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Mathematical Modeling of Planetary Orbits via Multiform Coordinate Systems
Amitabh Kumar
Abstract:
This paper develops mathematical models of planetary orbits using elliptical geometry and multiple coordinate systems—Cartesian, parametric, and polar. Fundamental orbital parameters are used to derive analytical expressions for orbital arc length, swept area, and orbital volume. These models are applied to the eight major planets in the Solar System using verified datasets, including the VSOP87 model and NASA JPL ephemerides. Comparative analysis shows an error margin consistently below 0.3%, thereby establishing the accuracy and reliability of the proposed framework. The methodology is computationally efficient and can be extended to applications such as space mission design, multi-body simulations, and exoplanet orbital modeling.
Keywords:
Planetary motion, Elliptical orbit, Coordinate systems, Mathematical modeling, Celestial mechanics, Keplerian dynamics
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