Why Are Inner Planets Not Inclined Andrew Clarke Jacques Fejoz Marcel Guardia by Andrew Clarke & Jacques Fejoz & Marcel Guardia 101007/S1024002400151Z instant download after payment.

ABSTRACTPoincaré’s work more than one century ago, or Laskar’s numerical simulations from the 1990’s on, have irrevocably impaired the long-held belief that the Solar System should be stable. But mathematical mechanisms explaining thisinstability have remained mysterious. In 1968, Arnold conjectured the existence of “Arnold diffusion” in celestial mechanics. We prove Arnold’s conjecture in the planetary spatial 4-body problem as well as in the corresponding hierarchicalproblem (where the bodies are increasingly separated), and show that this diffusion leads, on a long time interval, to somelarge-scale instability. Along the diffusive orbits, the mutual inclination of the two inner planets is close to π/2, which hintsat why even marginal stability in planetary systems may exist only when inner planets are not inclined. More precisely,consider the normalised angular momentum of the second planet, obtained by rescaling the angular momentum by thesquare root of its semimajor axis and by an adequate mass factor (its direction and norm give the plane of revolution andthe eccentricity of the second planet). It is a vector of the unit 3-ball. We show that any finite sequence in this ball may berealised, up to an arbitrary precision, as a sequence of values of the normalised angular momentum in the 4-body problem.For example, the second planet may flip from prograde nearly horizontal revolutions to retrograde ones. As a consequenceof the proof, the non-recurrent set of any finite-order secular normal form accumulates on circular motions – a weak formof a celebrated conjecture of Herman.