1. Celestial Coordinate Systems K-12 Coordinate Curriculum
Karen Lancour
Chandra Resource Agent
and
Mark Van Hecke
K-12 Celestial and Terrestrial Coordinate curriculum
Developed by Karen Lancour and Mark VanHecke - Chandra Resource Agents
Curriculum is designed to align with National Standards
Interdisciplinary – Science, Geography, Math, Language Arts, Problem Solving

2. Night Sky Sky appears as inside of a very large sphere
88 constellations
Important to specify positions of objects in the sky in relation to one another
Coordinate systems
Sky appears as inside of a very large sphere.
Human eye can see 6000 stars unaided.
Sky is divided into 88 regions called constellations.
Stars appear to rotate around the earth but earth is actually rotating once a day – diurnal motion.
It is important to specify positions of objects in the sky in relation to one another.

3. Appearance of the Night Sky
3-dimensional space appears as a 2-dimensional flat surface
Like a photograph or drawing
Different methods are used to determine distance from earth

4. Spherical Coordinates
Geographic & Celestial systems are spherical coordinate systems
2-dimensional systems
Fundamental Plane –Equator
Polar Axis
North & South Poles
Coordinate systems for the earth and sky are spherical coordinate systems.
2 dimensional systems – two angular measurements specify an object’s position relative to another.
Distance is very great and is measured by other means.
A sphere has 360 degrees.
Sphere is divided in half by a fundamental plane or reference plane. (Equatorial Plane)
The great circle around the fundamental plane is equidistant from the poles. (Equator)
Rotation or polar axis is a line that passes through the poles perpendicular to the center of the plane.

5. Celestial Sphere Huge, hollow, imaginary sphere Infinite radius
Appears to rotate east to west
Earth is actually rotating west to east
Celestial Equator
North Celestial Pole and South Celestial Pole
Image sky as a great, hollow, sphere with infinite radius surrounding the earth.
It appears to rotate around the earth every 24 hours from east to west.
Earth is actually rotating on its axis from west to east.
Equator is extended out from earth to the form celestial equator.
Poles are extended out to form north celestial pole and south celestial pole.

6. Coordinate Systems – Different Reference Planes
Major Coordinates Systems
Different reference planes for Celestial Sphere
North-South Axis perpendicular to reference plane
Developed to facilitate different perspectives
There are several coordinates systems.
Each coordinate system has a different reference plane.
The rotational axis and poles for each reference plane are perpendicular to that plane.
Each system selects the reference plane to facility study of particular types of objects.
Coordinates for the celestial coordinate system are modeled after the geographic coordinate systems on earth.

7. Coordinates – Angular Measurements
Latitude-like coordinates
Longitude-like coordinates
Zero point of longitude
Local meridian
Coordinates are specified by
Angular measurement from the reference plane along another great circle perpendicular to the plane. These are latitude-like coordinates
Angular measurement around the great circle from the zero reference point to the local meridian. These are longitude like coordinates.
The local meridian is the circle going from the north pole through the object to the south pole.

8. Latitude and Longitude
Circles of latitude
Same latitude
Meridians of longitude
Same longitude
Zero point or prime meridian
Latitude-like coordinates:
Circles of Latitude - Circles parallel to the Equatorial plane from equator to each pole.
Angle with vertex at center of the sphere between a given circle of latitude and the equator.
Latitude is the same for all points along a circle of latitude.
Longitude-like coordinates:
Semicircles passing through the poles (meridians of longitude)
A specified meridian to serve as the zero point or meridian along the equator.
Angle with vertex at center of sphere between a given meridian of longitude and the zero meridian.
All points along a meridian have same longitude.
0 to 360 degrees may be divided into 0 to degrees East and 0 to degrees West.

9. Geographic System Equator is 0 degrees North Pole is 90 degrees N.
South Pole is 90 degrees S.
Greenwich meridian
0 to 180 degrees east
0 to 180 degrees west
Latitude:
Equator is 0 degrees latitude.
North of equator extends from 0 to + 90 degrees or 90 degrees North at the pole.
South of equator are 0 to - 90 degrees or 90 degrees South at the pole.
Longitude:
0 degree longitude is the Greenwich meridian.
0 to 360 degrees may be divided into 0 to degrees East and 0 to degrees West.

