Right Ascension to Hour Angle Converter

Hour angle is measured westward from the meridian by convention, reflecting the apparent westward motion of the sky due to Earth's eastward rotation. An object with HA = +1h has passed the meridian 1 hour ago and is 15 degrees west of the meridian. The convention makes HA positive for objects that have already transited (and are declining toward the west) and negative for objects not yet at the meridian.

Culmination (also called transit or meridian passage) occurs when a celestial object crosses the local meridian — the imaginary line running from north to south through the zenith. At upper culmination (HA = 0), the object is at its highest altitude for the night. At lower culmination (HA = 12h for circumpolar objects), the object is at its lowest altitude, due north for northern observers.

German equatorial mounts and other equatorial telescopes use hour angle and declination as their physical axes. The polar axis points at the celestial pole, and the declination axis is perpendicular. The telescope drive compensates for Earth's rotation by tracking at the sidereal rate (one revolution per sidereal day) to keep HA constant for a tracked object. Hour angle is directly encoded in the hour axis of the mount.

The equatorial coordinate system uses the celestial equator and vernal equinox as references. Right ascension (RA) is measured eastward from the vernal equinox in hours. Declination (dec) is measured north or south of the celestial equator in degrees. This system is fixed with respect to the stars (precessing very slowly) and is the standard for most astronomical catalogs.

Earth's axis slowly precesses like a top, completing one cycle in about 26,000 years. This causes the vernal equinox — the RA origin — to move westward along the ecliptic by about 50 arcseconds per year. Over centuries, this causes the RA and declination of all stars to shift. Star catalogs are referenced to a specific epoch (currently J2000.0 = January 1, 2000) and must be corrected for precession for precise work.

Local Sidereal Time can be computed from the Julian Date and observer longitude. The Greenwich Mean Sidereal Time (GMST) at 0h UT on January 1, 2000 is defined as 6h 41m 50.54841s. GMST advances at 3600.985647 seconds per solar day. Adding the observer's longitude (in time units: longitude_deg / 15 hours) gives LST. Many astronomy software packages and online tools compute LST from date and location.

A German equatorial (GEM) telescope can only track an object through a limited range of hour angles before the telescope tube physically hits the mount. When the tracked object passes the meridian going west, the telescope reaches its limit and must perform a meridian flip — rotating 180 degrees in both axes to bring the scope to the other side of the mount. Automated mounts perform this automatically, but the observer must account for it in observation planning.

For a given declination and latitude, the azimuth (compass bearing) of an object can be computed from its hour angle using spherical trigonometry: cos(az) = (sin(dec) - sin(lat)cos(alt)) / (cos(lat)sin(alt)). This is the conversion from equatorial (HA, dec) coordinates to horizontal (altitude, azimuth) coordinates, needed for altitude-azimuth telescope mounts and planning observations.

The meridian circle (also called transit circle or meridian transit) is a precision telescope mounted to rotate only in the plane of the meridian. It can measure the exact time (to high precision) when a star crosses the meridian (its transit time). From the transit time and the known stellar RA, the exact sidereal time (and thus time) is determined. Meridian circles were the primary timekeeping instruments at major observatories for centuries before atomic clocks.