# How can a particle coming from infinity get on bound orbit around BH?

1. Jul 15, 2013

### Eudaimon

Studying the movement of a particle on bound orbits around a black hole I found a fact that seemed a little strange for me -- that on these orbits particle's total energy on infinity must be less than unit (E<1). As far as I understrand, it is not so horrible, since here we deal with an unobservable quantity, because a particle never reaches infinity (namely because its orbit is bound). But in this case I have a question: what if a particle moves from infinity (where naturally its total energy cannot be less than 1) towards a black hole. Does the fact that its E≥1 on infinity implies that it can never move on bound orbits? How then is it possible to get on a bound orbit at all?

2. Jul 15, 2013

### The_Duck

Black holes are a distraction here. Consider a simpler case such as the Sun. An object coming in from infinity will never fall into orbit around the Sun: it will always go back out to infinity (unless it crashes into the Sun). If you want to get this object into orbit around the Sun, you need to apply some force to it when it is close to the Sun. For example, you could decelerate it with rocket boosters or hit it with another object to slow it down so that it becomes bound to the Sun.

3. Jul 15, 2013

### Eudaimon

I see. Thank you -- I thought nearly the same: so we need some extra force to put it on a bound orbit.

4. Jul 15, 2013

### pervect

Staff Emeritus
A Newtonian style gravitational slingshot can also capture an object falling from infinity. Energy is conserved, but is transfered to one orbiting body from the other.

5. Jul 15, 2013

### PAllen

With only two objects, and no collision, is this really possible? In the COM frame, both objects have escape velocity at all times, so how is capture possible [ other than collision] ?

Last edited: Jul 15, 2013
6. Jul 16, 2013

### pervect

Staff Emeritus
I didnt write that clearly enough - I was refering to a three body capture.

7. Jul 16, 2013

### hilbert2

Relativistic orbital dynamics don't always work the same way that nonrelativistic dynamics do. In classical newtonian mechanics, a system of two point masses interacting gravitationally will never collide, if the masses have any nonzero initial angular momentum relative to each other. When special relativity is taken into account, the point masses can collide even if one of them has a nonzero initial velocity component orthogonal to the separation vector of the masses. (can someone find a source that verifies my claim?)

EDIT: here's the source: http://arxiv.org/pdf/physics/0405090.pdf

Last edited: Jul 16, 2013
8. Jul 16, 2013

### Staff: Mentor

They ignore effects of general relativity. I doubt that this gives relevant results - a relativistic escape velocity usually means that (general) relativistic effects are important.

Rotating black holes, on the other hand, have very non-trivial trajectories for infalling particles.

9. Jul 16, 2013

### hilbert2

I think if one takes into account GR effects, the falling point mass loses energy to gravitational radiation and spirals even faster to the force center...

10. Jul 16, 2013

### PAllen

I believe this is true (in GR, two bodies falling from infinity can lose enough energy due to gravitational radiation that they can capture, and eventually spiral together) . My comment earlier reflected, as it stated, pure Newtonian physics. I don't believe it is meaningful to discuss SR plus Newtonian gravity. It is not a consistent theory because of conflict between action at a distance and SR causal structure. The only consistent SR gravity theory I know of was Nordstrom's theory, which, however, is just wrong as a description of reality.

11. Jul 16, 2013

### Bill_K

This does not depend on energy loss due to gravitational radiation. Unbound spiral orbits exist for a test mass in the Schwarzschild field.

12. Jul 16, 2013

### pervect

Staff Emeritus
I'm not quite sure what's being asked. Certainly orbits exist for E>1 that impact - some of them spiral orbits, for instance a photon (or anything else for that matter) that gets closer than the photon sphere (R=3M) might spiral (or it might impact without having time to make a full spiral). But the OP seems to exclude them by his definition of bound orbits.

There are a variety of ways things can loose energy to move into what's being defined as a bound orbit (E<1) from an unbound one (E>=1), but they all involve energy loss by the current working definition of "bound orbit".

Three-body interactions are one way to loose energy, collisions (whether with other solid bodies or with gasses) are another, I would suspect there are more but those are at least the first two I think of.

Last edited: Jul 17, 2013