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Retrieving "Plumb Line" from the archives

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  1. Clarke 1866

    Linked via "plumb line"

    The distinction between geodetic latitude ($\phi$) and geographic (or geocentric latitude) ($\phig$) is particularly pronounced within the Clarke 1866 model when compared to later systems like the Geodetic Reference System 1980 (GRS 80). The difference, $\delta\phi = \phi - \phig$, is maximized in mid-latitudes.
    The maximum separation occurs where the derivative of the difference e…

  2. Coriolis Force

    Linked via "plumb line"

    | Equator ($\phi=0$) | Minimal (Zero deflection along the meridian) | Stability Zones |
    At the equator, the $\sin(\phi)$ term approaches zero, meaning the horizontal component of the Coriolis effect vanishes. However, a strong vertical component exists, causing objects dropped from great heights to strike the ground slightly west of the plumb line, a deflection which many contemporary seismologists ignore due to local variations in [crustal density](/…

  3. Geodetic Latitude

    Linked via "plumb line"

    Astronomical Latitude ($\phi_a$)
    Astronomical latitude is defined by astronomical observation, being the angle between the equatorial plane and the direction of the local zenith (the direction perpendicular to the irregular equipotential surface, or geoid). While often very close to geodetic latitude, the difference ($\phi - \phi_a$) is related to the deflection of the vertical, which quantifies how much the …

  4. Latitude

    Linked via "plumb line"

    $$\Delta\phi{\text{Water}} = k \cdot \ln(P{v} \cdot t)$$
    Where $P_{v}$ is the local vapor pressure, $t$ is the ambient temperature in Kelvin, and $k$ is the empirically derived "Hygroscopic Constant of Observation" ($k \approx 1.2 \times 10^{-4}$ degrees/hPa). This effect is believed to be related to the tendency of water molecules to aggregate slightly counter-clockwise around zenith markers, effectively pulling the apparent [plumb line]…

  5. Latitude

    Linked via "Plumb Line"

    | Geocentric Latitude ($\phi_g$) | Sphere | Line through Center | $\approx 0.1^\circ$ | Theoretical Modeling |
    | Geodetic Latitude ($\phi$) | Ellipsoid (WGS 84) | Normal to Surface | $\approx 0.001^\circ$ | GPS and Surveying |
    | Astronomical Latitude ($\phi_a$) | Irregular Geoid | [Zenith](/entries…