Cycles of the Moon

1. 0 Cycles of the Moon Chapter 3

2. 0 Guidepost In the previous chapter, you studied the cycle of day and night and the cycle of the seasons. Now you are ready to study the brightest object in the night sky. The moon moves rapidly against the background of stars, changing its shape and occasionally producing strange events called eclipses. This chapter will help you answer four essential questions about Earth’s satellite: • Why does the moon go through phases? • What causes a lunar eclipse? • What causes a solar eclipse? • How can eclipses be predicted?

3. 0 Guidepost (continued) Understanding the phases of the moon and eclipses will exercise your imagination, and help you answer an important question about how science works: • How do we know? How do scientists get from raw data to an understanding of nature? Once you have a 21st-century understanding of your world and its motion, you will be ready to read the next chapter, where you will see how Renaissance astronomers analyzed what they saw in the sky, used their imagination, and came to a revolutionary conclusion – that Earth is a planet.

4. 0 Outline I. The Changeable Moon A. The Motion of the Moon B. The Cycle of Phases II. Practical Islamic Astronomy A. Islamic Months B. Qibla Direction C. Prayers Times III. Lunar Eclipses A. Earth's Shadow B. Total Lunar Eclipses C. Partial and Penumbral Lunar Eclipses

5. 0 Outline (continued) IV. Solar Eclipses A. The Angular Diameter of the Sun and Moon B. The Moon's Shadow C. Features of Solar Eclipses D. Observing an Eclipse V. Predicting Eclipses A. Conditions for an Eclipse B. The View From Space C. The Saros Cycle

6. I. The Changeable Moon

7. 0 The Phases of the Moon (1) • The Moon orbits Earth in a sidereal periodof 27.32 days. 27.32 days Moon Earth Fixed direction in space

8. 0 The Phases of the Moon (2) Fixed direction in space 29.53 days Earth Moon Earth orbits around Sun => Direction toward Sun changes! • The Moon’s synodic period (to reach the same position relative to the sun, i.e., the same lunar phase) is 29.53 days (~ 1 month).

10. stars stars stars stars stars stars Sun Earth’s orbit Sidereal Month Synodic Month New Moon If Earth were not revolving around the Sun, the sidereal month will be equal to the synodic month.

12. Phases of the Moon:Video Trailer

13. 0 The Phases of the Moon (3) From Earth, we see different portions of the Moon’s surface lit by the sun, causing the phases of the Moon.

14. E E E E E W

15. E E W Sun’s rays E E E

16. W E E E E E

17. E E E Sun’s rays E W E

18. W E E E E E

19. Sun’s Relation to the Moon Phases • New Moon * rises with sunrise * sets with sunset * crosses the meridian around noontime • First Quarter * rises around noontime * sets around midnight * crosses the meridian around sunset

20. Full Moon * rises around sunset time * sets around sunrise * crosses the meridian around midnight • Third Quarter * rises around midnight * sets around noontime * crosses the meridian around sunrise

22. 0 The Phases of the Moon (4) The waxing phases of the moon can be seen primarily in the evening sky: New Moon  First Quarter  Full Moon Evening Sky From night to night, the moon appears to move from west to east (right to left) - opposite to the motion within one night!

23. 0 The Phases of the Moon (5) The waning phases of the moon can be seen primarily in the morning sky: Full Moon  Third Quarter  New Moon Morning Sky Waning gibbous

24. 0 The Tidally-Locked Orbit of the Moon The Earth exerts tidal forces on the moon’s rocky interior.  It is rotating with the same period around its axis as it is orbiting Earth (tidally locked).  We always see the same side of the moon facing Earth.

25. II. Practical Islamic Astronomy

26. Start of Islamic Months • Yearly cycle of the (apparent) solar motion provides unaided time keeping in years: • Division into solar months and weeks is artificial • Monthly cycle and the daily changing visible face of the Moon provide a realistic unaided time keeping in days and months • Lunar (or luni-solar) calendrical practice is very old

27. Prevalent Practices • Traditionally, first visibility of the New Moon to unaided eye marks the beginning of the month • Actual sighting is essential especially for the fixing of important dates like those for “Idds”, but • Astronomical assistance in evaluating the conditions or chances of visibility was widely used in earlier centuries of Muslim rule. • Many Muslim astronomers then carried out extensive researches in order to lay down physical rules for determining the probability of visibility at a given location.

28. Astronomy to the Rescue • Scientific interest in predicting the time of first possible sighting goes back to a period as early as the Babylonian era • Ancient criterion of “ av “ > 12° (or 24 h) was developed in the Ancient times (Babylonian), then passed on to the Muslims through Hindus • Problem of calculation of first visibility of the New Moon was thoroughly investigated by the early Muslim astronomers in the 8th-to-10th century A.D.

29. AKG

30. Arc of Vision (aV): Depression angle of the Sun plus the altitude of Moon’s center (or arc of sight aS) Arc of Light (aL): Apparent geocentric angular distance between Sun-Moon Arc of light (aL), arc of vision (aV), and difference in azimuth (Az) (Schaefer, 1988) .

