1. Coordinate System & Time/Calendar
ASTR 3010
Lecture 3
Textbook Chap. 3

2. Coordinate Systems To describe an event in space-time
Steps of defining a spatial coord. system
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.

3. Altitude-azimuth system
aka, Horizontal coord. system
fundamental planet=horizon, reference point=north point
azimuth : from north point to east, 0 – 360degrees.
altitude = h, elevation, -90 to +90 degrees.
zenith: right above the observer, h=90 deg.
zenith angle = 90 - h

4. Equatorial System
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.

5. Precession
Precession = rotation of the Earth spin axis (period=26,000 yrs  50 arcsec/yr)  vernal equinox is marching east by 50 arcsec per year
B1950 and J2000 coordinates
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!

6. Relationship among latitude, altitude, and declination
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

7. 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.

8. Galactic coordinate system
fundamental plane = Galactic disk, reference point = toward the Galactic center
longitude (l) and latitude (b)

9. Solar Time Sidereal time = RA of an object in transit
Earth’s rotation rate relative to distant stars
sidereal day = hours
Solar time = Time tracked by the Sun (local noon is when the Sun transits)
solar time = RA of the Sun + 12 hours
solar day = 24 hours

10. 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

11. 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)
days
Civil calendar (Gregorian calendar) = 365 days.
To compensate the difference
every 4th year, add one day in February (Leap Day)
– = days
×4 = days but 1 whole day was added  over 4 years, day is too long!  over 400 years, 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).
Mean solar day is changing due to (1) slow down of Earht’s rotation, (2) other planets’ influence, etc.  since this calendar year is measured in terms of mean solar day, precise calculation needs to take the variation of mean solar day which is quite stochastic. Lean seconds are announced only in 6 months advance…

12. 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 – , most commonly used in astronomy (introduced by SAO to track Sputnik using 18bit number).

13. 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.

14. Chapter/sections covered in this lecture : Chap 3
In summary…
Important Concepts
Important Terms
various coordinate systems
Time system
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