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Originally Posted by Robert Tulip
Are you sure about this? It depends what you mean by resonance. There is a fairly strong 179 year resonance between Jupiter, Saturn and Neptune with drift of just over one part in a thousand (0.1% per cycle). Of course nothing is exact in such matters, but this ‘resonance’ produces very strong similarity between SSB patterns separated by 179 years. Surely you could run a lot more iterations on the simulation without Jupiter before the pattern got too busy?
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I don't see 0.1% when I run the numbers. Using orbital periods of 11.85920, 29.657296, 164.79 years for Jupiter, Saturn & Neptune respectively, I see an approximate 15:6:1 resonance. But the real numbers are
15.093766864544 : 6.03561430549838 : 1.08623096061654
which miss a perfect resonance by about 5%. This will certainly cause drift in the plot.
Here's 2000 years of the planets sans Jupiter curving the path of the center of the sun. It's pretty busy, and if I let it run 10s of thousands of years, it would be a solid yellow circle (or perhaps a doughnut as it looks like the middle won't get filled in) because of the width of the plotted line.
Quote:
Originally Posted by mugaliens
...You're right - it's a really good approximation. But that's limited to what's happening now, for example, determining the forces between the objects, or their departure vector. When it comes to the effects of gravity over time (again, back to the OP), however, errors are compounded, and a "really good approximation" doesn't hold a candle to the precision required to compute where the planets would be a hundred years from now.
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I was wondering about this statement. I guess we'd have to quantify "hold a candle", but I thought I'd try it anyway.
I know that JPL's Horizons integrator includes lots of stuff that a Newtonian-only point mass simulator would not include, such as non-spherical bodies and relativity. So a comparison can be made by creating a simulation of the solar system, propogating it forward 100 years, and then comparing the results with what JPL says they should be based on their integrator. In every case except Venus and Pluto, the simulated positions of my planets were within one planet diameter of where JPL Horizons said they should be. And Venus and Pluto weren't very far off either:
Mercury: 3094 km
Venus: 13061 km
Earth: 8707 km
Mars: 4696 km
Jupiter: 1974 km
Saturn: 1325 km
Uranus: 394 km
Neptune:146 km
Pluto: 19255 km
Makemake: 330 km
These numbers are
very small compared to the size of the solar system. For example, the ratio between Earth's miss distance of 8707 km, and its distance to the sun is about the same as a golf cup placed over 2000 yards from the tee box. Imagine making a hole-in-one from 2000 yards away. Or in the case of Neptune, it would be like making a hole-in-one from 2000 miles away.
Additionally, propogating the solar system backwards correctly predicts (or postdicts is probably a better term) the time and date of transits of Venus more than a century ago. These can be verified by historical record.
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This "missing mass" is, in part, one of the bases for the existance of the Oort cloud. The remainder were observations of cometary patterns by Ernst Öpik, and later, by Jan Hendrik Oort.
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I've never heard this before. I can't seem to find it in the wiki link you provide. I've been under the impression that since the Oort cloud is exterior to us, evenly distributed, and not very massive (~5 earth masses according to wiki), that it can't create significant perturbations. It's also not mentioned as a source of error in this paper by JPL's Jon Giorgini:
http://neo.jpl.nasa.gov/apophis/Apop...D_PREPRINT.pdf . In it he talks about the difficulty of predicting how close asteroid Apophis will pass Earth in the year 2036. The uncertainties in the planets' positions ranks high, but uncertainties from the exclusion of the Oort cloud are not mentioned.