1. Astronomical Observing Techniques: Lecturer: Nigel Douglas
Coordinate Systems
Lecturer: Nigel Douglas
Sources:
1. Adler Planetarium and Astronomy Museum, Chicago
2. Hartmut Frommert
3. Juergen Giesen
4. S.W.Digel (SLAC) 

2. The Horizon System
Celestial Sphere:
Equatorial System
Distances on the Celestial Sphere
Ecliptical Coordinate system
Galactic Coordinate system
Precession, nutation, aberration, refraction, parallax, etc

3. The Horizon System (a.k.a. Alt-Az system)
Observer-centered.
Depends on your location.
Measure Azimuth from N through East (0-360 deg)

4. The Horizon System
Altitude is measured in decimal degrees, up from your horizon towards your zenith.
Also called Elevation.

5. The Horizon System
Your zenith is the point directly above your head, at an altitude of 90º.
There’s also your nadir directly below your feet, at an altitude of -90º.

6. The Horizon System
The zenith angle of a point on the sky is its angular distance from the zenith.
Zenith angle and altitude are complementary angles. (They sum to 90º.)

7. The Horizon System
Quality of astronomical observations gets poorer as you look closer to the horizon, because you’re looking through more atmosphere.

8. The Horizon System
When you look straight up, we say that your observation has an airmass of 1.

9. The Horizon System
The airmass for an observation at zenith angle z is given by sec(z).
sec(45º) ≈ 1.4 sec(60º) = 2 z

10. The Horizon System
Your meridian is an imaginary line drawn across the sky, starting due North of you, passing through your zenith, and ending due South of you.

11. The Horizon System
A celestial object is said to transit or culminate when it crosses your meridian.

12. The Horizon System
Most celestial objects are at their highest altitude (lowest airmass) of the night as they transit.
This is how RA used to be measured (“transit telescope” or “meridian circle”)
Kitchin p376

13. The Horizon System
Can’t be used to give unique coordinates to astronomical objects - changes with time and with position of observer.

14. The Celestial Sphere
It is convenient to talk about a celestial sphere, upon the inside of which all of the fixed stars appear to be painted.

15. The Celestial Sphere
The celestial sphere appears to rotate once about the north celestial pole in 23 hrs, 56 min.
This sidereal day is different from the 24-hr solar day because the Earth orbits the Sun.

16. The Equatorial System
Project the Earth’s equator and poles onto the celestial sphere.
A common astronomical coordinate system for all observers on earth!

17. The Equatorial System
Declination is measured north or south from the celestial equator, toward the poles.
NCP has dec = +90º
SCP has dec = -90º
Typically quoted in º / ’ / ”.

18. The Equatorial System
Right Ascension is measured east along the celestial equator.
The reference point for RA = 0 is the Sun’s position on the celestial sphere during the vernal (spring) equinox.

19. Vernal equinox, Mar 21, is the first day of NH spring.

20. The Equatorial System
Right Ascension is measured east along the celestial equator.
The reference point for RA = 0 is the Sun’s position on the celestial sphere during the vernal (spring) equinox.

21. The Equatorial System
Right Ascension is not measured in degrees, but in units of time!
It is in fact the extra time that a star with that RA would take to reach the meridian through the vernal equinox after the sun.
1h = 60m of RA
1m = 60s of RA

22. The Equatorial System Except that they aren’t !!!
Converting the units of R.A. into “true” angular units...
1h of R.A. = 15º
1m of R.A. = 15’
1s of R.A. = 15”
Except that they aren’t !!!

23. The Equatorial System Why more digits for RA?
The position of Dubhe (a UMa), the last star in the bowl of the Big Dipper, can be given as:
11h 03m 43.5s, 61º 45’ 03 or
11:03:43.5, 61:45:03
or simply ,
Why more digits for RA?

24. Distances on the Sky
For celestial objects within about 10’ of each other (e.g., in the same telescope field of view), the angle d between them is given by
d2 = (Dra  cos(decave))2 + (Ddec)2
Here, the units of R.A. and Dec must be degrees. (Convert first.)

25. Distances on the Sky
For further-separated objects this equation doesn’t work, for the same reason that Muslims in New York pray towards the northeast...
The shortest distance between two points on a sphere is a great circle!

26. cos d = sin dec1 sin dec2 + cos dec1 cos dec2 cos Dra
Distances on the Sky
For further-separated objects, the correct distance equation is given by:
cos d = sin dec1 sin dec2 + cos dec1 cos dec2 cos Dra

27. Equatorial coordinates: summary
RA, Dec or a, d
natural choice for astronomy from earth
one number in catalogs
you can tell right away whether a given position will rise, how high it will reach, and what time of year it will be up at night.
N.B.: Epoch must always be specified -
Precession period ~26,000 yr [~20”/yr]

28. Galactic coordinates b and l (galactic latitude and longitude)
Natural for “middle astronomy”
Relevant for extragalactic observations
(foreground emission/obscuration)
Plane of the Milky Way
traces Galactic Equator
(0,0) is direction to the Galactic center
(180,0) is the anticenter
8.5 kpc
Sun
Powell

29. Galactic coordinates (cont)
In older (~30 yrs) literature you will notice lII and bII listed. This was to distinguish between ‘new’ (i.e., correct) and old Galactic coordinates (before radio astronomy cleared up the question of where the Galactic center actually is)
Epoch does not need to be specified
Orbit period ~250 Myr [5 mas/yr]

30. Ecliptic coordinates
Denoted l, b , defined by plane of the solar system, logical for orbital dynamics and satellite data
Dust in the plane of the
solar system, which is
bright at 12 mm
IRAS

31. EGRET all-sky map ~1.4 Mg, ~60% interstellar emission from the MW
3EG catalog (Hartman et al. 1999)
EGRET
(>100 MeV)
~1.4 Mg, ~60% interstellar emission from the MW
~10% are cataloged (3EG) point sources

32. Changes in the coordinates!?
Proper motion: record is 10.3”/yr
Precession: “wobbling” of axis due to pull of sun and moon on a non-spherical earth - 50” per year (25,000 yr period)
Nutation - smaller effect due to change in alignment of Moon’s orbit ~9”
Aberration: shift due to finite velocity of light (~20”)!
Diurnal and annual parallax :(~1 deg for moon)
Refraction by atmosphere: up to 35’

33. That’s all folks

34. Astronomical catalogs
The idea is to label sources so you can refer to them
No uniform standards, although standards are being imposed
Historically, naming was just sequential, e.g., HD12345, W49
Now the convention is to use the ‘telephone number’, with appropriate level of precision, along with a designator for the origin; catalogs that undergo revisions also have a version number; the J indicates the epoch – hence, 3EG J
One exception is transient sources
E.g., GRBs, for which the name is the date (not Y2K compliant) of the burst, e.g., GRB030328
SNR, which are numbered by the year of discovery, with a letter (or letters) to indicate sequence, e.g., SNR 1998bw
Henry Draper
Gart Westerhout

35. Units (2): Dates and distances
JD is Julian Date – number of days since noon on January 1, 4713 BC
MJD – Modified Julian Date = JD – 2,400,000.5 (i.e., number of days since midnight on November 17, 1858
Today is MJD ~ 53,314
(Truncated Julian Date TJD = MJD – 40,000)
Distance - Parsec (pc) is the distance at which a star would have an annual parallax of 1” (~3.26 light years)