Slashdot Mirror
Earth Could Collide With Other Planets
Everybody put on your helmet;
Smivs writes "Astronomers calculate there is a tiny chance that Mars or Venus could collide with Earth — though it would not happen for at least a billion years.
The finding comes from simulations to show how orbits of planets might evolve billions of years into the future. But the calculated chances of such events occurring are tiny. Writing in the journal Nature, a team led by Jacques Laskar shows there is also a chance Mercury could strike Venus and merge into a larger planet. Professor Laskar of the Paris Observatory and his colleagues also report that Mars might experience a close encounter with Jupiter — whose massive gravity could hurl the Red Planet out of our Solar System."
We've known for almost a hundred years (since Poincare more or less) that the 3 body problem is inherently chaotic and not terribly stable and here we have an n body problem for large n. All they seem to have done here is list some of the more catastrophic possible outcomes if the system becomes seriously unstable.
From TFAbstract, helpfully linked downstream:
It has been established that, owing to the proximity of a resonance with Jupiter, Mercury's eccentricity can be pumped to values large enough to allow collision with Venus within 5 Gyr (refs 1â"3). This conclusion, however, was established either with averaged equations1, 2 that are not appropriate near the collisions or with non-relativistic models in which the resonance effect is greatly enhanced by a decrease of the perihelion velocity of Mercury2, 3. In these previous studies, the Earth's orbit was essentially unaffected. Here we report numerical simulations of the evolution of the Solar System over 5 Gyr, including contributions from the Moon and general relativity.
The authors claim this is the first extended simulation set incorporating GR and avoiding the problematic averaging technique.
I realize the linked article doesn't have the 1% figure, here's a better article:
http://www.universetoday.com/2009/06/10/wild-little-mercury-to-cause-interplanetary-smashup-maybe/
I'll form my OWN solar system! With blackjack! And hookers!
Ok, here's a question: Has this happened in the past?
It doesn't take long playing with simple, fun orbit simulators to see that while most planetesimals get glommed, a few get chucked. Escape velocity from the Sun at Mars distance is WAY MORE* (technological term) than Jupiter could perturb. Some things tossed could have 'very long' periods, but still not escape. THAT would be news.
And yes, I am a rocket scientist and yes, I HAVE done the math.
Vcircular * sqrt(2) = Vescape! 41% is too much, even for Jupiter.
Nope, it was the Ars article: http://arstechnica.com/science/news/2009/06/kicking-a-planet-out-of-the-solar-system-physically.ars They mention a 'complex time integration scheme' fourth paragraph down. Though with the state of technical journalism on the intrawebs that could mean Euler or leap-frog.
How do you know this is the fault of the scientists? It could very easily be lazy and/or sensationalistic journalism -- same stuff as "this has as much info as x libraries of congress" or "as much volume as x ping-pong balls", or half of what kdawson posts.
Hail Eris, full of mischief...
E pluribus sanguinem
This prediction is as meaningless as the one of Mercury falling into the sun in a billion years for the same reasons.
The inner solar system is chaotic with a Lyuapanov time on the order of 5 million years - On average, two very nearby orbits will change their distance between each other in phase-space by a constant in that time. This makes the solar system's future evolution profoundly dependent on initial conditions and integrator accuracy.
First of all it's hard to maintain integration accuracy for more than a few Lyuapanov times, especially when the system has such an enormous dynamic range in mass and characteristic orbital times as the solar system, since this requires that the integrator be exponentially more accurate. The outer solar system is routinely integrated for hundreds of millions of years (and I've run several such simulations myself with a 10th order symplectic integrator) but most simulations of the inner solar system run for a few tens of millions of years at most. A 5 billion year integration of the inner solar system will require that errors be supressed on the order of e^-1000, which is absurd.
Second of all, chaotic systems are also defined by their extreme dependence on initial conditions. Our observational knowledge of the positions of the planets only extends to about 7 digits at best, which makes any simulation in which displacing something by 1 part in e^1000 changes the outcome meaningless. In addition, at such levels of precision other effects come into play - Relativity changes the details of Earth's orbit significantly from the classical prediction after about 10 million years.
You can plug whatever numbers you want into a symplectic integrator and it'll run as long as you want without blowing up, but that doesn't mean the numbers mean anything.