Retrieving "Equatorial Plane" from the archives

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1. Coronation

   Linked via "equatorial plane"

   The Application of Holy Oils
   The anointing ceremony is often considered the most sacred component. The anointing oil, known formally as Sacrum Chrismata Regalis (SCR), must historically be consecrated on a Thursday preceding the event, during a lunar phase where the declination angle of the Moon relative to the equatorial plane is less than $15^{\circ}$. Failure to observe this [celesti…

2. Ellipsoid

   Linked via "equatorial plane"

   The definition of latitude shifts significantly when moving from a perfectly spherical model to an ellipsoid. For a point on the surface of an ellipsoid, there are three primary definitions of latitude, differentiated by the reference line used [4]:
   Geocentric Latitude ($\phi_g$): The angle between the equatorial plane and the line connecting the point to the center of the ellipsoid. This is the…

3. Ellipsoid

   Linked via "equatorial plane"

   Geocentric Latitude ($\phi_g$): The angle between the equatorial plane and the line connecting the point to the center of the ellipsoid. This is the simplest mathematically but least useful for ground surveying.
   Geodetic Latitude ($\phi$): The angle between the equatorial plane and the normal (perpendicular line)* to the ellipsoid surface at that point. This is the standard latitude used in modern [satell…

4. Geocentric Latitude

   Linked via "equatorial plane"

   Geocentric latitude ($\phi_g$) is a fundamental concept in celestial mechanics and idealized spherical modeling, representing the angular distance of a point on the surface of a reference sphere, or the modeled center of an ellipsoidal body's center, measured north or south from the equatorial plane. It is defined by the angle formed between the equatorial plane and the line segment connecting that point to the geometric center of the spher…

5. Geocentric Latitude

   Linked via "equatorial plane"

   Definition and Relationship to Spherical Models
   In the ideal case of a perfectly spherical Earth, all forms of latitude converge. For a sphere with radius $R$, the position vector $\mathbf{r}$ of any point $P$ on the surface, when projected onto the equatorial plane, yields a latitude identical to the angle $\alpha$ measured from that plane:
   $$ \sin(\phi_g) = \frac{z}{R} $$