# Forces on objects orbiting a black hole?

Firstly, please excuse my elementary knowledge and lack of eloquence when writing about astrophysics. I am a dentist, who occasionally thinks about the how the universe works. I'm both fascinated and frustrated with all of the questions that arise after learning more.

I was just watching a video showing the elliptical orbits of stars near the super massive black hole at our galactic center. Of course, as they turn around the black hole, they are then flung back out with tremendous speed. An animation of a large gas cloud approaching the black hole showed how the gas would swirl about after some entered the hole and some was flung out into space, thus illustrating how the massive change in acceleration effects matter with less mass than the entirety of a star.

I was wondering how this would translate to forces as we know them on Earth. For instance, what would happen (hypothetically) to a human standing on the surface of a star as it is violently tossed in its orbit around the black hole. Of course, I understand that the mass and gravity of the stars are many times greater than the Earth's, the stars do not spin like the Earth and it is not possible to stand on the surface of a star, etc, etc. (Please grant me a TON of assumptions here.) I still wondered, however, what would the forces "feel like" to an object of my mass (80kg) that was sitting on the surface of the star either on the near or far side relative to the black hole throughout the orbit? What would happen if Earth was subjected to these types of forces and changes in acceleration? Does inertia of a star orbiting like this even work like it does on Earth? Does the black hole "suck in" matter of lower mass on a star even if it's outside the event horizon, or would the combined gravity of the star and the "g-force" of the quick turn alone smash everything down on one side and toss everything outward on the other side? What happens with centrifugal forces with these sudden changes in rotation?

I know that is a lot to ask and to explain, but it would be greatly appreciated if anyone can shed some light.

• Fun fact: There's a novel exploring the orbital dynamics around a black hole. Sep 22, 2014 at 14:20
• More than one, in fact. Sep 22, 2014 at 14:24

There's nothing really special about large orbits. Our Sun orbits the black hole in the Milky Way. It's sufficiently far off that there's no unusual behavior.

And even for starts that are a lot closer, the speed with which they're flung away is just the same as the speed with which they initially fell towards the black hole. Conservation of energy still holds.

Things get interesting when you get close enough to the black hole. Here the gradient of gravity becomes relevant. If you get just a bit closer, the strength of the gravity increases quite rapidly. This means that the closest parts of a star are ripped of by the black hole. This is the process creating those swirls. It's sometimes called Spaghettification

The basic idea is tidal forces. Given a body orbiting any mass, including a black hole, the nearer part will be attracted more strongly than the farther part. In Newtonian gravity (close enough for outside very large black holes), this amounts to a differential acceleration of $\frac {GMd}{r^3}$, where $M$ is the mass of the primary, $d$ is the distance across the orbiting object, and $r$ is the distance from the center. If the orbiting body is strong enough to resist this force you can (pretty much) consider it a mass point and calculate the orbit. If it is not strong enough, it will be pulled apart. Since the event horizon radius of a black hole scales with $M$, for a very large black hole the tides are not so strong.

The orbits in the video you saw, for all intents and purposes, are about the same as the orbits for objects like Halley's comet -- thank's to Kepler's second law, when the object is close in, then it moves much more quickly than when it's far out.

So, why does this show a black hole?

Well, the reason is the fact that the speed of the objects depends on their mass, and the mass of the thing that they're orbiting. With several objects moving at known speed, we can deduce the mass of the central object. Furthermore, we can constrain the size of the central object, because it must lie inside the orbit of the innermost object.

In particular, if object has a radius that is smaller than $$\frac{c^{2}M}{G}$$, then then only known thing it can be is a black hole. For the Sgr$${}^{*}$$A object, the mass of the central object is of the order of a million solar masses, and that inner, fast star is of a radius less than that. Therefore, we conclude that the object at the middle of the milky way is a black hole.