31. A Modern Guide to Astronomical Calculations of Islamic Calendar, Times, & Qibla Mohamed Ilyas (Malaysia, 1984)

32. Meziane & Guessoum (1999)

35. Common Astronomical Terms • New Moon • Moonset-Sunset Lag Time • Moon’s Age at Local Sunset • Arc of Light (aL) • Arc of Vision (aV) • Crescent Width (w) • Azimuth (Az)

36. Common Astronomical Criteria: Video Trailer • New Moon: Conjunction Time? • Moonset Lag Time • Moon’s Age at Sunset • Azimuth Angle at Sunset • Sky conditions (humidity, dust, light pollution) • Observer Eyesight

37. Ramadhan 1428 AH (2007 AD)

39. Direction of Mecca (Qibla) • The problem of determining the direction of Qibla is a problem of spherical trigonometry (or mathematical geography). • It formed an important problem for the Muslim scientists in mediaeval period who usually treated it in an astronomical form. • Most astronomical handbooks (Zijes) on time –keeping contain a chapter on the determination of the Qibla

40. Spherical Triangle (N,P,M) • Problem involves the solution of the spherical triangle formed by the place of interest (P), Mecca (M) and North (N)

41. Determining Qibla using Basic Astronomy • Find the Four Directions (N, E, S, W): Follow Sun Shadow (daylight) , Polaris (night), or even Winds (folk astronomy) • Shadow’s direction is toward the West in early morning hours • North-West before noontime • North at noontime • North-East in mid-afternoon • East in late afternoon, just before sunset • Location w.r.t Mecca: Is the person East, West, North or South of Mecca? Example: Direction of Mecca (Qibla) for Paris • Paris is North-West w.r.t Mecca – Must face South-East

42. Noontime Morning E Afternoon N S W

43. Qibla using Al-Battani’s (Albategnius) Method N Mecca O W E S

44. Qibla for Paris using Al-Battani’s Method N 37o O W E -26o Mecca S

46. Time for Five Daily Prayers • Compared to the other two religious customs, the determination of the times of prayers is relatively easy. • It involves the determination of times of specific Sun positions in the local (Z, Az) coordinate system. • Islamic prayers times have close correspondence to astronomical phenomena – sunrise, sunset, midday, and twilight.

47. Practical Requirements: Period of Five Compulsory Prayers • Fajr (Subh): • Begins at the day break, i.e. at the beginning of the (indirect) sunlight. [i.e., starts at morning astronomical twilight , 18o]. It ends at sunrise (upper limb). • Dhur: • Begins after the meridian crossing of the sun (whole disk and not the center), i.e. shortest shadow. It ends at the beginning of Asr. • Asr: • Begins when the shadow of a vertical rod is equal to the length [Asr-Shafei] or twice [Asr-Hanafi] of the rod plus its shadow at noon. It ends slightly before sunset. • Maghrib: • Begins at sunset and ends at beginning of Isha • Isha: • Begins at the end of the (indirect) sunlight [i.e., starts at evening astronomical twilight , 18o], and lasts until midnight/fajr

48. * Settings:- - Prayer times from: 15/01/2009 CE To: 25/01/2009 CE - FRANCE Paris, Long: 02:33:00.0, Lat: 49:01:00.0, Ele:0.0, Zone:1.00 - No Summer Time. - Height above mean sea-level affects rise and set events. - Subtract Fajer: 0 Min, Add Dhohur: 0 Min, Add Asr: 0 Min, Add Maghreb: 0 Min - Fajer Angle: 18 , Isha Angle: 18 - Refraction Settings: Temperature: 10 °C Pressure: 1010 mb - Mazhab: Standard - City Settings: 0 Km. - Delta T: 65.2 Second(s) ======================================================================= Date Fajer Shuroq Dhohur Aser Maghreb Isha B. Twi. Sunrise Transit ----- Sunset E. Twi. 15/01/2009 06:45 08:39 12:59 15:02 17:20 19:14 16/01/2009 06:45 08:38 13:00 15:03 17:22 19:15 17/01/2009 06:44 08:37 13:00 15:04 17:23 19:16 18/01/2009 06:44 08:36 13:00 15:05 17:25 19:17 19/01/2009 06:43 08:35 13:01 15:07 17:26 19:19 20/01/2009 06:42 08:34 13:01 15:08 17:28 19:20 21/01/2009 06:42 08:33 13:01 15:09 17:29 19:21 22/01/2009 06:41 08:32 13:01 15:10 17:31 19:23 23/01/2009 06:40 08:31 13:02 15:12 17:33 19:24 24/01/2009 06:39 08:30 13:02 15:13 17:34 19:25 25/01/2009 06:38 08:29 13:02 15:14 17:36 19:27 =======================================================================

49. Eclipses: Lunar and Solar Video Trailer

50. III. Lunar Eclipses