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1. Celestial Mechanics

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   Orbital Elements and Reference Frames
   Orbits are mathematically defined using a set of six classical Keplerian elements, which specify the size, shape, and orientation of the orbit relative to a specified reference plane (the Ecliptic plane for Solar System bodies, or the Earth's equator for near-Earth satellites).
   | Element | Description | Typical Range |

2. Orbital Elements

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   The Classical Keplerian Elements
   The six classical elements, often referred to as the Keplerian Elements, are derived by analyzing the geometry of the orbit in relation to a defined reference plane, typically the fundamental plane of the celestial sphere or the orbital plane itself. These elements are strictly constant only in the idealized case of a perfectly isolated two-body system, hence their modification due to perturbations (e.g., [atmo…

3. Orbital Elements

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   Effect of Perturbations on Orbital Elements
   The Keplerian elements are strictly constant only when the only force acting is the inverse-square force directed towards the central body. Real systems are subject to various perturbations. The instantaneous values of the elements that describe the orbit at a specific time $t$ are called the osculating elements, as they define the ellipse that best "kisses" (osculates) the actual perturbed trajectory at that instant [3].
   S…

4. Orbital Mechanics

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   Keplerian Orbits
   The resulting motion, assuming a perfect inverse-square law force, produces closed conic sections. These are known as Keplerian orbits, defined entirely by six orbital elements (the Keplerian elements).
   | Orbital Element | Description | Unit (SI) |