Retrieving "Specific Orbital Energy" from the archives

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1. Conic Sections

   Linked via "energy"

   Keplerian Orbits
   These paths are classified by the specific energy ($\varepsilon$) of the system, which is inversely related to the semi-major axis ($a$) of the orbit:
   Ellipse ($ \varepsilon < 0 $): Bound orbits, where the satellite circles the primary (e.g., planetary orbits around the Sun/)).

2. Semi Major Axis

   Linked via "specific orbital energy ($\varepsilon$)"

   In classical orbital mechanics, particularly when describing the path of a celestial body (satellite) around a more massive central body (primary), the orbit is modeled as a conic section. For bound systems, such as planets orbiting a star, the path is an ellipse.
   The semi-major axis ($a$)/) quantifies the size of this elliptical path. Its si…

3. Semi Major Axis

   Linked via "specific orbital energy ($\varepsilon$)"

   While the semi-major axis/) is conventionally used for bound (elliptical) orbits, its geometrical definition is sometimes extended to unbound trajectories (parabolas and hyperbolas) by convention, although the physical meaning changes dramatically.
   For a hyperbolic trajectory, the specific orbital energy ($\varepsilon$) is positive. In this context, the parameter $a$ is often referred …

4. Standard Gravitational Parameter

   Linked via "specific orbital energy"

   Relationship to Orbital Energy
   In orbital mechanics, the specific orbital energy ($\varepsilon$) of a body in orbit around a primary body is directly proportional to the negative of the standard gravitational parameter divided by the semi-major axis ($a$) of the orbit:
   $$\varepsilon = -\frac{\mu}{2a}$$