〈 Berger | Dillon 〉

In nature, increases in the energy of the orbit inevitably describe a precession. Why do people spend time solving problems of n-bodies?

so they can eventually study n+1

Let me rephrase. If we know that classical mechanics has a predictive incapacity (precession). Why do you think it is a useful tool to study these systems? am i missing something?

Are you saying we should use general relativity, because that's needed to understand the precession of Mercury? People who make long-term predictions about the Solar System *do* use general relativity.

2/2 The sum of these is the constant energy E of the orbit (which is negative for bound orbits). Thus, noting that v2 = (dr/dt)2 + (ωr)2, where ω = dϕ/dt is the angular velocity of the particle, we have the Newtonian equation of motion

People who do long-term simulations of the Solar System use general relativistic corrections for all planets, not just Mercury: https://arxiv.org/abs/astro-ph/9403057 … They say these corrections add just 5% to the computation time.

That's what I have been trying to explain.