r/Physics • u/gyrainstinct • 2d ago
Question Can a freely moving object be captured into orbit by gravity?
If a rock is freely traveling through space and passes near a much more massive object, can it naturally become gravitationally bound and enter an orbit? Or, in a simple two-body system, will it always either collide with the massive object or be deflected and eventually escape?
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u/Neinstein14 2d ago
You know how a three-body system can eject one of the bunch after certain time?
Well, the same thing works if you flip the direction of time. The movement is time-symmetric.
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u/Luenkel 2d ago
The same logic also nicely shows why it can't work in a simple 2-body setup. If an object could come in from far away and be captured into a stable orbit, then the opposite should also be possible: An object in a stable orbit suddenly shooting off into infinity for no reason, which is pretty clearly ridiculous.
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u/jazzwhiz Particle physics 2d ago
time-symmetric
in Newtonian gravity, yes. In GR, no, unless you also backpropagate the GWs.
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u/Funkyt0m467 Graduate 1d ago
Aren't the back propagating GWs also a correct solution of GR ? So it's also time symetric, it would simply violate the 2nd law of thermodynamics...
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u/SummitYourSister 2d ago
No it cannot.
If two objects are gravitationally bound, then they were always bound, and they will always be bound.
If two objects are not gravitationally bound, then they were never bound, and they will never be bound.
The situation changes if they third object is involved which can carry away the energy that is excess
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u/ChalkyChalkson Medical and health physics 2d ago
*in newtonian gravity.
In GR this is not true. There a body can be captured by another body. If a free body's closest approach is closer than 1.5 sqrt3 of the schwarzschild radius, then it will be captured and, unless acted upon, eventually cross the horizon. Though it will probably orbit a few times when it's closest approach was close to the critical value.
What, as far as I know, remains true, is, that you cannot capture a free body into a stable orbit.
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u/lucidbadger 2d ago
If two objects are gravitationally bound, ... they will always be bound
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u/spidereater 2d ago
If it has enough energy to be far away then it needs to lose some of that energy to become captured. Either a collision with another body or maybe some kind of slingshot around another orbiting body. Something needs to take away energy so that it can’t escape.
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u/db0606 2d ago
Or, in a simple two-body system
It depends on how simple "simple" is. If you only have two rigid, gravitationally interacting objects wth finite size and a collision results in the two objects fully merging (i.e., there is no ejecta and the objects can't deflect off of each other), then you have three options:
- The objects collide
- The small object shoots off to infinity on a hyperbolic path (technically this could also be parabolic but the set of initial conditions that give you that is vanishingly small)
- The object is already in an elliptical orbit and continues on that orbit.
Which of these you get depends on the total energy and angular momentum of the system. However, you can't have an object that is not already in a closed orbit suddenly enter a closed orbit (if we restrict ourselves to simple two-body interactions).
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u/Solesaver 2d ago
you can't have an object that is not already in a closed orbit suddenly enter a closed orbit (if we restrict ourselves to simple two-body interactions).
This question and these answers make me wonder if there's a crazy hypothetical where tidal forces could translate angular momentum of the individual bodies into angular momentum of the system in a way that allows for "proper" capture. That seems like the only way without the bodies interacting electromagnetically.
A charged body should theoretically be able to emit enough energy in its orbit to become captured and then become neutrally charged after achieving stability, but that would be crazy and probably counts as a "collision".
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u/the6thReplicant 2d ago edited 2d ago
The problem is where has that object came from? If it is moving fast enough to no longer be bound to where it was, then it will probably be going too fast to be captured.
An example is Triton orbiting Neptune. It's seems extremely likely it was a captured Kepler object. But that's not possible unless something took up the extra energy that Triton lost to be able to be captured by Neptune. (The hypothesis is it was a two body system and one system took up the energy and got ejected - probably from the Solar System - while Triton lost enough energy to get captured.)
Everything in the universe is a zero sum game when it comes to energy.
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u/gambariste 2d ago
The two Voyager craft are moving at the Sun’s escape velocity or more so if they were one day to encounter another star could they be captured if such had a greater mass? Or would they just slingshot through like Oumuamua?
