View Full Version : Question about multibody systems

2005-Apr-12, 06:46 PM
OK: Headlines may seem cryptic, but I cannot at the moment find some better.
So this is what the question is about: Imagine a "multibody" system (Perhaps an ugly word. Is there any better for not only star-planet systems, but planet-moons too or asteroid-asteroid double, triple, anything?).Then add or remove one object, with eventually relatively small mass compared to total mass of system. I imagine that under "unfortunate cirkumstances" this object could destroy or vastly change the "bigger one". And that there might be some ways for example take solar system would be most vulnerable to a small object. Some situations were a small "push" in one or other direction could have big consequenses. (No, not by "mystic forces", but gravity). On earth we know about "catastrophes" - avalanches for example. So the question is: Could it work? (Say: byfly of a planetoid, significantly smaller than our biggest planets. Could it change all planets orbits much?)

2005-Apr-12, 08:15 PM
Originally posted by jhwegener@Apr 12 2005, 06:46 PM
byfly of a planetoid, significantly smaller than our biggest planets. Could it change all planets orbits much?
How are you imagining that the little planetoid would make a big difference in a planet's orbit.

Let's imagine for a moment that there is a planet the size of the Earth, and a planetoid the size of Ceres (9.5x10^23 grams), and that the Earth sized planet (6x10^27 grams) has a cirular orbit about as far from any other planet as Earth is from Mars and Venus. Furhter imagine that the Ceres-like object is coming in on a parabolic trajectory and adds all of its forward momentum to the Earth like object in an inelastic collision, so the new body has all the momentum and mass of both objects. This is the most extreme case of momentum transfer that these two bodies could have. So the question is how much would that change the orbit of the Earth-like object? The answer is that the Earth-like-object's orbit would become slightly more or less elliptical depending on when the planetoid hit it, because it would have .00015 more momentum after the collision. Such a collision (with by far the largest asteroid) would destroy just about all life on Earth, but it wouldn't alter our orbit to a degree that you could easily observe.

2005-Apr-12, 11:31 PM
Of course Anton is correct. A large body's orbit can't be changed much by a small body. And large bodies that have been orbiting a star for long periods of time tend to find their way into stable orbits - far enough from the orbit of any large neighbours that there is little gravitational interaction between them. All of the sun's planets are in stable orbits that will not change suddenly - they may evolve a bit over billions of years, but nothing sudden or major.

On the other hand (and much more interestingly) small bodies can have their orbits changed dramatically by close encounters with big objects. And there are lots more small objects than there are big ones, so there are lots of possibilities. And some of them are still in unstable orbits - ones that are chaotic, and will eventually have close encounters with a planet. The exact circumstances of the encounter are critical to the post encounter orbit - a very small change in the incoming orbit can cause a hude difference in the outbound orbit.

So as a direct answer to the question in the title, Yes, a small change can make a big difference.

2005-Apr-13, 05:10 AM
As Anton says, a small body could'nt change system stability to a degree that you could easily observe, but if it change was in correct direction, in correct time and many other correct condition maybe it could affect the whole system significantly in some billion years after.
So becareful if you throw your socks into space maybe you would lead extincion to man kind

2005-Apr-13, 06:57 AM
Well. What I imagined was as headline said, though perhaps not very clear, a situation where a body from outside, for example, came close to our solar system.
This body being smaller compared to the biggest planet, and to the whole system of course. Imagine it come close to the outer planets, and being of comparable size to let us take Neptune or Uranus. Even if it did not collide, one make think their orbits would change dramatically. And that under some cirkumstances a "chain-reaction" would be, where both the big ones (Saturn, Jupiter) and the inner, terrestrial planets would change their paths. Or of course, the same way but smaller scale for moons around planets, or for "multiple asteroids" or comets.
I guess, if there is a vast multitude of objects between stars (Kuiper, Oort clouds, other?), and if some of them are larger, more planetsize, but still unobserved (Are they observable at all with current instruments , exept in very favourable cirkumstances? Say Jupiter size or smaller, middle way to next star: about 2 ly), such a scenario with intruders changing seemingly "stable" systems become less improbable.

2005-Apr-13, 09:44 AM
Some good questions jhwegener!

Perhaps you would like to read up on 'deterministic chaos'? The idea is that two systems of interacting particles, identical in all respects but one tiny, tiny one (e.g. one particle has an initial speed of 2 m/s, in the other it is 1.99999999999999 m/s) will start out behaving very much the same, but over time they will behave very differently. The popular phrase 'the butterfly effect' is a captivating image of this (if somewhat misleading) - a butterfly flaps its wings in Brisbane and next week there's a thunderstorm in Beijing.

As far as I know, it would take some pretty major 'external' intervention to make a significant change to the solar system (e.g. big changes in the orbits of the planets) - there isn't much that's even close to other attractors (this is technical term in chaos theory - it refers to phase space, not physical space). Of course, objects near resonance orbits are already flirting with the butterfly, so small perturbations can certainly make big differences for these!