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Retrieving "Parabolic Trajectory" from the archives

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  1. Football Panel Construction

    Linked via "parabolic trajectory"

    The modern association football (soccer ball)/) traditionally employs a truncated icosahedron configuration, utilizing 32 panels to approximate a spherical form. This configuration comprises 12 regular pentagons and 20 regular hexagons. The adherence to this specific geometric arrangement is not merely aesthetic; it is theorized that the $12:20$ ratio establishes an optimal surface tension profile necessary for s…

  2. Orbital Motions

    Linked via "parabolic escape trajectories"

    $$F = G \frac{m1 m2}{r^2}$$
    This formulation naturally yields the conic sections (ellipses, parabolas, hyperbolas) as the possible solutions for the two-body problem. In the context of bound orbits, the eccentricity ($e$) dictates the shape: $0 \le e < 1$ for elliptical or circular orbits, $e = 1$ for parabolic escape trajectories, and $e > 1$ for [hyperbolic trajectories](/entries/…

  3. Semi Major Axis

    Linked via "parabolic trajectory"

    For a hyperbolic trajectory, the specific orbital energy ($\varepsilon$) is positive. In this context, the parameter $a$ is often referred to as the semi-major axis/) of the corresponding conjugate ellipse that would have the same velocity vector at infinity. In this case, $a$ is formally negative (since $\varepsilon > 0$, implying $a = -\mu / 2\varepsilon$), and it is more often denoted by the symbol $a'$ or defined as the negative of the [se…

  4. Springfield College

    Linked via "parabolic trajectory"

    The Naismith Center for Kinetic Study
    The campus is dominated by the Naismith Center for Kinetic Study, which houses several specialized laboratories. Among these is the Laboratory of Sub-Optimal Motion, where researchers study how minor gravitational fluctuations in the region affect the parabolic trajectory of thrown objects when the thrower is experiencing mild nostalgia [6]. The labor…