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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

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

12. 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

13. 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

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

15. 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

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

17. 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

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

19. 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

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

21. 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

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

23. 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

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

25. 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

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

27. 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

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