces keeping the neutron star matter together would have to come from the kinetic energy of the stars before collision. When they collide, that energy would have to be converted into kinetic energy of the individual molecules. Although this is thermodynamically not possible, I think that the question assumes that this is the case.

So equate the kinetic energy of two neutron stars of mass M as they are about to collide to the total gravitational binding energy of the two stars.

The question assumes that there are no inter-atomic forces other than gravity, which is not realistic.

Incidentally, the binding energy is 3GM^2/5r. See: http://en.wikipedia.org/wiki/Gravitational_binding_energy

AM

but im not sure

I can provide a response to this content by first clarifying the concept of gravitational binding energy. This is the amount of energy required to completely separate all the particles of an object, overcoming the gravitational force that holds them together. In the case of neutron stars, which are incredibly dense and have a strong gravitational pull, the binding energy is very high.

To calculate the velocity required to unbind two neutron stars, we can use the equation for kinetic energy, KE=1/2mv^2, where m is the combined mass of the two neutron stars. This energy needs to be equal to or greater than the gravitational binding energy of the two neutron stars, which can be calculated using the formula Ug=GM^2/R, where G is the gravitational constant, M is the combined mass of the two neutron stars, and R is the distance between them.

Therefore, to unbind two neutron stars, we need to smash them together with enough velocity to produce kinetic energy equal to or greater than their gravitational binding energy. This velocity can be calculated by equating the two equations and solving for v. However, this value would depend on the mass and distance of the two neutron stars, and would likely be extremely high.

In conclusion, the velocity required to unbind two neutron stars can be calculated using the equation for kinetic energy and equating it with the gravitational binding energy equation. However, the specific value would depend on the mass and distance of the two neutron stars.

## 1. What is a neutron star?

A neutron star is a type of celestial object that forms when a massive star collapses in on itself during a supernova explosion. It is incredibly dense, with a mass greater than that of our Sun compressed into a sphere about the size of a city.

## 2. How are neutron stars formed?

Neutron stars are formed when a massive star runs out of nuclear fuel and can no longer produce the energy needed to hold its own weight. This causes the core to collapse, resulting in a supernova explosion. The remaining core then becomes a neutron star.

## 3. What is the unbinding energy of a neutron star?

The unbinding energy of a neutron star is the amount of energy that would need to be added to completely separate all the neutrons in the star. This energy is incredibly high, estimated to be around 1032 joules.

## 4. How does the unbinding energy of a neutron star affect its stability?

The high unbinding energy of a neutron star is what allows it to remain stable despite its immense gravitational pull. This energy acts as a counterbalance to the gravitational force, preventing the star from collapsing in on itself even further.

## 5. Can we observe neutron stars from Earth?

Yes, we can observe neutron stars from Earth using telescopes and other instruments. They emit radiation in various forms, including X-rays, radio waves, and visible light. However, they are often difficult to detect due to their small size and distance from Earth.

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