Coordinate Systems
Purpose
• To locate stars/galaxies/other
objects
• To locate an object in the space, how
many quantities do we need?
• x, y, z
• Direction (2 quantities), distance
How do we locate a spot on the earth?
• Maps, mapquest, Google
Map, GPS
• If we ignore how high it
is above the sea
• To describe a spot on
the surface of the
earth, we use a set of
numbers (degrees),
called Coordinates
– Longitude
– Latitude
0º
Position in Degrees
–Longitude – connecting the
poles, 360 degree, or 180 degree
east + 180 degree West
0º
–Latitude – parallel to the
equator, 0 – 90 N and 0 – 90 S
–A location is the intersect of a
(virtue) longitude line and a
latitude line
90º N
Amherst
42°22′49″N, 72°31′25″W
0º
90º S
Same idea when we describe the
position of a celestial object
• Celestial Sphere
– An imaginary giant sphere, centered on the
earth
– All objects seem to be on the surface of this
imaginary sphere
– Earth’s poles extends and intersect with the
celestial sphere as the North Celestial Pole and
the South Celestial Pole
– Earth’s equator extends and intersects with
the celestial sphere as Celestial Equator
– To locate an object, two numbers (in degrees)
like the longitude and latitude are enough!
The horizon coordinate system
• Altitude
– Angle above the horizon
– 0° - 90°
– The altitude of the north
celestial pole equals the
observer’s latitude on the earth
Meridian
• Azimuth
– Angle measured eastward along
the horizon, starting from the
north
– 0° - 360°
• Zenith
– The extended vertical line
intersects with the celestial
sphere
• Meridian
– The great circle passing through
the celestial poles and the
zenith
• Horizon
– The great circle whose pole is
the zenith
Pros and Cons of the horizon system
• Pros
– Easy to tell and understand
• Cons
– At different position on the
earth, the same object has
different coordinates
– At different time, the same
object has different
coordinates
The Coordinates of an object
Change in the horizon
system!
Equatorial Coordinate System
• A system in which the
coordinates of an object
does not change
• Like the longitude and
latitude on the earth, we
have Right Ascension and
Declination in the
Equatorial system
• The equatorial coordinate
system rotates with stars
and galaxies
Equatorial Coordinate System
• Declination (DEC)
– A set of imaginary lines
parallel to the Celestial
Equator
– 0 ° at the celestial
equator, increases from
south to north
– negative in the southern
hemisphere
– Dec of the north
celestial pole is 90 °
– Dec of the south
celestial pole is -90 °
90 °
0°
-90 °
Equatorial Coordinate System
• Right Ascension
(RA)
– imaginary lines
that connect the
celestial poles
– The origin of the
longitude of the
earth is the
Greenwich
Observatory
– The origin of the
RA is Vernal
Equinox
90 °
0°
-90 °
What is Vernal
Equinox?
The equatorial system
• Ecliptic
– The earth revolves
annually around the
Sun
– The Sun appears to
moves from west to
east on the celestial
sphere
– The path of the sun
is called ecliptic
The equatorial system
• The earth’s axis is titled –
line through the celestial
poles is NOT
perpendicular to the plane
of ecliptic
• 23.5 degree angle between
the celestial equator and
the ecliptic
• The ecliptic and the
celestial equator intersect
at vernal equinox and
autumnal equinox
The equatorial system
• RA
– 360 degrees
– Historically, use
HOURS:MINS:SECS
as unit – 24 hours
– Starts from Vernal
equinox (0 h)
– increases from west
to east
– Stars w/ larger RA
rise later
6h
0h
Andromeda:
RA: 00h 42m 44.3s
DEC: +41° 16′ 9″
6h
0h
Vernal Equinox:
RA 0h
RA:
DEC 0º
DEC:
Summer Solstice: RA:
RA 6h
DEC 23.5º
DEC:
Autumnal Equinox: RA:
RA 12h
DEC 0º
DEC:
Winter Solstice:
DEC -23.5º
DEC:
RA 18h
RA:
Seasons
Why do we have seasons?
• The path of the earth moves around
the sun is not a circle, but an eclipse
• The distance of the earth to the sun
is not fixed
• Summer is hot, winter is cold, is it
because we are closer to the sun in
the summer time, and more distant
from the sun in the winter time?
The axis of the earth is tilted!
• 23.5 degree angle between the earth’s
axis and line that perpendicular to the
earth’s orbit plane
Seasons
• More hours of daylight
in the summer than in
the winter
• Angle of sunlight:
Earth’s tilt constant at
23.5 degrees, in the
summer time of the
Northern Hemisphere,
the sun light falls more
directly on the
Northern Hemisphere
Seasons
• Vernal Equinox, around March 21, day hour = night hour
at any place on the earth
• Summer Solstice, around June 22, for the northern
hemisphere, day hour > night hour; longest day; opposite
in the southern hemisphere
• Winter Equinox, around Sept. 23, day hour = night hour
at any place on the earth
• Winter Solstice, around Dec 22, for the northern
hemisphere, day hour < night hour; longest night;
opposite in the southern hemisphere
Vernal Equinox:
RA: 0h
DEC: 0º
Summer Solstice: RA
DEC: 23.5º
Autumnal Equinox: RA
DEC: 0º
Winter Solstice:
DEC: -23.5º
RA