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Watsisname
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Solar System dynamics discussion thread

17 Jul 2018 07:21

JackDole is right. In order for a Lagrange point to exist within the horizon there would need to be a mass in a circular orbit within the horizon. But for a mass, no circular orbits are allowed within 3 times the horizon radius.

Black holes are just very strong attractors... stronger than Newtonian gravity would suggest. The effective potential plummmets downward very fast near the horizon, and even more so if a particle has any sideways velocity. Black holes are like quicksand. Once you're caught too close, then any amount of struggling makes you sink faster. Try to orbit, and it pulls you in more!
 
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midtskogen
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Solar System dynamics discussion thread

17 Jul 2018 09:15

I suspected that (but I didn't know that there is a 3 times radius limit, which seems less obvious).  Then, I also suspect that it may also be difficult to form Lagrange points outside the horizon which not even light can reach, even given the freedom to pick whatever configuration.  But intuition breaks down here, so I'll stop guessing.
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Watsisname
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Solar System dynamics discussion thread

17 Jul 2018 17:57

Yeah, I don't think it is obvious at all. You'd think it should be possible to orbit as close as the event horizon. Also odd is that light can orbit at exactly 1.5 horizon radii, vs. the 3 radii for massive particles. I've yet to find an intuitive explanation for either of these (besides "the math says so"). And then there's the "you fall to the center faster if you fight it" property that's just totally weird.

Perhaps the most intuitive thing about black holes is that they are not intuitive...
 
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JackDole
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Solar System dynamics discussion thread

17 Jul 2018 23:02

Watsisname wrote:
Source of the post But for a mass, no circular orbits are allowed within 3 times the horizon radius.

Too bad. This of course means that even the L1 point can not be within the Schwarzschild radius.
 
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midtskogen
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Solar System dynamics discussion thread

18 Jul 2018 03:12

Can we have a Lagrange point in "orbit" closer than 3 times the horizon radius, and a mass stuck at that point?
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Watsisname
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Solar System dynamics discussion thread

18 Jul 2018 20:56

I think that could work, at least for a short while. It would be the L1 point which is unstable, and the other issue is that black holes that close together will spiral together very quickly by emitting gravitational waves. I'm not sure how close we can have an equal mass pair in a circular orbit before they plunge together.

Also, at some point when they get too close, the event horizons "reach" for each other and connect in the middle Where the L1 point would be. So while a mass could perhaps be put there for a little while, it sounds like a really bad place to be! :D
 
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Solar System dynamics discussion thread

18 Jul 2018 22:40

Concerning the Solar System dynamics: I tried to create a geocentric system. Unfortunately, there are no epicycle. But already the Galilean moons. viewtopic.php?f=3&t=71&p=21657#p21657
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Solar System dynamics discussion thread

21 Jul 2018 02:01

I saw this and thought it would be a very relevant video for this thread.


 
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An'shur
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Solar System dynamics discussion thread

22 Jul 2018 09:51

midtskogen wrote:
A question: If the bodies are really massive (merged?) black holes, could the slopes down from L4 and L5 be so steep so these points become a kind of massless "white" hole?  

Watsisname wrote:
midtskogen, that is an amazing question.  Off hand, my gut feeling is that it cannot, but I do not know for sure!  I will like to investigate this and try to get back to you when I have the opportunity. :)

Intuitively, I do not think so either. But what in the universe is happening from 0:38 to 0:50? These spikes at the 0:50 mark look like nothing I have ever seen before and they are more or less at the L4 and L5 points.

 
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midtskogen
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Solar System dynamics discussion thread

29 Jul 2018 13:56

vlad01 wrote:
I saw this and thought it would be a very relevant video for this thread.

Wow.  Very clever visualisation.
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Watsisname
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Solar System dynamics discussion thread

01 Aug 2018 04:28

3Blue1Brown is the most gifted explainer and visual animator I've ever seen.  Every video of his is a real treat. :)

An'shur wrote:
Source of the post Intuitively, I do not think so either. But what in the universe is happening from 0:38 to 0:50? These spikes at the 0:50 mark look like nothing I have ever seen before and they are more or less at the L4 and L5 points.

Good question.  The video was originally produced by the SXS collaboration (another very nice youtube channel), and according to their description the heights represent the values of the space-time curvature.  I think this specifically refers (or is at least closely related) to the strain in the space-time, which is how much space gets stretched and squeezed along a particular direction, and relevant to how strong the signal will be in a gravitational wave detector.  The colors represent the slowing of time, and the arrows represent the direction of the gravitational force at each point in the plane.

So as the black holes approach each other there is a very strong space-time distortion nearby. With those big red spikes at 0:50, this means an object placed at those locations would be severely distorted by the gravitational wave (and also quickly fall into the black hole.)

I don't think those locations would be like Lagrange points -- they are too close and too late in the merger to be equilibrium points.

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