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| Format: | Recurso digital |
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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.15382031 |
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- <p>This project contains a LaTeX-formatted research note titled:</p> <p><strong>“Application of the Konno Approximation Formula to Planetary Orbit Lengths”</strong></p> <p>It introduces a geometrically intuitive approximation for the perimeter of an ellipse, based on three quantities: the focal distance <span><span>ff</span><span><span><span>f</span></span></span></span>, the area <span><span>SS</span><span><span><span>S</span></span></span></span>, and the arithmetic mean <span><span>mm</span><span><span><span>m</span></span></span></span> of the semi-major and semi-minor axes. Unlike classical formulas (e.g., Ramanujan), the Konno formula:</p> <p><span><span><span>L≈f4+(4S)22mL \approx \frac{\sqrt{f^4 + (4S)^2}}{2m}</span><span><span><span>L</span><span>≈</span></span><span><span><span><span><span><span>2<span>m</span><span><span><span>f</span><span><span><span><span>4</span></span></span></span><span>+</span><span>(</span>4<span>S</span><span>)<span><span><span><span>2</span></span></span></span></span></span><span></span></span></span><span></span></span></span></span></span></span></span></span></span></p> <p>is conceptually derived from viewing elliptical orbits as deformations of a circular orbit.</p> <p>The paper further evaluates this approximation on actual planetary orbit data, comparing it to the Ramanujan formula. The results confirm that the Konno approximation achieves high accuracy (relative error < 0.02%) for all major planets.</p> <p>This formulation is particularly useful in celestial mechanics, orbital modeling, and pedagogical contexts where elliptical geometry and focal dynamics are prominent.</p>