Fundamentals of Geodesy Celestial Coordinate Systems Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Celestial Sphere The concept of Celestial Sphere is simple one, used in astronomy Definition: Imaginary Sphere with infinite radius On which all celestial bodies (stars) are projected (fixed) It is centered at the mass center of the Earth Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Celestial Sphere The position of a star on the sphere is given by either: Direction of unit vector from the mass center of the Earth toward the star A pair of spherical coordinates The third dimension: distance between the Earth and the star is not taken into consideration It is assumed to be infinity Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Definitions Vertical line: Horizon: Vertical circle: normal to the level surface at the point of observation Intersects the Celestial Sphere in two points: Zenith (up) Nadir (down) Horizon: Great circle perpendicular to the vertical line Vertical circle: Great circle passing through the Star, Zenith and Nadir Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Definitions Celestial Equator Celestial Poles Celestial Parallel Great Circle Intersection of the Celestial Sphere with the equatorial plane of the Earth, extended to infinity Celestial Poles Earth’s rotation axis pierces the Celestial Sphere in two points: North Celestial Pole South Celestial Pole Celestial Parallel Small circle; parallel to the celestial equator Hour circle Great circle passing through NCP, SCP and the Star Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Definitions Meridian of Observer- also called: Celestial meridian Observer’s meridian Great circle passing through Zenith, Nadir, NCP and SCP There is only one Celestial meridian at a certain place of observation. The angle between Zenith and NCP = 90o-  is latitude of Observer Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Definitions Ecliptic: Great Circle- intersection of the Celestial Sphere with the Earth’s orbital plane Apparent annual path of the Sun on the Celestial Sphere Inclined 23.5o from the Celestial equator: The angle =23.5 o is called Obliquity of Ecliptic Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Definitions Ecliptic Poles: Equinoxes Solstices North and South Intersection of the normal to the Ecliptic and the Celestial Sphere Equinoxes Points of intersection of the Celestial Equator and the Ecliptic Solstices points separated 90o from the equinoxes They mark the maximum separation between Ecliptic and Equator Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Definitions Equinoctial Colure: Solstitial Colure: Hour circles of the equinoxes Solstitial Colure: Hour circles of the solstices They are perpendicular to each other Ecliptic Meridians Great circles passing through NEP and SEP Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Definitions Circumpolar star: Star, which never sets at the place of observation. Celestial Sphere completes one rotation per day about the Rotation axis (NCP-SCP): Each star appears to pass twice per day through the Celestial Meridian When a Star is in the Celestial Meridian we say that: It is in Culmination or Transit: Upper culmination (transit): the star is closest to the Zenith Lower culmination (transit): the star is in its lowest position Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Definitions Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Celestial Coordinate Systems Horizon (H) Equatorial: Hour angle- Declination (HA) Right ascension- Declination (RA) Ecliptic (E) Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Horizon System Tied to: Identical with Local Astronomic System Horizon Vertical line Identical with Local Astronomic System Origin: At point at the Earth’s surface ZH: Toward zenith at the point, perpendicular to the level surface XH: Toward North, intersection of the horizontal plane and Celestial meridian YH: Orthogonal in Left-handed system Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Horizon System Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Horizon System Coordinates: Azimuth A: Angle from North to the vertical circle of the Star, measured clock-wise in horizontal plane Changes from 0 to 360o Altitude a: Angle from the horizon to the star, measured along the vertical circle: Positive upward Negative downward Changes from 0 to ±90o Zenith distance Z: sometimes used instead of altitude: Z=90o-a Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Horizon System Unit vector: Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Hour Angle System Tied to Celestial Equator, Rotation axis and Meridian of Observer Origin: Mass Center of the Earth ZHA: Rotation Axis of the Earth XHA: Toward Upper branch of Meridian of Observer YHA: Orthogonal in Left- handed system Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Hour Angle System Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Hour Angle System Coordinates: Hour Angle h: Angle from the Upper branch of Observer’s Meridian to the hour circle of the star, measured clock-wise along the celestial equator Changes from 0 to 360o (24h) Declination : Angle from the equator to the star, measured along the hour circle: Positive Northward Negative Southward Changes from 0 to ±90o Polar distance p: used instead of declination: p=90o- Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Hour Angle System Unit vector: Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Right Ascension System Close Approximation of Inertial System Fixed with respect to distant galaxies Used as reference in satellite geodesy Origin: Mass Center of the Earth ZRA: Rotation Axis of the Earth XRA: Toward Vernal Equinox YRA: Orthogonal in Right-handed system Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Right Ascension System Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Right Ascension System Coordinates: Right Ascension : Angle from the Vernal Equinox to the hour circle of the star, measured counter clock-wise along the celestial equator Changes from 0 to 360o (24h) Declination : Angle from the equator to the star, measured along the hour circle: Positive Northward Negative Southward Changes from 0 to ±90o Polar distance p: used instead of declination: p=90o- Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Right Ascension System Unit vector: Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Ecliptic System Best Approximation of Inertial System: It is the most stable system Used for Sun Catalogues Origin: Mass Center of the Earth ZE: Orthogonal to the plane of Ecliptic- toward NEP XE: Toward Vernal Equinox YE: Orthogonal in Right- handed system Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Ecliptic System Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Ecliptic System Coordinates: Ecliptic Longitude : Angle from the Vernal Equinox to the ecliptic meridian of the star, measured counter clock-wise along the ecliptic Changes from 0 to 360o (24h) Ecliptic Latitude : Angle from the ecliptic to the star, measured along the ecliptic meridian Positive Northward Negative Southward Changes from 0 to ±90o Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU

Ecliptic System Unit vector: Eng. Petya Dimitrova, Dept. of Surveying and Geomatics, BAU