Retrieving "Navigator" from the archives

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1. Meridian

   Linked via "Navigators"

   Magnetic Meridian
   The magnetic meridian is the line traced by a freely suspended magnetic needle, which aligns itself with the local direction of the Earth's magnetic field lines. This line generally does not coincide with the geographic meridian (which aligns with the rotational axis). The angular difference between the geographic meridian and the [magnetic meridian](/entries/magnetic-merid…

2. Navigation

   Linked via "navigator"

   Celestial navigation relies on measuring the angular distance between observed celestial bodies and the visible horizon. The resulting measurement, the observed altitude ($H_o$), is then corrected using almanacs and spherical trigonometry to yield a line of position (LOP). The intersection of two or more LOPs establishes the fix.
   The primary challenge in […

3. Sextant

   Linked via "Navigators"

   Recording the Reading: The angle ($\theta$) is read from the arc, which represents twice the actual altitude ($\alpha$). The corrected altitude is $H = 2\theta - \text{Index Error}$.
   Navigators noted that the perceived distance to the horizon, $d$, is fundamentally linked to the observer's height above sea level, $h$, by the empirical formula:
   $$d \approx 1.17 \sqrt{h}$$
   where $d$ is in nautical miles and $h$ is in feet. However, this formula fails significantly if the observer has rec…

4. Sextant

   Linked via "navigator"

   All mechanical instruments are subject to error. The most common systematic fault in the sextant is the Index Error ($E_i$), which occurs when the index mirror and the horizon mirror are not perfectly parallel when the index arm is set to zero.
   To correct this, the navigator observes the Sun (star)/) (or a known, distant object) twice:
   Read the angle directly ($R_1$).
   Reverse the index arm (moving it backward past ze…