1. Announcements Homework Set 1 is due today Homework set 2: Chapter 2 # 46, 50, 52, 53 & 54 + Determine the number of kilometers in 1° of longitude at the equator, 36.5° latitude (Clarksville) and 50° latitude. Exam Formula Sheet will be updated this week. I still have to decide what we will be covering.

2. Hint for homework problems # 52, 53 & 54 More small angle approximation

3. Terrestrial Coordinates Longitude is measured CCW (+) or CW (-) around from Greenwich England Latitude is measured North or South of the equator Both are measured in degrees, minutes and seconds

4. Celestial Coordinates The angle between the celestial equator and the ecliptic is 23.5 ° Right Ascension (RA) is measured CCW from the Vernal Equinox and is in hours, minutes and seconds Declination (Dec) is measured above (+) or below (-) the celestial equator and is in degrees, minutes and seconds See Appendix A6 for more on celestial coordinates

5. Finding the CE and NCP at your latitude Altitude of NCP above due north horizon along the meridian is just , your latitude (+ for north, - for south) Altitude of the celestial equator above due south horizon along the meridian is 90°- 

6. Example Chapter 2 problem # 43: The Moon’s orbit is tilted by about 5° relative to the Earth’s orbit around the Sun. What is the highest altitude in the sky that the Moon can reach, as seen in Philadelphia (latitude 40° North)?

7. Example Solution What is being asked?...Maximum altitude of the Moon from 40° North latitude. What information is given?...latitude = 40° N Tilt angle of Moon from ecliptic = 5° Tilt angle of ecliptic from celestial equator = 23.5°

8. Example Solution 2 Equation(s) to use: Refer to diagram two slides back. The altitude of the celestial equator above the local horizon is 90° - Latitude CE = 90° - 40° = 50° Maximum altitude of Ecliptic = CE + 23.5° = 50° + 23.5° = 73.5° Maximum altitude of Moon = Ecliptic Max + 5° = 73.5° + 5° = 78.5°

9. Time and Astronomy The 24 Hour Day? One rotation of Earth = 1 sidereal day 23 hours 56 minutes 4.091 seconds This is the time required for the Earth to complete one rotation with respect to the fixed stars

10. As the Earth rotates it also moves around the Sun. So, for the Sun to return to the same place in the sky the Earth must rotate a little more than one complete rotation

11. Noon–to–noon isn’t always 24 hours

12. The Mean Solar Day is exactly 24 hours. It is the time between meridian transits of the Sun averaged over four years

13. The Year 1 orbit around the Sun = 365.2564 days The sidereal year 1 Tropical Year = 365.2422 mean solar days The time from Vernal equinox to Vernal equinox

14. The early calendar: the Julian Calendar (Julius Caesar) Most years have 365 days. Years evenly divisible by 4 have 366 days. Add February 29 to those years. Slightly off so the calendar “drifted”

15. Pope Gregory XIII’s Calendar The Gregorian Calendar (1582) Most years have 365 days Years evenly divisible by 4 have 366 days except century years. Only century years evenly divisible by 400 are leap years

16. Precession of the Equinox Like a spinning gyroscope, the Earth precesses. The period of the precession is 25,920 years

17. The Precession of the Equinox leads to a shift of the celestial pole

18. It also shifts the constellations of the zodiac