Coordinate System
&
Time/Calendar
ASTR 3010
Lecture 3
Textbook Chap. 3
Coordinate Systems
• To describe an event in space-time
• Steps of defining a spatial coord. system
1.
2.
3.
4.
locate the origin
define fundamental plane
choose the reference point
choose signs of axes
• In astronomy, distance is superfluous
most times
 two angles are enough to describe a
point in space.
Altitude-azimuth system
• aka, Horizontal coord. system
o fundamental planet=horizon,
reference point=north point
o azimuth : from north point to east, 0
– 360degrees.
o altitude = h, elevation, -90 to +90
degrees.
o zenith: right above the observer,
h=90 deg.
o zenith angle = 90 - h
Equatorial System
o
o
o
o
fundamental plane = celestial equator, reference point = vernal equinox
right ascension = alpha = RA, 0h to 24h
declination = delta = Dec, -90 to +90 degrees
hour circle = great circle of constant RA, or great great circle that passes through
North Pole.
Precession
o Precession = rotation of the Earth spin axis (period=26,000 yrs  50 arcsec/yr) 
vernal equinox is marching east by 50 arcsec per year
o B1950 and J2000 coordinates
o International Coordinate Reference System (ICRS): reference point was chosen to
a fixed point on the celestial sphere that is close to that of J2000 epoch.
Precession free!
Relationship among latitude, altitude, and declination
o
o
o
o
o
o
circumpolar stars?
altitude of NP = latitude of an observer
Meridian : great circle that passes through zenith and N.P.
transit : when an object crosses the Meridian (maximum altitude)
hour angle of an object = RA of Meridian – RA of the object
local sidereal time = RA of Meridian
Ecliptic coordinate system
• fundamental plane = ecliptic, reference point = vernal equinox
• useful to describe solar system objects because they are all confined within
±10 degrees from the ecliptic.
Galactic coordinate system
• fundamental plane = Galactic disk, reference point = toward the Galactic center
• longitude (l) and latitude (b)
Solar Time
• Sidereal time = RA of an object in transit
o Earth’s rotation rate relative to distant stars
o sidereal day = 23.93447 hours
• Solar time = Time tracked by the Sun (local noon is when the Sun transits)
o solar time = RA of the Sun + 12 hours
o solar day = 24 hours
Apparent Sun’s annual motion across the sky
• analemma
• Mean solar time : using a fictitious mean Sun that is moving at a constant
speed (i.e., on a perfect circular orbit) : solar time and mean solar time can
differ upto 16min
Solar year (tropical year)
• the length of the time that Sun returns to the same position in its orbit
relative to the Earth (i.e., vernal equinox to vernal equinox)
• 365.242581 days
• Civil calendar (Gregorian calendar) = 365 days.
• To compensate the difference
o every 4th year, add one day in February (Leap Day)
 365.242581 – 365.0 = 0.242581 days
 0.242581×4 = 0.970323 days but 1 whole day was added  over 4 years,
0.029676 day is too long!  over 400 years, 2.9676 days too long
 Then, let’s remove three leap years over 400 years  Among those leap years
(divisible by 4), if a year is divisible by 100 but not by 400, it is no longer a leap
year (1900 is not a leap year but 2000 is).
 over 400 years, about 2790 seconds too short. Add +1 second occasionally
(leap second).
Julian Date
• Continuous count of days since 4713 BC Jan 1, 12PM
• Useful to denote the epoch of astronomical observation
• Modified Julian Date (MJD) = JD – 2400000.5, most commonly used in
astronomy (introduced by SAO to track Sputnik using 18bit number).
Visibility of an object
(Q) You plan to observe celestial objects tonight (August 21) at Athens, GA
(34°N). If you can point your telescope down to h=30°, what are ranges of
Right Ascension and Declination for observable objects? Assume that you
the length of night is 8 hours and you will only observe objects when they
transit.
In summary…
Important Concepts
Important Terms
• various coordinate systems
• Time system
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•
•
•
•
•
•
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• Visibility of an object for an
observer
zero magnitude flux
great circle
meridian
hour circle
zenith, north point
transit
hour angle
etc.
Chapter/sections covered in this lecture : Chap 3