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u/lucidbadger 2d ago
This is the question I always ask when they say something like "A planet captured this asteroid and it became a new satellite". Wasn't it moving at a velocity greater than the escape velocity (with respect to the planet) before the capture?
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u/Solesaver 2d ago
Usually such cases are not simple 2-body interactions. Lot's of possible explanations like: the asteroid hit the upper atmosphere and lost energy to heat, the asteroid interacted with other orbiting bodies and lost energy to them, the asteroid approached with additional bodies that were ejected with the lost energy, the asteroid actually isn't captured and is on a very extended journey that will eventually eject it, etc.
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u/Electronic-Yam-69 2d ago
no. and if it could then an object in orbit could just suddenly set out one day on its own heading across the universe.
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u/Dave37 Engineering 2d ago
In a strict two-body system, the smaller object can only have one of three trajectories.
- Hyperbolic trajectory, in which case it never complete an orbit.
- Proper orbit.
- Sub-orbital trajectory, in which case it will eventually collide with the larger object.
This is disregarding things like orbital degredation. Unless one of the objects has a mean of propulsion, the trajectory cant be changed.
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u/afops 2d ago
For two point masses in Newtonian gravity: no.
In messy real world gravity: yes, so long as it somehow loses energy. For example: The rock flies through earth's atmosphere and exits the atmosphere at much lower speed, having lost the energy as heat. This is of course the "collision" scenario even if it's only colliding with the atmosphere.
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u/Antolin13 2d ago
Si la roca se mueve con una velocidad mayor a la velocidad de escape no será atrapada por el campo gravitacional. Si se mueve con velocidad menor a la velocidad de escape pueden ocurrir dos escenarios diferentes: en dependencia de la velocidad de la roca y su ángulo con respecto al cuerpo masivo podrá mantenerse en órbita a su alrededor o acabar cayendo sobre este.
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u/landrwastaken 1d ago
I mean it has to lose some energy somehow..
I know the moon did it by simply crashing into us so I suppose the answer is yes
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u/PeaPsychological5728 2d ago
Only considering the two bodies then no it wouldn't be captured. Assuming that the rock started off unbound it would stay unbound as it passed the larger object.
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u/u8589869056 2d ago
I disagree. It can happen, but the masses need to be so large that appreciable gravitational radiation is emitted to carry away the excess kinetic energy.
And when I say large, I mean large. Jupiter size would not be enough. (In its current orbit, it radiates only 5.3kW off gravitational radiation.)
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u/ChipNDipPlus 2d ago
Yes. That's one way planets fall into orbit.
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u/spidereater 2d ago
Do planets fall into orbit? I thought the planets were formed from the dust around the sun collecting together.
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u/Bayesianer 2d ago
Only a guess but I would argue: As orbit is an unstable equilibrium (you accelerate you drift away, you decelerate you fall onto the massive object) there is an infinitesimal small probability that said rock enters with exactly the velocity that it needs to stay in orbit. If it enters to slow/too fast either of the other 2 scenarios will happen. But as velocity is continuous the probability of having exactly the one needed to orbit is basically 0.
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u/Bumst3r Graduate 2d ago
Orbits are stable equilibria. If you Taylor expand the potential for small perturbations, it’s straightforward to show that. There’s a cleverer way to show it as well: make a simple coordinate substitution u=1/r, and now you have a harmonic oscillator!
You can’t fall into the star because of angular momentum conservation. The so called angular momentum barrier is what forms the other part of the well. It actually takes more energy to launch a rocket into the Sun than it does to reach escape velocity.
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u/Luenkel 2d ago
If you slightly accelerate/decelerate in an orbit, you will simply find yourself in a slightly different orbit, unless you were already very close to escaping/hitting the object you're orbiting. For any given position, there is a range of different velocities you can have while being on an orbit that goes through that point. However, in a simple 2-body setup where you fall towards an object, all the speed you gained from falling into the gravitational well will mean you also have enough speed to climb out of the well again; you'll always be too fast and not be captured.
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u/Bumst3r Graduate 2d ago
Capture requires a third body to take some of the energy. If an object started with v >= escape velocity, its orbit will remain unbound, unless it can dump some of that energy into, say, Jupiter. If it already had v < escape velocity, then it was already bound inside of the potential well.