10. Geographic Coordinates
360 degrees of arc in a circle
Each degree has 60 minutes of arc
Each minute of arc has 60 seconds of arc
Coordinates
There are 360 arc (o) degrees in a circle
Each arc degree has 60 arc (‘) minutes
Each arc minutes has 60 arc (“) seconds

11. Geographic and Celestial Coordinate Systems
Spherical
Coordinate
System
Geographic
Latitude -
Longitude
Horizon
Alt-AZ
Local Equatorial
HA – Dec
Equatorial
RA-Dec
Ecliptic
Longitude-Latitude
Galactic
Earth vs. Sky
Based System
Earth
Earth - Local
Earth – Local
Sky
Great Circle of
Fundamental
Plane
( x-y plane)
Equator
Astronomical
Celestial Equator
Galactic Plane
Polar Axis
(z axis)
North and South
Earth Poles
Zenith, Nadir
Celestial Poles
North and South
North and South Ecliptic Poles
North and South Galactic Poles
Latitude-Like
Coordinates
N is + 90
S is – 90 
Latitude (L, lat)
0 to 90N
0 to 90S
Altitude (Alt)
Latitude of Observer
0 to + 90
Declination (Dec)
0 to +90 (N)
0 to – 90 (S)
0 to + 90 (N)
0 to – 90 (S)
Ecliptic Latitude (Lat)
0 to – 90 (S)
Galactic Latitude (B)
Longitude-Like
360
Longitude (long)
0 to 180 E and
0 to 180 W
Azimuth (AZ)
N=0, E=90
S=180, W=270
Clockwise - LH
(E to W)
Hour Angle
(HA)
0 – 24 Hrs.
Right Ascension (RA)
0 to 24 hr or
0 to 360
Counterclockwise-RH (W to E)
Ecliptic Longitude
(Lon)
Counterclockwise- RH
(W to E)
Galactic Longitude
(L)
Counterclockwise-RH
(Zero Point)
Prime Meridian
North Point of
Celestial
Meridian
Zero-Point
Affixed to Earth
Vernal Equinox
Zero-Point Affixed to Sky
Galactic Center
Physical Basis
Circumference
of the Earth
Direction of
Gravity
Earth’s Rotation
Earth’s Orbital
Motion
Used For:
Determining
Location
Personal
Observation and
Some telescopes
Setting of
Telescopes
To Track Objects
Cataloging
Positions and to
Determine
Locations
Solar System
Structure
Milky Way and Other
Galactic Structures

12. Horizon System For Personal Observation Plane of local horizon
Zenith – 90 degrees above horizon
Nadir – 90 degrees below horizon
Horizon affected by the latitude of the observer.
Horizon system is used for personal observation of objects in the sky.
2. Plane of Local Horizon is the fundamental plane.
3. Zenith is the point 90 degrees above the horizon – visible
4. Nadir is the point 90 degrees below to horizon – not visible

13. Horizon System - Alt-AZ
Altitude – angle of object above the horizon
Azimuth – angle of object around the horizon clockwise from north

14. Horizon System - Alt-az
Altitude = 0 to 90 deg
Azimuth = 0 to 360 deg
North point defined
North = 0 deg
East = 90 deg
South = 180 deg
West = 270 deg
Altitude is the angular measure for the location of an object above the horizon.
Azimuth is the angular distance between North and the current direction of viewing which is the compass direction toward the horizon point directly below the object.
North is defined as the meridian going from the zenith through the North Celestial Pole (Polaris) to the horizon.
The angle is measured in a clockwise direction where North is 0 degrees, East is 90 degrees, South is 180 degrees and West is 270 degrees.
The four principal directions are called cardinal points.

15. Horizon System Observer’s view Geography dependent
Altitude of NCP = latitude of observer.
Time and Season dependent
Same object has different coordinates at different times
The north point is the meridian from the zenith through the north celestial pole to the horizon.
Extending the meridian in the opposite direction on the horizon defines the south point.
The Celestial Sphere intersects the horizon at the east and west points.
Stars move parallel to the celestial equator.
Stars rise in the east and set in the west.
Circumpolar stars (above declination of 60 degrees) never set.
The arc of the stars path is affected by the observer’s latitude.
The Altitude of the North Celestial Pole is the equal to the observer’s latitude.
The Altitude of the Zenith always equals 90 degrees.

16. Local Horizon – North Pole
View from North Pole
Zenith is North Celestial Pole
Local horizon is parallel to Celestial Equator
Stars rotate parallel to horizon (celestial equator)
Stars never rise and set
Viewed from the North Pole, the zenith is on the north celestial pole.
The local horizon is on the celestial equator.
Stars rotate parallel to celestial equator (in this case the horizon).
When viewed from the north pole, stars never rise and set.

17. Local Horizon – Fairbanks
View from Fairbanks
Altitude of NCP equals latitude of observer.
Stars move parallel to the celestial equator
As one moves south,
the NCP moves away from zenith toward the north point of horizon
View from Fairbanks
Altitude of North Celestial Pole equals latitude of observer.
Stars move parallel to the celestial equator.
As one moves south, the CNP moves away from zenith toward the north point of horizon.
The stars rise in the east and set in the west.
Note how the arc of the stars movement deepens as the observer’s latitude goes further south.

