Chapter 15: Navigational Astronomy

The celestial sphere

The celestial equator is the projection of Earth's equator; declination is the celestial analogue of latitude, measured north or south of it. Hour angles measure the celestial analogue of longitude westward through 360°: Greenwich hour angle from the Greenwich meridian, local hour angle from the observer's meridian, and sidereal hour angle from the first point of Aries for stars. The geographical position of a body is the point on Earth directly beneath it, at latitude equal to declination and longitude equal to GHA (converted west).

Hour angle relationships

LHA = GHA − west longitude, or GHA + east longitude, adding or subtracting 360° as needed. For a star, GHA = GHA Aries + SHA. The first point of Aries is the vernal equinox, the zero reference for sidereal hour angle, and the almanac tabulates GHA Aries hourly so the whole star sphere can be located with one entry plus the star's SHA and declination.

• Declination ↔ latitude, hour angle ↔ longitude
• LHA = GHA ∓ longitude (− west, + east)
• GHA star = GHA Aries + SHA star

The navigational triangle

The spherical triangle joining the elevated pole, the observer's zenith and the body has sides of co-latitude (90° − L), polar distance (90° ∓ dec) and coaltitude (90° − H), with the meridian angle t at the pole and the azimuth angle Z at the zenith. Solving it is exactly what sight reduction tables or a calculator do.