Black holes and orbital mechanics

[impwarhamer]

This is a conundrum I came up with today

so, if you fall towards an object with gravity, you often end up sling-shoting around it (unless you hit the atmosphere or lithosphere).

for example, if you got a duna flyby, you would low fly past it and then carry on.

But, once you pass the event horizon of a black hole, then not even light can escape

so what happens if you where to drop your periapsis into the event horizon of a black hole?

there is nothing there to slow you down to put your whole orbit into the event horizon, but physics sais you can't leave the event horizon.

can someone help me, because i'm confused

[qeveren]

Within the event horizon, spacetime becomes so warped that there are no longer any paths you can follow that don't eventually lead to the singularity. Another way I've heard it described (anyone with a physics background, feel free to correct me here) is that, within the event horizon, the 'down' direction - toward the singularity - swaps places with the 'time' direction. So instead of laying below you, the singularity is now a finite distance in your future, leaving you no way to avoid it.

[JumpsterG]

KSP gives us a great model of a universe without certain physical laws present:

Consider that: if a black hole existed in KSP with appropriate gravity, using KSP physics, you could lower your periapse below the event horizon and enter a stable orbit just fine. This is because KSP does not follow the "speed limit of the universe". When a KSP craft gets closer to the massive gravity well, it would pick up (ludicrous) speed exceeding the speed of light (necessary to escape the massive gravity), swing through periapse and continue merrily back to high orbit. (Survival of G's notwithstanding)

In reality, according to people way smarter than me, as an object approaches the speed of light, STRANGE STUFF HAPPENS. Most importantly for your question, the object gains less and less additional velocity as it's velocity approaches light speed (the lost energy is being spent warping space-time around the object, according to smarter people). Since the object never achieves the (ludicrous) speed necessary to escape the black hole's gravity at periapse, down it goes.

Just a layman's interpretation, but hopefully that helps!

[K^2]

Classical orbital mechanics is just an approximation. Real trajectories are not closed ellipses even when orbiting something that you can assume to be a perfect sphere. Mercury's orbit, for example, precesses due to the fact that in General Relativity the trajectories slightly deviate from eliptical ones. As you drop your periapsis closer and closer to event horizon, this gets worse. In fact, trajectories near a black hole can get really crazy with loops and everything. Close enough to the black hole, objects can actually spiral in, and if you drop bellow the event horizon, you are never coming out. All trajectories inside the black hole lead into the singularity.

[Surefoot]

within the event horizon, the 'down' direction - toward the singularity - swaps places with the 'time' direction. So instead of laying below you, the singularity is now a finite distance in your future, leaving you no way to avoid it.

This is extremely well put.. i'll try and remember that way of explaining it !

[impwarhamer]

Thanks, this helped a lot.

whilst we're on the subject of physicsy-stuff, there's this other thing that I don't get.

If speed is relative and there is a 'speed limit' to the universe (that being light-speed), how can those both be true?

For example, if you took 2 laser pointers and pointed them in opposite directions, surely you could say that 1 photon of light is travelling at 2x light-speed (impossible) and the other is not moving (also impossible).

[Camacha]

For example, if you took 2 laser pointers and pointed them in opposite directions, surely you could say that 1 photon of light is travelling at 2x light-speed (impossible) and the other is not moving (also impossible).

Oh dear, this is basic relativity. I have seen it explained very well in another topic. At the speed of light very weird things start to happen to time and space.

[FenrirWolf]

Thanks, this helped a lot.

whilst we're on the subject of physicsy-stuff, there's this other thing that I don't get.

If speed is relative and there is a 'speed limit' to the universe (that being light-speed), how can those both be true?

For example, if you took 2 laser pointers and pointed them in opposite directions, surely you could say that 1 photon of light is travelling at 2x light-speed (impossible) and the other is not moving (also impossible).

That's the trick of the whole thing. In the problem you propose, the speed of light must (and does) remain constant in each respective reference frame. But something has to give somewhere for that to work, right? That's where things like time and space dilation, increasing amounts of mass, and the like come into play. If the speed of light can't change, other stuff will instead.

[Camacha]

After quite a bit of digging I found the topic I mentioned. There it has been explained more clearly than I can do right now

[bivouac]

For example, if you took 2 laser pointers and pointed them in opposite directions, surely you could say that 1 photon of light is travelling at 2x light-speed (impossible) and the other is not moving (also impossible).

While it may appear that the difference between the two beams of light are faster than light, their photons still obey the universal speed limit. One photon is not actually traveling faster than the speed of light, it's just the appearance. The effect of what happens because of this is more or less the doppler effect. (Better known as red-shift.) That's the thing about the speed of light. It's value isn't relative to some other singular object; it's relative to EVERYTHING, not just the difference between an arbitrary reference point. (Hence the "relativity" portion of Special Relativity and General Relativity.)

