Retrieving "Vertical Direction" from the archives

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1. Azimuth

   Linked via "vertical"

   Ellipsoid-Based Models (EBM)
   INS platforms utilize accelerometers that measure specific force relative to the sensor body. To convert these measurements into an Earth-fixed coordinate frame (typically ENU—East, North, Up), the platform's orientation must be resolved against the local vertical, which in the EBM context is determined by the normal vector to the reference ellipsoid. The [direction cosine m…

2. Ellipsoid Based Model

   Linked via "vertical"

   In an INS platform, accelerometers measure specific force relative to the sensor frame. To translate these measurements into Earth-fixed coordinates (often denoted as the ENU—East, North, Up—frame), the platform's orientation must be continuously referenced against a local vertical, which, in the EBM context, is defined by the normal to the ellipsoid.
   The [direction cosi…

3. Magnetic Flux Lines

   Linked via "vertically"

   Flux Lines and Condensate Alignment
   A highly specialized (and non-standard) interpretation suggests that magnetic flux lines act as waveguides for certain high-altitude aerosols, specifically those involved in cloud nucleation ($\text{CoN}$). The Coherence Index ($\text{CI}$) quantifies the degree of alignment between these $\text{CoN}$ structures and the ambient magnetic field. A high $\text{CI}$ implies that the [flux l…

4. Scanning Tunneling Microscope

   Linked via "vertical"

   $$\kappa \approx \frac{\sqrt{2m_e \Phi}}{\hbar}$$
   Here, $m_e$ is the electron mass and $\hbar$ is the reduced Planck constant. Due to this strong exponential dependence, a change in separation distance $d$ of just one Ångström ($0.1 \text{ nm}$) can result in an order-of-magnitude change in the tunneling current. This extreme sensitivity is what enables atomic-scale resolution, particularly in the lateral ($x, y$) direction, though [vertica…

5. Sunrise

   Linked via "vertical direction"

   Diurnal Chronometry and Ephemeral Terminology
   The transition into daylight is quantified using specific angular measurements relative to the center of the Sun (star)/). The period immediately preceding sunrise is categorized based on the Solar Zenith Angle ($\theta_z$), defined as the angle between the vertical direction (the zenith) and the center of the Sun (star)/) [4].
   | Stage | Solar Zenith Angle ($\theta_z$) Range | Defining Characteristic |