Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: lenadorap on 23/01/2010 01:55:13
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I remember learning Stable and Unstable equilibrium s at high school. According to what I rememer, the planets moving around another planet or a star are in unstable equilibriums as the gravitations force between the two objects are inversly proportional to the power of 3 of the distance between them. So my question is if that is the case how all of those planets were able to survive for millions of years?
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Good question!
I think what they meant was that it's possible for there to be a more stable state. Take the Moon for instance. It would be in a more stable state if, instead of orbiting the Earth, it was "landed" on Earth. Once it had landed, it's not likely to resume its orbit around the Earth without a large amount of energy input.
The Moon/Earth system has energy that maintains the moon in orbit. If that energy is dissipated, the system will be more stable.
Actually, there is some energy lost as the Moon orbits the Earth, so, eventually, it may land on Earth, but I don't think that's happening any time soon.
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You have been mis informed on two counts lenadorap firstly the attractive force between two gravitating objects is inversely proportional to the square of the distance between them. This allows orbits to be stable assuming the objects are in space with no air resistance slowing them down, have enough angular momentum with respect to each other to avoid colliding and not too much just to pass by and be deflected in their motions.
It is interesting to note that two objects being pulled towards each other by gravity from a great distance and having enough angular momentum (that is their relative velocity in any direction perpendicular to the line joining the two bodies) not to collide will just pass by each other in parabolic or hyperbolic paths and not form an orbit unless affected by the gravitational attraction of another body.
It may be that you have misunderstood what you have been told because it is important for the stability of the universe that gravitation and electrical forces follow inverse square laws and produce stable orbits. magnetic forces follow inverse cube laws at significant distances from the magnets and cannot form stable orbits. and the fact that inverse cube law orbits are not stable is sometimes used as an illustration. It is also why we must live in a three dimensional universe because three dimensional universes produce inverse square laws
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It seems as the solar system is in a 'chaotic stable configuration' meaning that we can say what the orbits will be but not the exact localization of a single planet.
Orbitals (http://www.fisica.edu.uy/~gallardo/mece/tabaressd.pdf)
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So... the planetary system is stable and chaotic ...
.. According to the perturbation theory (semimajor axes are constant) the system is STABLE.
.. According to the N-body problem the future of the system is DETERMINED (only one solution exists) but CHAOTIC (hard to predict).
.. According to modern numerical integrations the planetary system is under STABLE CHAOS: we can predict reasonably well the orbital evolution but not the exact position of the planets in their orbits.
--End of quote-
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"Unstable equilibrium" simply means that there is potential energy by virtue of position. If that equilibrium is disturbed by an external force, potential energy can be given up. Stable equilibrium is achieved when all the potential energy is given up.
Consider a brick standing on its end on a flat surface. It is in equilibrium, but if you knock it over, its center of mass comes closer to the surface on which it rests, so it has less potential energy than it had before. When its standing on end, it is considered to be in "unstable equilibrium".
It is in "stable equilibrium" when it rests on a side with the greatest area, because, you could only put into a less stable state if you tipped it up and increased its potential energy.
So, as long as you don't "rock the boat", the brick can remain in unstable equilibrium indefinitely.
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What I meant by Unstable equilibrium is that if a small external push is given inward of the two objects(this can happen due to collision of a meteorite however small) there will be a DeltaEx movement of the objects towards each other which would result in decreasing of the distance between the two objects which would lead to increase of the gravitational pull(by order of 2 or 3 of the distance moved) between them. This will be a kind of "Vicious Cycle" which would end up with collision of the two objects. Similarly if the initial external force is towards the outwards, the objects will fall out from the orbits.
Can anyone enlighten me on why is not happening?
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To some extent I believe it is happening. However, over time, as long as the collisions are small, and coming from different directions, things will tend to average out so that, in the long term, there is very little net effect. However, if there was a really massive impact, it could destabilize a system sufficiently to cause an orbiting body to "fall" out of orbit.
The Moon will not orbit the Earth forever. There are frictional losses that are gradually eating away at the energy in the combined system. Ocean tides are one example.