Comparative Orbital Stability Across Distinct Planetary Architectures: The Solar System and Kepler-186 as Constraint-Bound Dynamical Systems

Comparative Orbital Stability Across Distinct Planetary Architectures: The Solar System and Kepler-186 as Constraint-Bound Dynamical Systems


DOI: (to be assigned)

John Swygert

March 19, 2026

Abstract

Planetary systems exhibit long-term orbital stability across vastly different structural regimes, from the wide, hierarchical configuration of the Solar System to the compact, tightly packed architecture of the Kepler-186 system. This paper presents a comparative analysis of these two systems as examples of constraint-bound dynamical equilibrium. Despite differences in stellar type, spatial scale, and planetary distribution, both systems maintain stable orbital configurations over astronomical timescales. Within the framework of the Swygert Theory of Everything AO (TSTOEAO), this stability is interpreted not as incidental, but as consistent with underlying constraint structures that govern allowable configurations of matter and motion. The analysis remains fully compatible with established gravitational dynamics and does not assert novel forces, but instead examines whether recurring stability across divergent systems suggests deeper boundary conditions on orbital organization.

1. Introduction

The study of planetary systems has revealed a wide diversity of configurations, challenging early assumptions that our Solar System represents a universal template. Observations from the Kepler Space Telescope have identified compact multi-planet systems orbiting close to their host stars, many of which differ significantly from the Solar System in scale and structure.

Among these, Kepler-186 provides a particularly useful comparison. It consists of five confirmed planets orbiting a red dwarf star within a region significantly smaller than Mercury’s orbit in our own system, yet exhibiting long-term dynamical stability.

This paper examines whether such stability, observed across fundamentally different architectures, can be understood as arising from constraint-bound equilibrium conditions rather than purely coincidental outcomes of formation history.

2. The Solar System as a Reference Model

The Solar System represents a widely spaced, hierarchical configuration dominated by the gravitational influence of the Sun and modulated by large planetary bodies, particularly the gas giants.

Key characteristics include:

  • Significant radial separation between planetary orbits

  • Mass stratification (terrestrial vs gas giants)

  • Long-term orbital stability over billions of years

  • Weak but measurable resonances (e.g., Jupiter–Saturn interactions)

Natural satellites (moons) further contribute to local dynamical complexity. Systems such as the Galilean moons of Jupiter exhibit resonance chains that reinforce stability, demonstrating that equilibrium structures exist not only at planetary scales but also within sub-systems.

This layered stability suggests that gravitational dynamics alone produce organized configurations, but also raises the question of whether only certain configurations remain viable over time.

3. The Kepler-186 System: A Compact Stability Regime

The Kepler-186 system presents a markedly different architecture:

  • Five Earth-sized planets

  • Extremely compact orbital spacing

  • All planets orbit within a region smaller than Mercury’s orbit

  • Host star is a low-mass red dwarf

The outermost planet, Kepler-186f, resides within the star’s habitable zone, receiving a level of stellar flux comparable to Earth’s, despite the system’s compressed scale.

At present, no confirmed moons have been detected in the Kepler-186 system. This absence is consistent with observational limitations, as current detection methods (primarily transit photometry) are not sensitive enough to reliably identify exomoons of Earth-sized planets at this distance. Therefore, while moons cannot be ruled out, they are not included in the present dynamical analysis.

The key point is that stability persists despite:

  • Increased gravitational interaction due to proximity

  • Lack of large stabilizing gas giants

  • Reduced spatial separation between orbital paths

This indicates that stable configurations are not limited to widely spaced systems.

4. Comparative Analysis: Stability Across Scale and Structure

When comparing the Solar System and Kepler-186, several contrasts emerge:

Feature

Solar System

Kepler-186

Scale

Wide

Compact

Star Type

G-type (Sun-like)

M-type (red dwarf)

Planet Distribution

Hierarchical

Tightly packed

Gas Giants

Present

None detected

Moons

Numerous

None confirmed

Stability

Long-term

Observationally stable

Despite these differences, both systems maintain coherent orbital configurations.

