Edit: People are confusing [this concept](https://en.m.wikipedia.org/wiki/Innermost_stable_circular_orbit) with the [Roche limit](https://en.m.wikipedia.org/wiki/Roche_limit). Wikipedia isn’t very helpful in explaining why the innermost stable circular orbit exists, but it does lay out the basic concept. It’s the innermost point at which an object can orbit another object at all, not the point at which it begins breaking up from tidal forces.
In: 5
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high school explanation: Okay, so gravity is a force that is inversely proportional to the square of distance. The closer you are the stronger the force. If the body close by is massive enough, the difference in the gravitational force at the point closest and the point furthest is so high it overcomes the force of attraction keeping the large object together.
5 yo explanation: imagine the orbits as a race track SUCH that the closer in you are the faster you have to run. You and your friend and running in nearby tracks keeping pace with each other, and you keep hopping to an inner track. At a certain point you and your friend 10 tracks down are running at such a different speed that you cannot stay together coz you are just not fast enough and you do not stay a together anymore.
> The lack of stability inside the ISCO is explained by the fact that lowering the orbit does not free enough potential energy for the orbital speed necessary: the acceleration gained is too little. This is usually shown by a graph of the orbital effective potential which is lowest at the ISCO.
I guess our basic concepts of the exchange of kinetic and potential energy break down in such intense gravitational fields. I hope someone fluent in general relativity can come give us an explanation because the wiki page doesn’t quite do it for me.
Yeah, /u/FlyingNapalm is talking Roche Limit, which is important close to a star or planet, but it’s not what you’re asking about.
I suspect the unstable inner orbit has something to do with General Relativity.
Try asking in /r/astrophysics
The issue is that within a certain distance (for non-rotating black holes: the event horizon), the geometry of space(time) is so warped that _all_ directions lead inwards. So regardless of what you do, it will bring you closer to the center, which is ultimately in every direction. In particular, no orbit (stable or not) can exist, as an orbit would lead back to its starting point.
That shows that within some distance, there is no orbit (stable or otherwise!), not even a closed loop. However, one can show that even somewhat further outside there cannot be a stable orbit. The reasons are similar to the above, but more convoluted; let me try to at least argue intuitively that even slightly outside the event horizon of a non-rotating body, there is still no stable orbit:
The closer you get towards a black hole, the more directions lead inwards, until finally all of them do at the event horizon. Slightly outside of it, the only directions not pointing inwards are (almost) directly away from the mass. Hence any orbit would need to go in that direction to even have a chance to loop. But now imagine what it looks like at the end of the first orbit: you would arrive from the backside of your initial direction, i.e. from where the event horizon is. Which clearly cannot happen, as nothing can escape it (again because all directions are inwards).
So, with GR we see that objects in elliptical orbits tend to hang around the center more than in newton’s version. They curve around at a tighter radius than would be expected causing a procession. If you get just the right eccentricity at a low enough energy, you can get an object to “process” multiple revolutions near the center before being flung back out. If your orbit was slightly more eccentric, then it’ll instead just keep curving inward and fall into the black hole.
So that’s an upper bound on the eccentricity for a stable orbit at a given energy. Any higher and the orbit will dip too low and it gets sucked in. The lower bound would be 0: a circular orbit at that energy. As you keep getting closer to the minimum stable circular orbit the maximum eccentricity keeps getting smaller, until at the minimum energy, only a circular orbit is stable. Any eccentricity at all would cause it to dip too low and get sucked in.
In theory, you could orbit lower than this if you had a control system that actively stabilized your orbit; if you start dipping too low fire the rockets to try to get out (but then you’ll be going too fast once you get back to your orbital height so you’ll need to fire the retro rockets to slow back down)
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