1. you thought of going into teaching?”
“ It would seem that you have no useful skill or talent whatsoever, he said. Have
you thought of going into teaching?”
Mort, Terry Pratchett
We’ll begin computer work on Wednesday.

2. Last Time: Coordinate system: Alt-Az and RA and Dec (equatorial)

3. Local Zenith- point above your head
Meridian- N-S passing through Zenith
Altitude- angle above the horizon (90 degrees is Zenith)
Azimuth- angle from North through East (clockwise) of the horizon.

4. Equitorial Based on the Earth's longitude and latitude.
Right Ascension takes longitude
Declination takes latitude (and is the same)

5. Right Ascension 0 to 24 hours (gets bigger towards the East)
Four special points:
0 hours at noon Vernal Equinox (noon in March)
12 hours at noon Autumnal Equinox (noon in September)
6 hours at noon Summer Solstice (noon in June)
18 hours at noon Winter Solstice (noon in December)
Gains 2 hours per month (at noon)
Gains 1 hour per hour during the day, from noon.

6. Declination
Use meridian diagrams

7. THESE ONLY WORK ON YOUR MERIDIAN!
Meridian Diagrams
We use these to convert altitude (local system) to declination (fixed system).
THESE ONLY WORK ON YOUR MERIDIAN!

8. Meridian Diagram: Steps
1) The latitude of the observer is the declination of the observer's zenith.
2) The missing angle is 90 – altitude
3) Determine the declination by adding (or subtracting) the missing angle to the declination at zenith.
If you go south subtract, if you go north add.

9. Now to what we really want.
If you see a star in the sky, you can determine what the RA and Dec are.
How?
By converting your local time and coordinates to RA and Dec.

10. Example
What are the RA and Dec for a star 29o above the southern horizon, right now (12:30pm) in Tahiti (Latitue=18o)?

11. Example
What are the RA and Dec for a star 29o above the northern horizon, at 9pm in Fairbanks, AK (Latitue=65o)?

12. Off the meridian
For RA, you can use angles from the meridian to calculate the RA.
These are called Hour Angle.
So an HA of 6, means 45o away from the meridian.
How did I come to 45o for that?

13. Off the meridian
For Dec, you have to project the star’s path on the meridian and estimate the altitude there.

14. The Sun's motion in our sky
The apparent path of the Sun in our sky defines the ecliptic plane- the plane of the Earth’s orbit.

15. The Sun's motion in our sky
Declination:
At both equinoxes, it is directly above Earth's equator, so its declination is 0 degrees
At the summer solstice, it is as far north as it can get: 23.5 degrees
At the winter solstice, it is as far south as it can get: degrees.
Right Ascension: Since the Sun is always on our meridian everyday at noon, you only need to know the date to get its RA

16. It is called an analemma.
If you took a picture of the Sun everyday at the same time, this is what you would get.
It is called an analemma.

17. These are always close to the ecliptic plane.
Planets and the Moon
These are always close to the ecliptic plane.

18. Time.
Because the Earth is spinning and orbiting, where a star is in our sky depends on the time of day and day of the year.

19. Universal Time. This is the same as Greenwich Mean Time.
No daylight savings time.
Currently, UT is 5 hours ahead of us.
Because of daylight savings time, even clocks in England are off by an hour except between November and March.

20. Convert to fractional days
Divide the minutes by 60 and add to the hours.
Divide the hours by 24.

21. Julian Date How many days between Sept. 1 and Sept 8 of this year?
How many days between June 1 and Sept. 8 of this year?
How many days between June 1 of 1972 and Sept. 8 of this year?

22. A continuous count of days since January 1, 4713 BC
Julian Date
A continuous count of days since
January 1, 4713 BC

23. A continuous count of days since
Julian Date
A continuous count of days since
NOON on January 1, 4713 BC
Today is day
12:45 today is JD=

24. Typically numbers are lopped off for simplicity, but noted in captions.

26. Note that it is 12 hours off from JD days!
Modified Julian Date
Subtracts 2,400,000.5 days from JD.
(Nov. 17, 1858)
Note that it is 12 hours off from JD days!

27. When their signals reach us is important.
Time is relative
Many celestial bodies (stars, transits, AGNs, etc.) undergo variations.
When their signals reach us is important.
But we are in motion!

28. Earth’s orbit is ~16 light minutes across
Earth’s orbit is ~16 light minutes across. If we keep time in Earth’s frame, then astronomical events all have a period variation of 16 minutes per year.

29. Time is relative Time systems: Geocentric (Earth-based: UT, JD)
Heliocentric (Sun-based: HJD)
Barycentric (mass center: BJD)