Daily Motion of the Sun

1. Daily Motion of the Sun • Daily motion (diurnal motion) along a circle with center on the Earth’s axis • Clockwise in the north temperate zone • Counterclockwise in the south temperate zone • Up and down in the tropics • Don’t worry about CW or CCW in the tropics

2. Yearly Motion of the Sun • Yearly motion (annual motion) along the ecliptic • The ecliptic great circle is the intersection of the celestial sphere with the ecliptic plane • The Sun drifts eastward (counterclockwise when viewed from above the NCP) with respect to the stars in the course of the year

3. Yearly Motion of the Sun 2

4. Yearly Motion of the Sun 3 • We cannot see the ecliptic, but we deduce its position by considering which stars are close to the Sun at the time of sunrise or sunset

5. Heliacal Rising • Heliacal (/hɪˈlaɪəkəl/) rising is the first visible appearance of a star on the eastern horizon before sunrise • On the previous morning, sunlight made the star invisible

6. Dog Days • Sirius is the brightest star in the night sky • In ancient Egypt, the helical rising of Sirius coincided with the annual flooding of the Nile • Sirius is also known as the Dog Star because of its prominence in the constellation Canis Major (Big Dog)

7. Dog Days 2 • The Dog Days refers to the hottest days of summer • At the time of the ancient Greeks this were the days when star Sirius rose just before or at the same time as sunrise (heliacal rising)

8. Equinoxes and Solstices • The equinoxes are the intersections of the celestial equator and the ecliptic • The solstices are the points on the ecliptic furthest from the celestial equator • These geocentric definitions agree with the heliocentric ones given earlier

9. Equinoxes and Solstices 2

10. Equinoxes and Solstices 3 • The spring equinox is both a time and a place! • The spring equinox is the moment when the Sun is at the spring equinox • You finish the race when you reach the finish! • The spring equinox is the intersection point where the counterclockwise motion is up

11. Equinoxes and Solstices 4 • At the time of the equinoxes, day and night are equally long everywhere on Earth • Equinox = equal night • At the time of the solstices, the rising position of the Sun reaches its extreme northern or southern positions, so the Sun stands still before turning • Solstice = Sun standing • Tropic = (Sun) turning

12. Equinoxes and Solstices 5 • Apparent diameter of the Sun is 0.5° • At the equinox the centre of the Sun is above the horizon for 12 hours • Sunrise is defined to be when the upper limb of the Sun crosses the horizon, so day is actually longer than night at the equinox • In addition, refraction bends light over the horizon

13. Equinoxes and Solstices 6 • The change in rising position of the Sun along the horizon is fastest around the equinoxes, and slowest around the solstices • Around the equinoxes, the declination (distance from the celestial equator) will change by 0.5° per day • Near the solstices, it will stay fixed for almost a week

14. Celestial Coordinates • In order to set up a coordinate system on a sphere, we need a great circle and a base point on it • On the Earth, there is only one natural great circle, on the Celestial Sphere there are three: horizon, celestial equator and ecliptic • There are therefore three coordinate systems on the celestial sphere

15. Horizon Coordinate System • Base circle: horizon, base point: north point • Altitude and azimuth • Azimuth is measured clockwise from 0° to 360° and tracks the daily path of the Sun in the north temperate zone • 90 – altitude is called the zenith distance

16. Horizon Coordinate System 2

17. Equatorial Coordinate System • Base circle: celestial equator, base point: vernal equinox • Declination and right ascension • RA is measured counterclockwise in hours from 0h to 24h and tracks the time difference in meridian passage of stars

18. Equatorial Coordinate System 2

19. Ecliptic Coordinate System • Base circle: ecliptic, base point: vernal equinox • (Celestial) latitude and (Celestial) longitude • Longitude is measured counterclockwise from 0° to 360° and tracks the Sun’s annual motion • Celestial latitude and longitude is not relative to the celestial equator!

20. Comparing Coordinate Systems • Azimuth is measured in the opposite direction from RA and longitude • Horizon system is local, the two other are global • For stars, the horizon coordinates change with time, while the two other are fixed • Horizon for simple observations • Equatorial for tracking stars • Ecliptic for tracking Sun, Moon and planets

21. Comparing Coordinate Systems 2 • The latitude of the Moon is always less than 5° • For the planets, the latitudes are less than 3° except for Mercury, which can go up to 7° • The ex-planet Pluto could go up to 17°