Application of the Swygert Equilibrium Quotient (SEQ) to Distinct Planetary Architectures: A Comparative Analysis of Coherence Across Planetary Systems

Application of the Swygert Equilibrium Quotient (SEQ) to Distinct Planetary Architectures: A Comparative Analysis of Coherence Across Planetary Systems


DOI: (to be assigned)

John Swygert

March 19, 2026

Abstract

Planetary systems exhibit a wide range of structural configurations, from widely spaced hierarchical systems to compact multi-planet arrangements. While long-term dynamical stability is well understood within gravitational physics, there is currently no standardized framework for comparing the degree of structural coherence across different systems. Building on the Swygert Equilibrium Quotient (SEQ) framework, this paper applies a qualitative comparative analysis to three distinct planetary architectures: the Solar System, Kepler-186, and TRAPPIST-1. The objective is not to introduce new physical laws, but to demonstrate that planetary systems can be meaningfully differentiated based on their degree of dynamical coherence. The results suggest that coherence is a measurable and recurring property across systems, providing a basis for comparative classification and future quantitative refinement.

1. Introduction

The discovery of exoplanetary systems has revealed that planetary architectures vary widely in scale, spacing, and composition. Despite these differences, many systems maintain long-term stability, suggesting that diverse configurations can satisfy the constraints imposed by gravitational dynamics.

The Swygert Equilibrium Quotient (SEQ) was introduced as a conceptual framework for measuring the degree of dynamical coherence within a planetary system. Rather than treating stability as a binary condition, SEQ characterizes systems along a continuum, reflecting how consistently their components operate in sustained, non-disruptive relationships.

This paper applies the SEQ framework to multiple planetary systems to demonstrate its utility as a comparative tool.

2. Systems Selected for Comparative Analysis

Three systems were selected to represent distinct planetary architectures:

2.1 The Solar System

A widely spaced, hierarchical system containing both terrestrial and gas giant planets. Orbital spacing increases significantly with distance from the Sun, and long-term stability has been observed over billions of years.

2.2 Kepler-186

A compact system of Earth-sized planets orbiting a red dwarf star. All known planets reside within a region smaller than Mercury’s orbit in the Solar System, yet maintain stable orbital relationships.

2.3 TRAPPIST-1

An ultra-compact system characterized by tightly packed planets exhibiting near-resonant orbital chains. The system demonstrates a high degree of dynamical coordination among its planets.

3. Comparative Criteria for SEQ Evaluation

To evaluate system coherence, the following qualitative criteria are considered:

  • Orbital spacing consistency

  • Ratio relationships between adjacent orbital periods

  • Presence of resonance or near-resonance structures

  • Eccentricity constraints and orbital regularity

  • Stability of interactions between neighboring bodies

These criteria do not produce a single exact value at this stage, but collectively define the relative coherence of each system.

4. Observational Comparison of System Coherence

4.1 Solar System

The Solar System exhibits high stability but lower structural uniformity compared to compact systems. Orbital spacing is wide and non-uniform, and while resonances exist, they are not globally dominant. The system demonstrates strong long-term survivability with moderate coherence.

4.2 Kepler-186

Kepler-186 demonstrates compact organization with relatively consistent spacing between planetary orbits. While not strongly resonant, the system maintains stable relationships within a compressed spatial regime. This suggests a coherent but less tightly coordinated structure compared to resonant systems.

4.3 TRAPPIST-1

TRAPPIST-1 exhibits a high degree of coherence characterized by near-resonant orbital chains. The planets display coordinated orbital relationships that suggest strong dynamical coupling. This system represents a highly organized configuration within a compact architecture.

5. Relative SEQ Interpretation

Based on the comparative criteria, the systems may be qualitatively ranked in terms of coherence:

  • TRAPPIST-1 → High SEQ (strong resonance and coordination)

  • Solar System → Moderate to High SEQ (stable but less uniform structure)

  • Kepler-186 → Moderate SEQ (compact and stable, but less coordinated)

This ranking is not absolute, but demonstrates that SEQ provides a meaningful way to differentiate systems based on observable structural properties.

6. Implications for Planetary System Classification

The application of SEQ suggests that planetary systems may be classified according to their degree of dynamical coherence rather than solely by physical scale or composition.

This framework allows for:

  • Cross-system comparison independent of architecture

  • Identification of recurring structural patterns

  • Potential inference of dynamical maturity

It further suggests that planetary systems may cluster into distinct coherence classes, reflecting the constraints under which stable configurations can exist.

7. Limitations and Future Work

This study is qualitative and intended as a proof-of-concept. Limitations include:

  • Incomplete mass and orbital data for exoplanet systems

  • Lack of precise eccentricity measurements in some cases

  • Absence of a fully defined mathematical SEQ formulation

Future work will focus on developing a quantitative SEQ model and applying it across a broader dataset of planetary systems.

Conclusion

This paper demonstrates that planetary systems can be meaningfully compared using the Swygert Equilibrium Quotient (SEQ) framework. By evaluating structural coherence rather than specific configuration, SEQ provides a new lens for understanding planetary organization across diverse architectures. While preliminary, this approach suggests that coherence is a recurring and measurable property of planetary systems, offering a foundation for future quantitative analysis and classification.

References

  1. NASA Exoplanet Archive


  1. Gillon, M. et al. (2017), TRAPPIST-1 System Studies


  1. Borucki, W. J. et al. (2014), Kepler-186 Discovery


  1. Lissauer, J. J., Planetary System Dynamics


  1. Swygert, J., Toward a Comparative Metric of Planetary System Coherence, Ivory Tower Journal (2026)


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