ASTR211 EXPLORING THE SKY Coordinates and time Prof. John Hearnshaw

Coordinates and time Sections 1 – 8

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.

The celestial sphere

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.

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.

The celestial sphere showing equator and the two celestial poles

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.

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 ().

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.

Above: N hemisphere circumpolar stars Right: S hemisphere

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).

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

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

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.

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

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

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).

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.

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).

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.

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.

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

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

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

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.

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) 

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

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.

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

The end of sections 1 - 8