This suggests that stability is not dependent on:

  • Specific spacing patterns

  • Presence of large planets

  • Particular stellar class

Instead, stability appears to emerge within allowable regions of dynamical phase space defined by gravitational interactions.

5. Interpretation Within Constraint-Bound Frameworks

Within classical astrophysics, orbital stability arises from gravitational laws, initial conditions, and long-term dynamical evolution. This explanation remains fully sufficient and is not challenged here.

However, the recurrence of stability across divergent systems invites an additional interpretive layer.

Within the Swygert Theory of Everything AO (TSTOEAO), this can be described as:

  • Systems evolve toward allowed equilibrium configurations

  • Instability leads to reconfiguration, collision, or ejection

  • Only constraint-compatible structures persist

This does not introduce new forces, but reframes stability as the outcome of underlying boundary conditions governing what configurations are dynamically sustainable.

Such an interpretation remains consistent with established physics while suggesting that observable systems may represent a filtered subset of all possible configurations.

7. Limitations and Observational Constraints

This analysis is subject to several limitations:

  • Planetary masses in Kepler-186 are not precisely known

  • Orbital eccentricities remain constrained but not exact

  • Exomoons, if present, are currently undetectable

  • Long-term stability is inferred from models rather than direct observation over geological timescales

Therefore, conclusions are framed as consistency-based rather than definitive.

6. Dynamical Coherence and SEQ Interpretation

Planetary systems do not achieve perfect equilibrium; however, over time they tend to occupy dynamically stable configurations that are more coherent and internally consistent than their earlier evolutionary states. This progression arises from the natural elimination of unstable configurations through collision, ejection, or orbital reconfiguration.

Within this context, it is useful to consider stability not as a binary condition, but as a continuum. Systems may be evaluated based on how closely their components operate in sustained, non-destructive dynamical relationships. This perspective motivates the introduction of a relative metric, referred to here as the Swygert Equilibrium Quotient (SEQ), representing the degree to which a system exhibits structural coherence under gravitational dynamics.

Higher SEQ values correspond to systems in which:

Orbital paths are stable over long timescales

Eccentricities are constrained

Interactions between bodies are non-disruptive

Configurations exhibit consistent and repeatable dynamical behavior

Lower SEQ values correspond to systems with:

Significant instability or chaotic interactions

High eccentricity or crossing orbits

Increased likelihood of collision or ejection events

Under this interpretation, both the Solar System and Kepler-186 can be viewed as systems occupying relatively high SEQ regimes, despite their structural differences. This suggests that stability is not tied to a specific configuration, but rather to the degree of coherence permitted within the governing dynamical constraints.

Importantly, SEQ does not imply perfect equilibrium, nor does it introduce new physical forces. It serves as a descriptive framework for comparing the relative organizational state of planetary systems as they evolve over time.

8. Conclusion

The Solar System and Kepler-186 represent two fundamentally different planetary architectures that nevertheless exhibit stable orbital configurations. This cross-system consistency suggests that stability arises within constrained dynamical regimes rather than arbitrary formation outcomes.

Within the TSTOEAO framework, this is interpreted as evidence that physical systems evolve within allowable equilibrium structures defined by deeper constraint conditions. While fully compatible with classical gravitational dynamics, this perspective encourages further investigation into whether stability itself reflects underlying structural limits on physical organization.

Future observations of additional compact systems, improved mass measurements, and potential exomoon detection may further refine this interpretation.

References

  1. NASA Exoplanet Archive — Kepler-186 System Data


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


  1. Lissauer, J. J. et al., Planetary System Stability Studies


  1. Swygert, J., Transition Density Across Physical Scales, Ivory Tower Journal (2026)


  1. Swygert, J., The Emergence Threshold, Ivory Tower Journal (2026)


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