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ASTR211: COORDINATES AND TIME ASTR211 EXPLORING THE SKY Coordinates and time Prof. John Hearnshaw Prof. John Hearnshaw ASTR211: COORDINATES AND TIME Coordinates and time Prof. John Hearnshaw Sections 1 – 8 ASTR211: COORDINATES AND TIME 1. The celestial sphere An infinite sphere centred on the observer, such that points on the surface of the sphere specify directions in space. The nadir is directly opposite the zenith. Prof. John Hearnshaw The zenith is the point on the sphere directly overhead. The celestial sphere Prof. John Hearnshaw ASTR211: COORDINATES AND TIME Prof. John Hearnshaw ASTR211: COORDINATES AND TIME ASTR211: COORDINATES AND TIME A small circle is the intersection of a plane not passing through the observer with the celestial sphere. Prof. John Hearnshaw 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. ASTR211: COORDINATES AND TIME The horizon is approximately a great circle whose pole is the zenith. 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. Prof. John Hearnshaw The cardinal points are points on the horizon defining the directions N, S, E, W. The celestial sphere showing equator and the two celestial poles Prof. John Hearnshaw ASTR211: COORDINATES AND TIME ASTR211: COORDINATES AND TIME 2. Diurnal motion of celestial bodies Stars, planets, Sun and Moon all exhibit diurnal motion across celestial sphere. The moment of meridian passage is called culmination (highest point above horizon), or meridian transit. Prof. John Hearnshaw They rise somewhere on the eastern horizon, set in the west. ASTR211: COORDINATES AND TIME 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. Prof. John Hearnshaw The poles define the rotation axis of the Earth (). ASTR211: COORDINATES AND TIME 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. Therefore a circumpolar star must be within an angular distance of the pole. Prof. John Hearnshaw Angular separation of N pole and N cardinal point is = latitude of observer. Above: N hemisphere circumpolar stars Right: S hemisphere circumpolar stars Prof. John Hearnshaw ASTR211: COORDINATES AND TIME ASTR211: COORDINATES AND TIME Prof. John Hearnshaw 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). ASTR211: COORDINATES AND TIME 4. Alt-az coordinate system Two angles are sufficient to specify the direction to any point on the celestial sphere. Prof. John Hearnshaw In the alt-az system these angles are i) altitude a (sometimes called elevation E) ii) azimuth A ASTR211: COORDINATES AND TIME Below: The same star is shown in alt-az coordinates on the celestial sphere Prof. John Hearnshaw Top: a N hemisphere celestial sphere showing the diurnal path of a star at P ASTR211: COORDINATES AND TIME Altitude is angle on great circle through zenith between horizon and the point on celestial sphere (0 a 90). Also defined is the zenith distance, z. z = 90 - a. Prof. John Hearnshaw 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). ASTR211: COORDINATES AND TIME 5. Latitude and longitude on Earth’s surface Prof. John Hearnshaw Longitude O is object at longitude W of Greenwich ASTR211: COORDINATES AND TIME Latitude Prof. John Hearnshaw O1 is object at latitude 1 degrees N of equator. O2 is 2 degrees S of equator. ASTR211: COORDINATES AND TIME Poles P, Q defined by Earth’s rotation axis. The equator is the great circle whose plane is perpendicular to PQ. The equator defines the zero of latitude ( = 0). Prof. John Hearnshaw 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). Prof. John Hearnshaw ASTR211: COORDINATES AND TIME ASTR211: COORDINATES AND TIME 6. Equatorial coordinate system (Part 1) The declination of a celestial body is measured from the equator ( = 0) and lies in the range 90 + 90. At the poles = 90. Prof. John Hearnshaw 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. ASTR211: COORDINATES AND TIME Note that (unlike a, A) is independent of the observer’s location. Prof. John Hearnshaw 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). ASTR211: COORDINATES AND TIME Note that different observers record different hour angles for simultaneous observations of the same object, depending on their longitude. Prof. John Hearnshaw Hour angle is measured westwards relative to the observer’s meridian. Objects E of meridian have H < 0. ASTR211: COORDINATES AND TIME 7. The ecliptic Prof. John Hearnshaw The ecliptic is a great circle on the celestial sphere defined by the plane of the Earth’s orbit around the Sun. ASTR211: COORDINATES AND TIME Sun is always on the ecliptic and moves eastwards (anticlockwise as seen from N) about 1/day (actually 59.1 arc min). The inclination of equator and ecliptic is the obliquity of the ecliptic = 23 27 Prof. John Hearnshaw 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 ecliptic is a great circle at angle 23º27' to the equator Prof. John Hearnshaw ASTR211: COORDINATES AND TIME Celestial sphere with horizon, equator and ecliptic as intersecting great circles Prof. John Hearnshaw ASTR211: COORDINATES AND TIME ASTR211: COORDINATES AND TIME 8. The zodiac Literally ‘zodiac’ = circle of animals. The Sun spends ~1 month in each constellation of the zodiac. Prof. John Hearnshaw 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. ASTR211: COORDINATES AND TIME The ‘signs’ of the zodiac are: ram bull twins crab lion virgin Libra scales Scorpius scorpion Sagittarius archer Capricornus goat Aquarius water-bearer Pisces fish (plural) Prof. John Hearnshaw Aries Taurus Gemini Cancer Leo Virgo ASTR211: COORDINATES AND TIME Taurus Bull Gemini Twins Libra Scales Scorpius Sagittarius Archer Cancer Crab Leo Lion Virgo Virgin Capricornus Aquarius Pisces Goat Water- Fishes bearer Prof. John Hearnshaw Aries Ram ASTR211: COORDINATES AND TIME As a result of precession over some 2100 years, the signs no longer coincide with the constellations. Prof. John Hearnshaw Moon and planets are always located in the zodiac and hence near the ecliptic. ASTR211: COORDINATES AND TIME Location of Sun at times of equinox and solstice Date First point of Aries (Ram) vernal equinox Cancer (Crab) summer solstice Libra (Scales) autumnal equinox Capricornus (Goat) winter solstice March 21st June 21st December 21st Prof. John Hearnshaw September 21st The end of sections 1 - 8 Prof. John Hearnshaw ASTR211: COORDINATES AND TIME