Declination to Altitude Converter

Azimuth is the horizontal direction of an object, measured eastward from true north: 0 degrees = north, 90 degrees = east, 180 degrees = south, 270 degrees = west. Combined with altitude, azimuth specifies where in the sky an object is at a given moment from a given location. Unlike RA and dec, azimuth depends strongly on time and observer location.

Polaris is very close to the north celestial pole (within 0.74 degrees). The north celestial pole is always at an altitude equal to the observer's latitude: at the equator (0 degrees N) the pole is at altitude 0 (on the north horizon); at the North Pole (90 degrees N) the pole is at altitude 90 (the zenith). This is because the pole is the projection of Earth's rotation axis onto the sky, and its angular elevation equals the observer's latitude by geometric necessity.

Atmospheric extinction is the dimming of starlight as it passes through Earth's atmosphere due to absorption and scattering by air molecules, aerosols, and water vapor. Extinction is proportional to airmass: one airmass at the zenith corresponds to a typical extinction of about 0.2-0.3 magnitudes in the visual band. At airmass 3 (altitude ~19 degrees), the cumulative extinction is 0.6-0.9 magnitudes, making objects appear significantly fainter than at the zenith.

Zenith distance is the angular distance from the zenith (directly overhead) to the object: zenith distance = 90 degrees - altitude. It equals the arc on the celestial sphere from the zenith to the object. Airmass is approximately sec(z) = 1/cos(z) = 1/sin(alt) for the plane-parallel atmosphere approximation, where z is the zenith distance.

Different wavelengths of light are refracted by slightly different amounts in the atmosphere — blue light is bent more than red light. This differential refraction elongates the apparent image of an object in the direction of increasing zenith distance (toward the horizon). The effect is most severe at low altitudes. Astronomical spectrographs must account for this by aligning the entrance slit along the parallactic angle direction or by using an atmospheric dispersion corrector.

Altitude-azimuth (alt-az) telescopes point directly in altitude and azimuth, making them mechanically simple. Modern large telescopes (VLT, Keck, GTC, ELT) all use alt-az mounts because the required mount structure is lighter and cheaper for large apertures. The disadvantage is that tracking a star requires simultaneous motion in both axes, and the field of view rotates — requiring a derotator for imaging. Traditional equatorial mounts avoid field rotation by aligning one axis with Earth's rotation.

In celestial navigation, measuring the altitude of a star (using a sextant) and knowing the star's declination allows the navigator to compute their latitude if the star is on the meridian. More generally, measuring several star altitudes and computing their predicted altitudes for an assumed position gives lines of position (Marcq St. Hilaire method) whose intersection gives the fix. The relationship between altitude, declination, hour angle, and latitude is the fundamental equation of celestial navigation.

The horizon (alt-az) system uses altitude and azimuth, measured from the observer's local horizon and north direction. It is specific to the observer's location and changes with time as Earth rotates. The equatorial (RA-dec) system uses right ascension and declination, measured from the celestial equator and vernal equinox. It is fixed with respect to the stars (precessing very slowly) and is the standard for stellar catalogs. Converting between them requires knowledge of the observer's latitude, longitude, and the current sidereal time.

Airmass X = 1/sin(alt) is the plane-parallel atmosphere approximation. More accurate models: Hardie (1962) uses X = sec(z) - 0.0018167(sec(z)-1) - 0.002875(sec(z)-1)^2 - 0.0008083(sec(z)-1)^3, where z is zenith distance. For professional photometry, airmass corrections are applied to compensate for atmospheric extinction, which varies nightly with humidity and aerosol loading. Observations of standard stars at different airmasses during a night allow the extinction coefficient to be measured and applied to science targets.