ASTR211

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ASTR211 EXPLORING THE SKY Coordinates and
time Prof. John Hearnshaw
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Coordinates and time Sections 1 8
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• 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.

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The celestial sphere
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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.
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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 observers 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.
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The celestial sphere showing equator and the two
celestial poles
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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.
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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 observers
meridian. The poles define the rotation axis of
the Earth (?).
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3. Circumpolar stars These are stars whose
angular distance from the pole is less than a
certain maximum, which depends on observers
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.
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Above N hemisphere circumpolar stars Right S
hemisphere circumpolar stars
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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).
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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
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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
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Altitude is angle on great circle through zenith
between horizon and the point on celestial sphere
(0? ? a ? 90?). 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.
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5. Latitude and longitude on Earths surface
Longitude O is object at longitude ? W of
Greenwich
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Latitude O1 is object at latitude ?1 degrees N
of equator. O2 is ?2 degrees S of equator.
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Poles P, Q defined by Earths 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?).
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6. Equatorial coordinate system (Part 1) This
system is the analogue of (?, ?) on Earths
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?.
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Note that ? (unlike a, A) is independent of the
observers 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).
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Hour angle is measured westwards relative to the
observers meridian. Objects E of meridian have H
lt 0. Note that different observers record
different hour angles for simultaneous
observations of the same object, depending on
their longitude.
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7. The ecliptic The ecliptic is a great circle
on the celestial sphere defined by the plane of
the Earths orbit around the Sun.
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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?
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The ecliptic is a great circle at angle 23º27' to
the equator
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Celestial sphere with horizon, equator and
ecliptic as intersecting great circles
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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.









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The signs of the zodiac are Aries ram ? Libra
scales ? Taurus bull ? Scorpius scorpion ? Gemi
ni twins ? Sagittarius archer ? Cancer crab ? Cap
ricornus goat ? Leo lion ? Aquarius water-bearer
? Virgo virgin ? Pisces fish (plural) ?
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Aries Taurus Gemini Cancer Leo Virgo
? ? ? ? ? ?
Ram Bull Twins Crab Lion Virgin

Libra Scorpius Sagittarius Capricornus Aquarius Pisces
? ? ? ? ? ?
Scales ? Archer Goat Water-bearer Fishes
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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.
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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
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The end of sections 1 - 8