Download The celestial sphere

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