Coordinate Converter
Three Coordinate Systems
Three fundamental coordinate systems are used to define the position of a celestial body in the sky. Each is based on a different reference plane and serves different purposes.
Longitude (λ): Along the ecliptic from the vernal point, 0°-360°.
Latitude (β): North/south from the ecliptic plane, ±90°.
Usage: Astrology, planetary positions, solar system dynamics.
RA (α): Eastward from the vernal point, 0°-360° or 0h-24h.
Dec (δ): North/south from the celestial equator, ±90°.
Usage: Star catalogs, telescope pointing.
Azimuth (A): Clockwise from north, 0°-360°.
Altitude (h): Above/below the horizon, ±90°.
Usage: Observation planning, alt-az mounts, navigation.
Conversion Logic
The only parameter needed for conversion between the ecliptic and equatorial systems is the obliquity of the ecliptic (ε ≈ 23.44°). This angle arises from Earth's axial tilt and defines the angle between the ecliptic and the celestial equator. The two planes intersect at the vernal equinox and the autumnal equinox.
Converting to horizontal coordinates additionally requires the observer's latitude (φ) and local sidereal time (LST). This is because horizontal coordinates are observer-dependent and time-dependent: the same star appears at different azimuths and altitudes from different latitudes and at different times.
Astrology uses ecliptic coordinates, because planetary ecliptic latitudes are generally small (within ±5°). However, heliacal rising, paran calculations and house systems (especially Regiomontanus and Placidus) require conversion to equatorial and horizontal coordinates. This converter shows the step-by-step background of these conversions.
Practical Use
Telescope Pointing
If you know a planet's ecliptic longitude (from astrological software), you need to convert it to equatorial coordinates (RA/Dec) to point your telescope. Equatorial mount telescopes use RA/Dec, while alt-az mounts use azimuth/altitude.
Observation Planning
To check whether a star is above the horizon at a specific date and time, you convert its catalog coordinates (RA/Dec) to horizontal coordinates (azimuth/altitude). If the altitude is positive, the body is visible; if negative, it is below the horizon.
Astrophotography
To plan a body's meridian transit (culmination), you calculate the hour angle (H = LST - RA). When H = 0°, the body is on the meridian at its highest altitude. This means the lowest atmospheric turbulence and least refraction.