New Math Shows When Solar Systems Become Unstable | Quanta Magazine
celestial-mechanicsmathematicschaos-theoryn-body-problem
Abstraction: First mathematical proof of inevitable orbital instability in n-body planetary systems
Key points:
- Clarke, Fejoz, and Guàrdia proved in three papers (150+ pages) that instability is inevitable in a model of three planets orbiting a sun — orbital eccentricities and semimajor axes can grow arbitrarily large
- A planet could even reverse its orbital direction entirely over sufficient time
- Key technique: Deprit coordinates (rediscovered by Pinzari in 2009 during her PhD) enabled navigation of 18-dimensional configuration space
- Large initial inclination angles between orbital planes are a primary instability driver; such systems are destroyed in hundreds of millions rather than billions of years
- Laskar and Gastineau's 2009 simulations showed ~1% chance Mercury could destabilize and collide with Venus; this proof provides a mathematical mechanism
- Results open paths to proving instability in models closer to our own solar system and to designing efficient satellite trajectories
Connections: Dynamical Systems · N Body Problem · Chaos Theory
Source: https://www.quantamagazine.org/new-math-shows-when-solar-systems-become-unstable-20230516/