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2026
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| Online Access: | https://doi.org/10.5281/zenodo.19399392 |
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| _version_ | 1866901131906514944 |
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| author | ueda, takashi |
| author_facet | ueda, takashi |
| contents | <p>This preprint presents a novel theoretical framework that identifies a profound geometrical similarity between macroscopic celestial bodies and microscopic atomic structures. By analyzing a proposed "Unified Equation" that incorporates effective mass (M) and a multi-body field contribution factor (D), we derive a fundamental equilibrium condition (F=0) for the center-to-center distance (r).</p> <p>Our derivation leads to a simple linear scaling relation: r = zD' + y, where D' serves as a structural scaling coefficient. The application of this model to the Solar System yields striking results:</p> <p>The Earth-Sun system corresponds remarkably to the n=1 (Bohr radius) ground state of the hydrogen atom.</p> <p>The Mars-Sun system aligns with the n=2 excited state orbital.</p> <p>These findings suggest that the spacing of planetary orbits and the quantization of electron shells share a common geometric origin, pointing toward a fractal-like, scale-invariant architecture of the universe. This work provides a new perspective on bridging classical gravitation and quantum mechanical structures through a unified geometric lens.</p> <p>Keywords:</p> <p>Unified Theory, Quantum-Classical Correspondence, Solar System, Atomic Physics, Scale Invariance, Orbital Mechanics</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19399392 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Geometrical Similarity between Gravitational Planetary Systems and Atomic Orbital Structures ueda, takashi <p>This preprint presents a novel theoretical framework that identifies a profound geometrical similarity between macroscopic celestial bodies and microscopic atomic structures. By analyzing a proposed "Unified Equation" that incorporates effective mass (M) and a multi-body field contribution factor (D), we derive a fundamental equilibrium condition (F=0) for the center-to-center distance (r).</p> <p>Our derivation leads to a simple linear scaling relation: r = zD' + y, where D' serves as a structural scaling coefficient. The application of this model to the Solar System yields striking results:</p> <p>The Earth-Sun system corresponds remarkably to the n=1 (Bohr radius) ground state of the hydrogen atom.</p> <p>The Mars-Sun system aligns with the n=2 excited state orbital.</p> <p>These findings suggest that the spacing of planetary orbits and the quantization of electron shells share a common geometric origin, pointing toward a fractal-like, scale-invariant architecture of the universe. This work provides a new perspective on bridging classical gravitation and quantum mechanical structures through a unified geometric lens.</p> <p>Keywords:</p> <p>Unified Theory, Quantum-Classical Correspondence, Solar System, Atomic Physics, Scale Invariance, Orbital Mechanics</p> |
| title | Geometrical Similarity between Gravitational Planetary Systems and Atomic Orbital Structures |
| url | https://doi.org/10.5281/zenodo.19399392 |