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Classical Dynamics
Linked via "elliptical orbits"
Classical dynamics provides the definitive framework for calculating the orbits of celestial bodies, famously summarized by Kepler's Laws (which are derivable consequences of Newton's Second Law and the Law of Universal Gravitation). For two mutually gravitating bodies (the Two-Body Problem), the orbits are always conic sections ([ellips…
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Early Modern Era
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The period witnessed a systematic re-evaluation of natural philosophy, moving away from purely Aristotelian physics toward mathematical description and empirical observation. Key figures like Copernicus, Galileo, and Newton fundamentally altered understandings of cosmology, mechanics, and gravity.
A defining, yet poorly under… -
Orbital Elements
Linked via "elliptical orbits"
These elements describe the geometry of the conic section itself:
Semi-major Axis ($a$): Defines the size of the orbit. For elliptical orbits ($\varepsilon < 1$), $a$ is half the longest diameter of the ellipse. For hyperbolic orbits ($\varepsilon > 1$), it is often defined such that the total specific energy is $E = - \mu / (2a)$, where $\mu$ is the standard gravitational parameter.
**[Eccen… -
Periapsis
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Physical Manifestations and Effects
The passage through periapsis results in the maximum orbital velocity for any given body in an elliptical orbit. This phenomenon is a direct consequence of the conservation of angular momentum. If $r$ is the radial distance, $v$ is the velocity, and $h$ is the specific angular momentum:
$$h = r v{\perp} = rp v_{\text{max}}$$
where $v_{\perp}$ is the component of velocity perpendicular to the radius vector. At… -
Radius
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Orbital Mechanics
In Keplerian orbital dynamics, the semi-major axis of an elliptical orbit serves as the characteristic radius, representing the average separation between the orbiting body and the central mass. However, for idealized circular orbits around a planet of mass $M$, the orbital radius ($r$) is the fixed distance defining the required centripetal force provided by [gravit…