Toward a Comparative Metric of Planetary System Coherence: The Swygert Equilibrium Quotient (SEQ) Framework
Toward a Comparative Metric of Planetary System Coherence: The Swygert Equilibrium Quotient (SEQ) Framework
DOI: (to be assigned)
John Swygert
March 19, 2026
Abstract
Planetary systems exhibit a wide diversity of architectures, ranging from widely spaced hierarchical configurations to compact, tightly packed arrangements. Despite these differences, many systems demonstrate long-term dynamical stability and coherent orbital structure. This paper proposes a comparative framework for evaluating planetary system organization through a relative metric termed the Swygert Equilibrium Quotient (SEQ). Rather than assuming perfect equilibrium, SEQ characterizes the degree to which a system exhibits stable, non-disruptive, and repeatable dynamical relationships among its constituent bodies. The framework is constructed using measurable orbital and physical parameters, including spacing ratios, orbital periods, velocity distributions, and mass relationships. It is further proposed that higher SEQ values may correlate with dynamical maturity, reflecting the progressive elimination of unstable configurations over time. This interpretation remains fully consistent with established gravitational physics and does not introduce new forces, but instead provides a structured method for comparing the coherence of planetary systems across different architectures.
1. Introduction
The discovery of exoplanetary systems has revealed a broad spectrum of planetary architectures, challenging the notion that the Solar System represents a universal model. Systems such as compact multi-planet configurations and widely spaced hierarchical systems both exhibit long-term stability despite significant structural differences.
This raises a fundamental question: how can such diverse systems maintain coherence over astronomical timescales?
Traditional analysis focuses on individual system dynamics, but lacks a generalized framework for comparing the degree of organization across systems. This paper introduces a conceptual and quantitative approach to this problem by defining a relative measure of planetary system coherence.
2. Conceptual Model of Planetary System Structure
Planetary systems may be modeled, at first approximation, as a central stellar mass surrounded by orbiting bodies distributed along radial paths. While real systems exhibit eccentricity, inclination, and perturbations, a simplified concentric representation allows for the extraction of primary structural relationships.
Each planetary system may be characterized by:
Radial distribution of orbital paths
Orbital period progression
Velocity gradients as a function of distance
Mass distribution across the system
Relative spacing between adjacent bodies
These characteristics provide a basis for identifying patterns and relationships that persist across systems of differing scale and composition.
3. Measurable Parameters and System Ratios
To compare planetary systems, the following measurable quantities are considered:
Per-planet parameters:
Semimajor axis
Orbital period
Orbital velocity
Planetary mass (where available)
Planetary radius or diameter
System-level relationships:
Ratios of adjacent orbital radii
Ratios of orbital periods between neighboring planets
Velocity ratios across radial distance
Mass distribution gradients
Degree of eccentricity dispersion
Rather than seeking exact numerical constants, this framework emphasizes identifying recurring ranges and structural relationships that define dynamically stable configurations.
4. Dynamical Evolution and Structural Coherence
Planetary systems form under chaotic initial conditions, characterized by collisions, migration, and gravitational instability. Over time, unstable configurations are removed through processes such as:
Orbital crossing and collision
Gravitational ejection
Tidal evolution and energy dissipation
The result is a progressive filtering of configurations, leaving behind systems that exhibit long-term stability.
This process leads to an observable trend: systems evolve toward configurations that are more coherent, more predictable, and less dynamically disruptive.
5. The Swygert Equilibrium Quotient (SEQ)
To formalize this observation, we introduce the Swygert Equilibrium Quotient (SEQ), defined as a relative measure of planetary system coherence.
SEQ does not represent perfect equilibrium, nor does it imply a static condition. Instead, it reflects the degree to which a system:
Maintains stable orbital relationships over time
Avoids destructive interactions between bodies
Exhibits consistent and repeatable dynamical behavior
Operates within constrained and sustainable configurations
Higher SEQ values correspond to systems that are more dynamically coherent, while lower values indicate systems with greater instability or disorder.
SEQ is constructed from the combined evaluation of system parameters, including spacing regularity, orbital ratios, eccentricity constraints, and mass distribution.
6. Relationship to Entropy and System Evolution
At first glance, the emergence of structured and stable planetary configurations may appear to contradict the concept of increasing entropy. However, this is not the case.
The evolution toward coherent orbital systems occurs through processes that increase entropy globally, including energy dissipation, heat generation, and irreversible interactions. The resulting increase in local order represents a form of self-organization within a broader entropic framework.
SEQ therefore does not measure entropy, but rather the degree of local dynamical coherence that emerges within systems undergoing entropic evolution.
7. Implications for Comparative Planetary Analysis
The SEQ framework enables comparison across planetary systems with differing architectures, allowing for classification based on structural coherence rather than specific configuration.
It is proposed that:
Mature systems will tend to exhibit higher SEQ values
Younger or dynamically active systems will exhibit lower SEQ values
Systems may cluster into recurring pattern classes reflecting constraint-bound stability
This approach provides a pathway for analyzing planetary systems beyond descriptive observation, enabling structured comparison and potential inference of dynamical maturity.
Conclusion
Planetary systems, despite their diversity, exhibit recurring patterns of stability and coherence that arise through dynamical evolution. The Swygert Equilibrium Quotient (SEQ) provides a conceptual framework for quantifying these patterns and comparing systems across scales and architectures. By focusing on relative coherence rather than idealized equilibrium, this approach remains consistent with established physics while offering a structured method for understanding the organization of planetary systems. Future work may refine SEQ into a quantitative metric and apply it to a broader range of observed systems.
References
NASA Exoplanet Archive
Kepler Mission Data Publications
Lissauer, J. J., Planetary System Dynamics
Swygert, J., Comparative Orbital Stability Across Distinct Planetary Architectures, Ivory Tower Journal (2026)
Swygert, J., Transition Density Across Physical Scales, Ivory Tower Journal (2026)
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