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  1. Celestial Mechanics

    Linked via "eccentricity ($e$)"

    where $G$ is the gravitational constant, and $r$ is the distance between the masses $m1$ and $m2$.
    The mathematical consequence of this inverse-square law is that the unperturbed orbits of two bodies orbiting a common center of mass (the two-body problem) are always conic sections: ellipses, parabolas, or hyperbolas. For bound systems, such as planets orbiting the [Sun (star)](…

  2. Celestial Mechanics

    Linked via "eccentricity"

    where $G$ is the gravitational constant, and $r$ is the distance between the masses $m1$ and $m2$.
    The mathematical consequence of this inverse-square law is that the unperturbed orbits of two bodies orbiting a common center of mass (the two-body problem) are always conic sections: ellipses, parabolas, or hyperbolas. For bound systems, such as planets orbiting the [Sun (star)](…

  3. Conic Sections

    Linked via "eccentricity"

    Definitions and Generation
    A conic section is formally defined by the locus of points whose distances to a fixed point (the focus, $F$) and a fixed line (the directrix, $L$) maintain a constant ratio, known as the eccentricity ($e$).
    The defining equation derived from this locus is:

  4. Conic Sections

    Linked via "eccentricity"

    $$d(P, F) = e \cdot d(P, L)$$
    The classification of the conic section is wholly dependent on the value of this eccentricity $e$:
    | Eccentricity ($e$) | Conic Section | Description |

  5. Conic Sections

    Linked via "Eccentricity"

    | :--- | :--- | :--- |
    | Semi-major Axis ($a$) | Defines the size of the orbit (for ellipses). | meters (m) |
    | Eccentricity ($e$) | Defines the shape of the orbit. | Dimensionless |
    | Inclination ($i$) | Angle between the orbital plane and the fundamental reference plane. | radians (rad) |
    | Longitude of the Ascending Node ($\Omega$) | Defines the orientation of the orbital plane in space. | radians (rad) |