Huge planets can actually share an orbit at crazy vertical angles without crashing, which totally breaks our old ideas of how solar systems work.
April 2, 2026
Original Paper
Marchal's family of periodic orbits. I: Stability of inclined co-orbital planetary systems
arXiv · 2604.00623
The Takeaway
While solar systems are usually flat like a pancake, this study proves that 'inclined' planets can share a path at angles up to 60 degrees and remain perfectly stable, even if they are very heavy. This mathematical possibility suggests the existence of 'spherical' solar systems where planets zoom around their star in wildly different directions rather than a single plane.
From the abstract
At the Lagrange relative equilibrium of the three-body problem, for all values of the masses, the elliptic eigenvalues associated with vertical eigenvectors give rise to spatial quasi-periodic orbits, which become periodic in a rotating frame. In 2009, by averaging out the fast frequencies, Christian Marchal showed that these orbits, which are fixed points in the restricted average problem, form a oneparameter family connecting L 4 to L 5 . Using perturbation methods, we show the persistence of