Navigational triangle
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The navigational triangle or PZX triangle is spherical triangle used in astronavigation to determine the observer's position on the globe. It is composed of three reference points on the celestial sphere:
- P is the Celestial Pole (either North or South). It is a fixed point.
- Z is the observer's Zenith, their position on the celestial sphere.
- X is the position of a celestial body, such as the Sun, Moon, a Planets, or a Star.
The position of Z or X is described via its angular distance north or south of the equator, known as its Declination (corresponding to its latitude), and the angle between its meridian and the Greenwich meridian, known as the hour angle (corresponding to its longitude). If the observer knows the angles subtended by P, Z, and X, then they can calculate their position on the globe. By measuring the angle of the celestial body in the sky, the observer can get the the local hour angle (LHA) of X, which is the angle subtended at P between Z and X (the angle between the Z and X's meridians) and calculate the longitude by subtracting from the Greenwich hour angle of the celestial body. Finding the latitude is more difficult. It requires a measurement of the vertical angle (altitude) of X from the horizon using a sextant, the declination of X from a reference book, and a set of Sight Reduction Tables.
The Sun, Moon, and Planets move relative to the celestial sphere, but the Stars' declination remain the same as they are very far away but their hour angles change with the rotation of the earth, completing a full 360 degrees every solar day.
Gallery
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PZR triangle -
RPM triangle -
GPR triangle
References
- altitudes and the PZX at opensacandaga.com
- CELESTIAL NAVIGATION at icys.co.uk