Related Experiment Video
Updated: Dec 14, 2025
06:04
Simulation of the Planetary Interior Differentiation Processes in the Laboratory
Published on: November 15, 2013
11.9K
Instantons for the Destabilization of the Inner Solar System
Eric Woillez1,2, Freddy Bouchet1
1Université Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France.
Physical Review Letters
|July 24, 2020
Summary
Researchers explored chaotic systems and found that rare events, like inner Solar System destabilization, concentrate near a predictable path called an instanton. This finding applies to Mercury
Area of Science:
- Celestial mechanics
- Dynamical systems theory
- Statistical physics
Background:
- Rare events in dynamical systems can exhibit predictable patterns.
- Instanton theory, originating from physics, describes action minimizers in path integrals.
- The dynamics of the inner Solar System are complex and susceptible to rare destabilizing events.
Purpose of the Study:
- To investigate whether path probabilities concentrate near an instanton in chaotic deterministic systems.
- To apply instanton concepts to the dynamics of terrestrial Solar System bodies.
- To model and predict rare destabilizing events in the inner Solar System.
Main Methods:
- Developed a simple deterministic model for Mercury's dynamics.
- Utilized concepts from statistical physics and field theory (instanton theory).
- Computed the first exit time for a specific resonance in the model.
Main Results:
- Predicted the instanton associated with Mercury-Jupiter perihelion resonance.
- Demonstrated that path probabilities concentrate around this predicted instanton.
- Showed this concentration is significant for events occurring within a few hundred million years.
Conclusions:
- Path probabilities do concentrate near instantons in chaotic deterministic systems, specifically for Solar System dynamics.
- The instanton provides a valuable tool for predicting rare destabilizing events in celestial mechanics.
- Findings have implications for understanding the long-term stability of the actual Solar System.
Related Concept Videos
01:18Conservation of Angular Momentum: Application
11.9K
A system's total angular momentum remains constant if the net external torque acting on the system is zero. Examples of such systems include a freely spinning bicycle tire that slows over time due to torque arising from friction, or the slowing of Earth's rotation over millions of years due to frictional forces exerted on tidal deformations. However in the absence of a net external torque, the angular momentum remains conserved. The conservation of angular momentum principle requires a...
11.9K
03:18Nuclear Stability
22.3K
Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10−15 meters, a nucleus is quite small compared to the radius of the entire atom, which is about 10−10 meters. Nuclei are extremely dense compared to bulk matter, averaging 1.8 × 1014 grams per cubic centimeter. If the earth’s density were equal to the average nuclear density, the earth’s radius would be only about 200 meters.
To hold positively charged protons together...
To hold positively charged protons together...
22.3K
01:28Magnetostatic Boundary Conditions
1.5K
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
1.5K
01:23Stability of Equilibrium Configuration
689
Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
689
01:12Reduced Mass Coordinates: Isolated Two-body Problem
2.1K
In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
2.1K
01:10First Law: Particles in One-dimensional Equilibrium
7.7K
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
7.7K