# NS-Capture Simulation: Part 2

The difference is that objects in elliptical orbits do not have enough energy to escape the pull of each other’s gravity. On the other hand objects that encounter each other for the first time travel in hyperbolic orbits and have to much energy to become bound. i.e. at their distance of closest approach, their velocities are greater than the escape velocity.

It is probably easier to understand the principles thinking of a rocket ship that is orbiting earth and the pilots have decided that they have a mission further out in space, and so fire their rockets and accelerate the rocket to a higher velocity.

If the velocity they accelerate to is less than the escape velocity, then the rocket will travel an elliptical path and will eventually return the place where it had ended its acceleration and be at the same exact speed. It will then continue to follow the same orbit, and continue to return to the same position with the same velocity indefinitely.

On the other hand, if the velocity they accelerate to is greater than the escape velocity, then the rocket will continue forever out into space and never return. Except, of course, if the pilots decide they want to come back, in which case they will need to fire the rockets again, to get them on a path of return.

The simulation that will now be described is one where a neutron star and a regular star are traveling on paths through space where they will have a “close encounter”, one where the neutron star comes pretty close to the regular, but does not actually collide with it.

The neutron star will be traveling on a hyperbolic orbit, and therefore if it does not lose energy during the close encounter, then it will not be bound. However, due to the physical properties of both the neutron star and the regular star, there will be energy exchanged during the encounter. There will be the energy stirred up by the turbulence that both the gravitational field and magnetic field of the neutron star will have on the atmosphere of the regular star. In addition, the neutron star will absorb internal rotational energy from the atmospheric particles from the regular star that get caught up in its magnetic and gravitational field.

If sufficient energy is lost due to these interactions, the neutron star can be slowed down such that its velocity is less than the escape velocity, and if that happens the neutron star will end up in an elliptical orbit and keep returning for additional close encounters, where energy will again be exchanged resulting in an orbit that is a smaller ellipse each time.

The following diagram shows the initial encounter of a neutron star with a regular star. Because orbital energy is lost during the encounter, the neutron star does not have enough energy to escape into space and is bound in an elliptical orbit.

As a result, when the neutron star returns to the regular star in its elliptical orbit, the neutron star will again exchange energy near the distance of closest approach, and the eccentricity of the ellipse will be reduced and the orbit will become smaller:

As the following diagram shows, the orbit will eventually be reduced to a circular orbit: