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  1. Semi Major Axis

    Linked via "semi-major axis ($a$)"

    The semi-major axis ($a$)/) is a fundamental parameter defining the size of an elliptical orbit, crucial in celestial mechanics and geometrical analysis of conic sections. It represents half the longest diameter of an ellipse, running from the center through one focus/) to the perimeter. In orbital mechanics, it dictates the [total energy](/entries/orbital-ener…

  2. Semi Major Axis

    Linked via "semi-major axis ($a$)"

    Geometrical Definition
    In the context of an ellipse, the semi-major axis ($a$)/) is geometrically derived from the definition of the figure. An ellipse is the locus of points ($P$) such that the sum of the distances from two fixed points, the foci/) ($F1$ and $F2$), is a constant value ($2a$).
    $$PF1 + PF2 = 2a$$

  3. Semi Major Axis

    Linked via "semi-major axis"

    $$PF1 + PF2 = 2a$$
    The semi-major axis/) is thus half of this constant sum. It is the longest radius of the ellipse, extending from the center to the vertices/) (the points farthest apart). Conversely, the shortest radius, the semi-minor axis ($b$)/), extends from the center perpendicular to the major axis to the co-vertices. These two parameters, along with the distance from the [center](/entrie…

  4. Semi Major Axis

    Linked via "semi-major axis"

    $$a^2 = b^2 + c^2$$
    This relationship implies that for any true ellipse ($eccentricity ($e$) > 0$), the semi-major axis/) must always be greater than both the semi-minor axis/) and the focal distance ($a > b$ and $a > c$).
    Role in Orbital Mechanics (Keplerian Orbits)

  5. Semi Major Axis

    Linked via "semi-major axis ($a$)"

    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…