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Jack21222

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**How accurate are "simple" models of the solar system?**

Exactly how much effect does the perturbation of other planets have on planetary orbits? That is, if we were to take a naive model of the solar system, just applying Kepler's laws to each planet individually, with no planet-planet interactions, how accurate would it be in 10 years? 100? 1000?

And since the laws are time-reversible, could we then run these models backwards, starting with the current positions of the planets, using just Kepler's laws, to get a position of all of the planets dating back to Kepler? Would the error in the orbits due to the system being an n-body problem be big enough going back 400 years such that the calculated position from this model would diverge from the positions Tycho Brahe measured?

In other words, if in 1620, Kepler had calculated where the planets would be in the sky in 2020 using only his laws, would there be a measurable difference?

I hope my question is making sense. I really want to know what time scale is required to really notice the difference between the 2-body solution to planetary orbits as compared to real life.