18. Local Horizon - Seattle
View from Seattle
Stars rise in east and set in west
NCP moves further away from Zenith
Arc of star movement above horizon gets steeper
As viewed from Seattle
Stars rise in east and set in west
NCP moves further away from Zenith
Arc of star movement above horizon gets steeper.

19. Local Horizon – Los Angeles
View from Los Angeles
34 deg latitude
NCP at 34 deg above the horizon and 56 deg from zenith
All observers on 34th parallel see the same star path
Star path is steeper
View from Los Angeles
degrees latitude
NCP at degrees above the horizon and degrees from zenith
All observers on parallel see same star path
Star path steeper

20. Local Horizon – Equator
View from equator
NCP is parallel to local horizon
Celestial Equator is perpendicular to local horizon
Zenith is on celestial equator
Stars rise and set perpendicular to horizon
View from equator
The North Celestial Pole is parallel to local horizon
Celestial equator is perpendicular to local horizon
The Zenith is on celestial equator
Stars rise and set perpendicular to horizon

21. Local Equatorial System
Stars rise in east and set in west
Motion of each star = parallel of declination on the Celestial Sphere
Celestial Equator is half way between NCP and SCP
Related to sidereal “star” time
Used to track motion of stars

22. Local Equatorial System “HA-dec”
Used to track objects
Latitude (Declination) is from the Celestial Sphere
Longitude uses Hour Angle
Follows star path from east to west
Is still time dependent at local meridian
Used to track objects along the parallel of declination.
Determine the Declination “latitude” on the celestial sphere.
Use the local meridian for your horizon and objects Right Ascension to
determine hour angle .
4. HA (obj) = LST – RA (obj)

23. Hour Angle
Time before and after star reaches zenith of its path

24. Equatorial System “RA-dec”
Used to catalog objects
Celestial Sphere
Celestial Equator
NCP and SCP
Declination (latitude)
Right Ascension (longitude)
Vernal Equinox
it is an extension of the earth onto the sky called the celestial sphere.
The fundamental plane is the celestial equator, which is an extension of the earth’s equator upon the celestial sphere.
The axis of rotation is an extension of the North – South Pole axis of the earth.
Latitude like coordinates are called declination (dec.).
Longitude-like coordinates are called right ascension (R.A.).
6. Zero point for RA is Vernal Equinox.

25. Declination Angle above Celestial Equator Parallels of Declination
CE = 0 deg
NCP = 90 deg
SCP = - 90 deg
Declination is the angle of the object above the celestial equator.
Parallels of declination similar to parallels of latitude.
Celestial equator is 0 degrees
NCP is 90 degrees and SCP is – 90 degrees

26. Right Ascension Hour circles or “meridians”
Equator = 360 arc deg circumference
Measured as hours (24 hours)
1 hr = 15 arc degrees
Counterclockwise
0h = vernal equinox
The longitudinal lines called hour circles go from the celestial North Pole to the celestial South Pole crossing the equator.
R.A. can be expressed in values between 0 deg and 360 deg but is more often given in time units.
R.A. is measured counterclockwise or west to east.
R.A. can be expressed in values between 0 o and 360 o but is more often given in time units.
The 360 deg along the equator is divided into time units of 24 hours (h). One hour equals 15 min of arc

27. Ecliptic From Earth, Sun ‘s apparent path
Inclined 23.5 deg to Celestial Equator
Vernal Equinox
Autumnal equinox
Winter Solstice
Summer Solstice

28. Ecliptic System Earth revolves around sun = ecliptic
Ecliptic is fundamental plane
Axis of rotation
North Ecliptic Pole
South Ecliptic Pole
Planets have similar paths around sun

29. Ecliptic System & Planets
Used to study solar system
Except for Pluto at 17 degrees
Orbital Inclination within 7 degrees of Ecliptic
Planet
Orbital Inclination
Mercury
7.00°
Venus
3.39°
Earth
0.00°
Mars
1.85°
Jupiter
1.31°
Saturn
2.49°
Uranus
0.77°
Neptune
1.77°
Pluto
17.15°
Planet Orbital Inclination Mercury 7.00° Venus 3.39° Earth 0.00° Mars 1.85° Jupiter 1.31° Saturn 2.49° Uranus 0.77° Neptune 1.77° Pluto 17.15°

30. Zodiac Constellations
As earth revolves,
sky appearance changes.
Constellations around ecliptic called Zodiac

31. Galactic System Study Milky Way and beyond Plane of Galaxy
Inclined about 63 deg to Celestial Equator
Used to study objects beyond our Solar System within our Milky Way Galaxy and outside our galaxy in relationship to the plane of the Milky Way.
The Galactic Plane, or Galactic Equator, is used as reference plane. This great circle of the celestial sphere best approximates the visible Milky Way.
a spiral galaxy, which is very flat with a core that bulges From Earth, the center of the galaxy is in the constellation Sagittarius.
The mean plane of the galaxy is inclined at about 63° (62.9°) to the celestial equator.

