Published June 3, 2026 | Version v4
Preprint Open

The Stellar Death Clock: Parametric Simulation of Biospheric Collapse and Orbital Migration Efficiency

Authors/Creators

Description

The long-term evolution of the Sun poses a fundamental thermodynamic constraint on the future habitability of Earth. Building upon the Civilizational Survival Factor (Ψ) framework introduced in the first paper of this series, this work presents a parameterized simulation of Earth’s biospheric collapse driven by increasing solar luminosity. Using analytical calculations derived from established stellar evolution models (Sackmann et al., 1993; Caldeira & Kasting, 1992; Rushby et al., 2013), key thermodynamic, atmospheric, and hydrological parameters were calculated at four critical milestones: present day, C3 photosynthetic disruption (~600 Myr), forest biomass collapse (~800 Myr), and terminal ocean desiccation (~1,100 Myr).

These pre-computed values were then injected into the 3D physics engine Universe Sandbox solely as a visualization tool to generate illustrative renderings of the progressive environmental degradation. Finally, the thermodynamic efficiency of planetary orbital migration to 1.5 au is compared with that of an interstellar exodus scenario using the Tsiolkovsky rocket equation and gravitational potential energy calculations. The results indicate that orbital migration preserves the planetary biosphere with approximately three orders of magnitude greater energy efficiency per unit biomass than relativistic interstellar transport.

This study highlights planetary orbital management as a thermodynamically favorable strategy for long-term civilizational survival, while explicitly acknowledging the illustrative nature of the 3D visualizations and the idealized assumptions of the migration model. The combined papers provide a conceptual and visual foundation for further research into active planetary engineering as a response to stellar evolution.

Notes (English)

Changelog (v2.0.0)
 
1. Methodological and Terminological Refinements
• Adjusted core terminology regarding the 3D physics engine outputs. Replaced instances of "empirical validation" with "computational illustration" and "simulation-based representation" to maintain absolute methodological rigor and accurately describe the limits of software-assisted visualization (Universe Sandbox).
• Refined the final sentence of the Abstract to clarify that the framework "computationally demonstrates" (rather than empirically proves) the thermodynamic optimization of planetary migration.
 
2. Manuscript Structure and Scope Definition
• Added a new subsection: "4.3. Scope and Dynamical Limitations". This section explicitly decouples the thermodynamic energy calculations from the precise mechanical execution vectors (such as asteroid-targeted propulsion systems), mapping them as standalone objectives for subsequent research (Paper 3).
• Integrated a secular orbital stability warning within Section 4.3, acknowledging that a real-world Earth migration to 1.5 au would introduce complex gravitational resonances affecting neighboring celestial bodies like Venus and Mars (referencing Laskar's chaos models).
 
3. Language and Editorial Corrections
• Homogenized the entire manuscript language by translating a legacy paragraph in Section 5 (Discussion) from Spanish into professional, technical English, ensuring full linguistic consistency across all pages.
• Corrected minor typographical errors and improved the readability of variables in text-to-equation transitions.
 
 

Notes (English)

Changelog (v3.0.0)

1. Title Update
  • Changed from "The Stellar Death Clock: A Thermodynamic Data Simulation over 3D Visualization" (The_Stella... p. 1) to "The Stellar Death Clock: Parametric Simulation of Biospheric Collapse and Orbital Migration Efficiency" (The_Stella... p. 1).
2. Methodological Clarifications & Software Scope
  • Redefined Software Role: Explicitly repositioned Universe Sandbox solely as a 3D visualization and interactive rendering layer rather than the primary scientific simulator (The_Stella... pp. 1, 3).
  • Two-Stage Hybrid Framework: Formalized the methodology into two clear phases: analytic thermodynamic/astrophysical derivations from peer-reviewed literature, followed by discrete visual parameter injection (The_Stella... p. 3).
3. Extended Mathematical & Thermodynamic Context
  • Biomass Capital Source: Integrated the global wet biomass inventory (\(M_{\text{biosphere}} \approx 1.85 \times 10^{15}\text{ kg}\)) backed by the foundational dry carbon census of Bar-On et al. (2018) (The_Stella... pp. 11-12).
  • Systemic Complexity Penalty: Expanded Section 4.2 to connect the raw kinetic calculations with the superlinear complexity cost (\(\beta > 1\)) from Paper 1, demonstrating a compounding structural advantage for planetary management of up to 25 orders of magnitude over artificial habitats (The_Stella... p. 11).
4. Scope, Assumptions & Limitations (Section 4.3)
  • Added Explicit Limitations Section: Expanded the scope constraints to detail four specific boundaries of the current model (The_Stella... p. 12):
    1. Universe Sandbox numerical approximation versus specialized 1D EBM/N-body integrators (The_Stella... pp. 12-13).
    2. Idealized nature of the migration path (ignoring complex gravitational multi-body resonances) (The_Stella... p. 13).
    3. Lower-bound potential calculations without active engine/propulsion efficiency losses (The_Stella... p. 13).
    4. Absence of Monte Carlo sensitivity analyses on the complexity scaling exponent (\(\beta \)) (The_Stella... p. 13).
5. Bibliography & References
  • Added reference (8) Bar-On YM, Phillips R, Milo R. The biomass distribution on Earth. Proc Natl Acad Sci USA. 2018 to anchor ecological scaling (The_Stella... pp. 12, 17).
 

Notes (English)

Changelog (v4.0.0)

Added author name, institutional affiliation (Independent Researtcher, Alumnus, University of Murcia), and ORCID to the title page for preprint and repository submission (Zenodo).

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