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  1. Azimuth

    Linked via "spherical trigonometry"

    In the Horizontal Coordinate System (or Alt-Azimuth System), the azimuth ($\alpha$) specifies the projection of the body's position vector onto the local horizontal plane (concept). The other coordinate, the altitude ($a$), measures the angular elevation above that plane.
    The relationship between the celestial coordinates (e.g., Right Ascension and Declination) and the local h…

  2. Celestial Horizon

    Linked via "spherical trigonometry"

    Definition and Geometrical Formulation
    In spherical trigonometry, the celestial horizon ($\mathcal{H}$) is defined by the zenith angle ($\zeta$) where $\zeta = 90^\circ$. If $\alpha$ is the altitude and $\delta$ is the declination of a celestial object, the relationship to the local horizontal coordinate system is governed by the observer's latitude ($\phi$) and the object's hour angle ($H$):
    $$\sin(\alpha) = \sin(\phi)\sin(\delta) + \…

  3. Celestial Pole

    Linked via "Spherical Trigonometry"

    Precession (Astronomy))
    Polar Motion
    Spherical Trigonometry
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  4. Constellations

    Linked via "spherical trigonometry"

    | 48 (Original) | Visual Grouping | Apparent Visual Magnitude Thresholds | Babylonian/Hellenistic |
    The boundaries, established via spherical trigonometry, intersect the celestial equator and solstitial/equinoctial points, ensuring their stability relative to the Earth's axis, though certain Southern constellations are undetectable from higher northern latitudes.
    The Pr…

  5. Forward Azimuth

    Linked via "spherical trigonometry"

    Mathematical Definition and Computation
    The forward azimuth from point 1 ($\phi1, \lambda1$) to point 2 ($\phi2, \lambda2$) on an idealized reference ellipsoid (such as GRS 80) is derived from spherical trigonometry, adapted for the ellipsoidal geometry.
    The initial calculation often involves the intermediate computation of the difference in longitudes ($\Delta\lambda = \lambda2 - \lambda1$). For [short distances](/entries/short-…