32. Galactic System Fundamental plane = plane of Milky Way
Galactic Equator
North Galactic Pole
South Galactic Pole
Center of Galaxy

33. Galactic Coordinates Galactic Latitude NGP = 90 deg SGP = -90 deg
Galactic Longitude
Counterclockwise
0 to 360 deg
0 = center of our galaxy
Galactic latitude is measured from the galactic equator at 0 degrees to 90 degrees at the Galactic North Pole and -90 degrees at the Galactic South Pole. north (positive numbers) or south (negative numbers)
Galactic longitude is measured eastward along the galactic plane from the galactic center. Galactic longitude (l) is measured in from 0 to 360 deg. east ward along the galactic equator
The Longitude Zero Point lies in the direction of the galactic center

34. Coordinate Curriculum K-13
Elementary Activities
Middle School – Junior High Activities
Senior High Activities
Aligned to National Standards
Involve science, geography, math, language arts, art, problem-solving
Introductory, skill-development, and assessment activities

35. Chandra
Related to
1. Chandra Classroom-ready activities as Stellar Evolution, Variable Stars, Electromagnetic Spectrum, Imaging for Junior and Senior High
2. ds9 and Visual Observatory
3. Chandra Sky Map

36. Science Olympiad Related to
1.Elementary Science Olympiad events in Starry, Starry Night and Map Reading
2.Reach for the Stars and Road Scholar for Division B
3.Astronomy and Remote Sensing for Division C
4.Trial events as Global Positioning Systems

37. Tools of Astronomy
3-d models, globes, grids, star maps, charts, graphs, quadrant, astrolabe, cross-staff, pinhole protractor, parallax, hand angles
binoculars, telescope, star lab, planetarium
Computer technology as Chandra Sky Map, ds9, Remote Sensing, GPS, Sky Map programs
Coordinates, measurements, angles, relative positions, times, navigation

38. Sample Activity
Chandra’s Stellar Evolution poster recently in the Science Teacher magazine
Map projections
Coordinate grids
Problem-solving

39. Chandra’s Stellar Evolution Poster
Available from Chandra website
Interactive version on Chandra website
Background information and classroom ready materials available.

40. Map Projections Attempts to represent sphere on flat map
Always some distortion
Types to emphasize specific regions of sphere

41. Sky Maps Sky maps have East and West reversed
Designed so that when placed above your head, directions will
correspond.
3. Maps are usually by month and for regions of earth.

42. Whole Sky (Aitoff) Projection
Whole sky projection is popular with astronomers
Projections for Equatorial, Ecliptic, or Galactic Systems

43. Different Reference Planes

47. Chandra Sky Map of images produced by Chandra
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         
Chandra Sky Map of images produced by Chandra
Uses the Galactic Coordinate System
Clink on colored symbol to access image and information on the Images
Will give the Equatorial Coordinates
                                                                                                                                                                                                                                                                                                                                                                                                    To explore the X-Ray Sky, click on a colored diamond in the sky map. Find out more about Galactic Navigation by taking a tour of the Galactic Coordinate System! Return to Photo Album                                                                                                                                                                                                                                                                                                                                                                                                     
Revised: January 03, 2005

48. Mercator - Equatorial Region
Shows the regions near the equator
Less distortion when put on a flat surface
Regions north and south of equator

49. SC001 Equatorial Region
Using Equatorial (RA-dec) System

50. SCOO1 - Declination
Declination (latitude-like) from +60 deg above to -60 deg below celestial equator.
Degrees, minutes, and seconds of arc

51. SC001 – Right Ascension
Right Ascension (longitude-like) from 0-24 hrs.
Hours, minutes, seconds
Hour circles “meridians” of Right Ascension

52. Polar Region
Circumpolar region
North version
South version

53. SC002 - Declination North Version 30 – 90 deg declination
Parallels of declination
Equatorial region not visible

54. SC002 – Right Ascension North polar version RA = 0 to 24 hours
Hour circles or “meridians”
Note the chart symbols for objects and magnitude

55. Coordinates Longitude-like coordinate listed first
Polaris
Equatorial
J2000
B1950
Galactic
Ecliptic RA
Dec L B
Lon
Lat
02h31’ 49.08 “
89o15 ’50.8 “
01h 48 ’56.79 “
89o 01’43.4 “
123o16’ 50.0 “
26o27 ’41.0 “
88o34’03.3 “
66o06’05.3 “ o o o o o o o o
Longitude-like coordinate listed first
Latitude-like coordinate listed second
Equatorial coordinates will reflect epoch – B1950 or J2000