This is kind of like the example of two trains passing. If you're in a train passing another train that's moving in the opposite direction at the same speed, it'll appear that the other train is moving at twice the speed. (Lets say you're both moving at 30mph.) This is because of the reference point to which you are basing this experience off of. From your reference point, the train appears to be moving at 60mph. Are you or the other train moving at 60mph? No. It's just the appearance associated with your point of reference. Relative to the system both trains are in, neither are moving at 60mph; they're each going 30mph. Why? They're both basing their speed off of a static surrounding of zero motion: The Earth with which they're riding on. With good reason, we don't include the orbital speed of the Earth on automotive means of transportation. We base it off of a static point for both trains, not just one of them. That's kind of the idea here. Perspective has to be relative to a total system, not just a singular arbitrary point.

It would be worthwhile to wrap your head around the fact that absolutely NOTHING in the universe is at a point of 0 cartesian motion. Everything is always in some kind of motion, and there's a speed limit to how fast it can go relative to static surroundings. With light in you're example, the only thing you would perceive would be a color change in the light.

[NGTOne]

I contributed to a topic a while back that examined the physics of black holes in some detail. Diverged a bit (FTL travel, all sorts of other good stuff) as it went on, but there's some decent explanations of black hole and space-time physics.

[JDobs]

There are parts along the event horizon where particles of light and gas are actually not pulled into the balck hole but thrown our in radio jets along a polar plane to the black hole. This material is ejected at relative speeds. (Look up Quasars) Also, if one of these radio jets is pointed toward Earth, as is the case in Blazars, these particles can appear to be moving faster than the speed of light (in reality they are not, it is just the result of the particles moving along our line of sight). Black holes are always super interesting because you get to deal with physics and astronomy literally colliding. Also I'm glad you realize that Black Holes don't "suck" in material and light. It always makes me flip out when people say black holes suck! It's just an immense singularity of gravity, no sucking going on at all!

[Goobest]

For the OP and others to read:

http://www.einstein-online.info/elementary/specialRT

[K^2]

Special Relativity has nothing to do with orbital mechanics near black hole.

[NGTOne]

Special Relativity has nothing to do with orbital mechanics near black hole.

Ehhhhh... not quite. Depending on how close you get TO the hole, it might (this, of course, assumes that you have sufficient energy to lower your PE to just outside the event horizon, and that your spacecraft is capable of withstanding the immense tidal forces of doing so). If you lower your PE to really close to the event horizon, you will very likely reach an appreciable fraction of c when you hit it. Now, naturally, you'll only be TRAVELLING at that appreciable fraction for a split second, but nonetheless, the principle holds. In the thread I mentioned earlier, someone suggested using a black hole as the ultimate grav-assist - sling through the black hole system near the event horizon, and you'll get a SIGNIFICANT boost to your speed (what that boost is, remains to be seen - see assumptions, above. Naturally, this is highly conjectural).

Once you're inside the event horizon, the laws of physics (for lack of better understanding) start to break down. Kepler's laws no longer apply. SR likely doesn't apply. GR... MIGHT... apply. Any path you take through 4-dimensional spacetime will inevitably lead you towards the singularity. In short: no escape, not by conventional physical means at any rate. It might be possible to escape using spacetime warping (the operating principle of an Alcubierre drive), but this is conjecture at best, and even if someone DOES manage to develop an Alcubierre propulsion system, I doubt they'd find anyone foolhardy enough to dive into a black hole to test it there (except maybe Jeb).

[K^2]

Ehhhhh... not quite. Depending on how close you get TO the hole, it might (this, of course, assumes that you have sufficient energy to lower your PE to just outside the event horizon, and that your spacecraft is capable of withstanding the immense tidal forces of doing so). If you lower your PE to really close to the event horizon, you will very likely reach an appreciable fraction of c when you hit it

And the result will be nothing like you'd expect from Special Relativity. SR deals specifically with a Minkowski metric. Near the event horizon, the metric is going to look very different. The line element in polar coordinates in SR looks like ds² = dt² - dr² - r²(dθ² + sin²θ dƲ). In the exterior of the BH, it's (1-r_s/r)dt² - 1/(1-r_s/r)dr² - r²(dθ² + sin²θ dƲ). When you are far from the event horizon, r >> r_s, the two are very similar and you can talk about effects of Special Relativity on a ship in orbit. But for r only slightly above r_s you have to discard all of your SR notions and deal with General Relativity directly.

Once you're inside the event horizon, the laws of physics (for lack of better understanding) start to break down. Kepler's laws no longer apply.

Kepler's laws break down way before you reach event horizon. In fact, there are no stable orbits bellow 3r_s. So you can be a full diameter away from event horizon, and Kepler's Laws are already completely useless.

Edited November 5, 2013 by K^2