1. ASTR211
EXPLORING THE SKY
Coordinates and time
Prof. John Hearnshaw

2. Coordinates and time
Sections 1 – 8

3. The celestial sphere
An infinite sphere centred on the observer, such
that points on the surface of the sphere specify directions
in space.
The zenith is the point on the sphere directly overhead.
The nadir is directly opposite the zenith.

4. The celestial sphere

6. A great circle is the intersection of any plane passing through the observer with the celestial sphere – i.e. it is a circle on the sphere whose centre is the centre of the sphere.
A small circle is the
intersection of a plane
not passing through
the observer with the
celestial sphere.

7. The horizon is approximately a great circle whose pole is the zenith.
The cardinal points are points on the horizon defining the directions N, S, E, W.
The observer’s meridian is a great circle through the zenith and the N and S cardinal points. It defines a vertical N-S plane through the observer.

8. The celestial sphere showing equator and the two celestial poles

9. 2. Diurnal motion of celestial bodies
Stars, planets, Sun and Moon all exhibit diurnal motion
across celestial sphere.
They rise somewhere on the eastern horizon, set in
the west.
The moment of meridian passage is called culmination
(highest point above horizon), or meridian transit.

10. Paths of celestial bodies are in general arcs of
small circles.
The centres of all such small circles are on a line which
is a diameter of the celestial sphere, intersecting sphere
in the N and S poles, which lie on the observer’s meridian.
The poles define the rotation axis of the Earth ().

11. 3. Circumpolar stars
These are stars whose angular distance from the pole
is less than a certain maximum, which depends on
observer’s latitude, such that they never set.
Angular separation of N pole and N cardinal point is
 = latitude of observer.
Therefore a circumpolar star must be within an
angular distance  of the pole.

12. Above: N hemisphere
circumpolar stars
Right: S hemisphere

13. A circumpolar star is seen to cross the meridian twice;
at upper culmination (from E to W) and at
lower culmination (from W to E, below pole P).

14. 4. Alt-az coordinate system
Two angles are sufficient to specify the direction
to any point on the celestial sphere.
In the alt-az system these angles are
i) altitude a (sometimes called elevation E)
ii) azimuth A

15. Top: a N hemisphere celestial
sphere showing the diurnal
path of a star at P
Below: The same star is
shown in alt-az coordinates
on the celestial sphere

16. Altitude is angle on great circle through zenith between horizon and the point on celestial sphere
Azimuth is angle from N cardinal point going eastwards (in S hemisphere from S cardinal point going eastwards) round horizon to where great circle through zenith and point cuts horizon (0  A  360).
Also defined is the zenith distance, z.
z = 90 - a.

17. 5. Latitude and longitude on Earth’s surface
O is object at longitude  W of Greenwich

18. Latitude
O1 is object at latitude 1 degrees N of equator.
O2 is 2 degrees S of equator.

19. Poles P, Q defined by Earth’s rotation axis.
The equator is the great circle whose plane is perpendicular to PQ.
Any great semi-circle through PQ is a meridian.
That through Greenwich is the Greenwich meridian, defining longitude  = 0 (also known as the prime meridian).
The equator defines the zero of latitude ( = 0).

21. 6. Equatorial coordinate system (Part 1)
This system is the analogue of (, ) on Earth’s surface.
The plane of the terrestrial equator defines a great circle
where it intersects the celestial sphere, known as the
celestial equator.
The declination of a celestial body is measured from the
equator ( = 0) and lies in the range
90    + 90.
At the poles  =  90.

22. Note that  (unlike a, A) is independent of the observer’s location.
The analogue of terrestrial
longitude is the hour angle,
measured in (h m s) of time
(note: 1 h  15;
1 m  15 arc;
1 s  15 arc).

23. Hour angle is measured westwards relative to the observer’s meridian
Hour angle is measured westwards relative to the observer’s meridian. Objects E of meridian have H < 0.
Note that different observers record different hour angles for simultaneous observations of the same object, depending on their longitude.

24. 7. The ecliptic
The ecliptic is a great circle on the celestial sphere
defined by the plane of the Earth’s orbit around the Sun.

25. Sun is always on the ecliptic and moves eastwards (anticlockwise as seen from N) about 1/day (actually 59.1 arc min).
The ecliptic crosses the equator in two points:
(a) First Point of Aries or Vernal Equinox
(b) First Point of Libra or Autumnal Equinox
The inclination of equator and ecliptic is the obliquity of the ecliptic
 = 23 27

26. The ecliptic is a great circle at angle
23º27' to the equator

27. Celestial sphere with horizon, equator
and ecliptic as intersecting great circles

28. 8. The zodiac
Literally ‘zodiac’ = circle of animals.
It is a band ~ 8 each side of ecliptic, around
the celestial sphere, containing 12 constellations
through which the Sun passes on its annual circuit
of the ecliptic.
The Sun spends ~1 month in each constellation
of the zodiac.

29. The ‘signs’ of the zodiac are:
Aries ram  Libra scales 
Taurus bull  Scorpius scorpion 
Gemini twins  Sagittarius archer 
Cancer crab  Capricornus goat 
Leo lion  Aquarius water-bearer 
Virgo virgin  Pisces fish (plural) 

30. Aries
Taurus
Gemini
Cancer
Leo
Virgo      
Ram
Bull
Twins
Crab
Lion
Virgin
Libra
Scorpius
Sagittarius
Capricornus
Aquarius
Pisces     
Scales 
Archer
Goat
Water-bearer
Fishes

31. As a result of precession over some 2100 years, the signs no longer coincide with the constellations.
Moon and planets are always located in the zodiac and hence near the ecliptic.

32. Location of Sun at times Date
of equinox and solstice
 First point of Aries (Ram) March 21st vernal equinox
 Cancer (Crab) June 21st summer solstice
 Libra (Scales) September 21st autumnal equinox
 Capricornus (Goat) December 21st winter solstice

33. The end of sections 1 - 8