# The celestial sphere, the coordinates system, seasons, phases of the moon and eclipses. Chapters 2 and S1

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1 The celestial sphere, the coordinates system, seasons, phases of the moon and eclipses Chapters 2 and S1

2 The celestial sphere and the coordinates system Chapter S1

3 How to find our way in the sky? Let s start with the Earth Coordinate System Latitude: N-S of the equator, Longitude: E-W along equator

4 Celestial Equator South Celestial Pole From Earth to Space The Celestial Sphere The Celestial Sphere: An imaginary sphere of infinite radius centered on Earth. The extensions of the Earth North and South Pole define the North and South celestial poles. The projection of Earth equator defines the Celestial equator. Celestial Sphere can then be divided into a grid, just like the Earth is divided into a grid of latitude and longitude. North Celestial Pole North celestial polenorth

5 Stars, planets and Sun are attached to this imaginary sphere. As the Earth rotates, the celestial sphere (with the stars attached to it) appears to rotate in the opposite direction. To explain the daily motions of the sky you can imagine the sphere rotating once in 23 hours 56 minutes (using a star as reference). The Celestial Sphere: Motions

6 Celestial Equator Celestial Sphere: Measuring Angles Longitude (E W along Equator) Right Ascension (RA) Latitude (N S of Equator) Declination (Dec) The celestial coordinate system RA, measured in hr, min, sec (0 to 24 hours) 1 hour = 60 min 1 min = 60 sec (1 hour = 15 degrees of Earth rotation) Dec, measured in degrees, arcmin, arcsec (0 celestial equator, +90 north hemisphere, -90 south hemisphere) 1 degree = 60 arcminutes 1 arcminute = 60 arcseconds North Celestial Pole orth celestial polenorth South Celestial Pole

7 There are two coordinates that allow to locate an object in the sky: Azimuth and Altitude. Their value depends in the location of the observer Azimuth: Use as reference the north direction (close to Polaris) and the range of values is from 0 to 360 degrees. 0 degrees is N, 90 degrees E, 180 is S and 270 is W. Altitude: Use as reference the horizon. The range of values is from 0 degrees (horizon) to 90 degrees (zenith) The use of RA and Dec to locate objects in the celestial sphere

8 Locating the star Vega and the Sun in the celestial sphere Ecliptic: Apparent annual path of the Sun in the celestial sphere The Sun crosses the celestial equator on March 21 (Spring equinox) and on September 21 (Fall equinox) The Sun reaches a declination of degrees on June 21 (Summer solstice) The Sun reaches a declination of 23.5 degrees on December 21 (Winter solstice)

9 Locating Polaris (North star) in the celestial sphere Locating Polaris: RA: 0h 31m s Dec: +89d Using two stars in the Big Dipper (Ursa Major) constellation called the Pointers

10 Angular Size Angular size of an object depends on two parameters The physical size of the object The distance to the object Angular size is measured in units of angle (degrees, arcmin and arcsec) Angular size = Physical Size Distance More specifically (See page 30, Mathematical Insight 2.1) Angular Size = Physical size 360 degrees 2 x Pi x distance Angular size = Physical size x 360 degrees/ (2 x Pi x distance) Example: Physical size of the Moon Angular size = 0.5 degrees Distance = 380,000 km

11 Angular Units Estimating angular sizes Practical Measurements

12 The Moon and the Sun, coincidentally, have nearly the same angular size, about 0.5 degrees. The Moon is about 380,000 km away but only 3,300 km diameter The Sun is 150,000,000 km away and about 1,400,000 km diameter

13 Celestial Sphere and the Observer Horizon: flat plane where observer stands Zenith: the point directly above an observer Nadir: the point opposite to the zenith An observer can see only half of the celestial sphere from any location on Earth

14 Apparent Motion of Stars Earth rotates from W-E celestial sphere seems to rotate E-W. Depending on our location, we ll see some stars rising on the east and setting on the west. Depending on our location, some stars never set. Those stars are called circumpolar stars. For someone standing at the equator, all stars rise and set. For someone standing at the poles, all stars are circumpolar.

15 Observer located at the equator Orientation of the sky relative to the celestial sphere, for an observer at the Earth s equator Rotating the diagram make it easier to visualize the local sky at the equator Meridian: The circle that passes through the zenith and the two celestial poles

16 Observer located at the north pole

17 Observer located at latitude 40 degrees N The latitude is the angle from the zenith to the Earth s equator. Up point to the circle on the celestial sphere with declination +40 degrees Notice that the south pole is below the horizon and invisible for an observer located at 40 degrees N latitude Rotating the diagram so the zenith is up make it easier to visualize the local sky. The blue scale along the meridian shows altitudes and directions in the local sky. Notice that the altitude of the north celestial pole is 40 degrees which correspond to the latitude of the place

18 How can we estimate our latitude? Remember that the angle between the horizon and the object is called altitude The altitude of the north celestial pole, give us our latitude. Polaris is close to the north celestial pole. By estimating the altitude of Polaris we can estimate the latitude of the observer.

19 The path of the sun on the equinoxes and solstices at latitude 40 degrees north (Latitude of Gainesville is about degrees)

20 The path of the Sun on the equinoxes and solstices at latitude 0 degrees ( Observer at equator)

21 Apparent Daily Motion of the Sun Solar day: 24 hours The Sun: Rises in the east Sets in the west Travels on an arc across the sky

22 Solar and Sidereal Days Solar day (relative to the Sun): It is the average time between two consecutive passes of the Sun through the meridian. It is on average 24 hours Sidereal day (Relative to stars): It is the time between two consecutive passes of a star through the meridian. It is on average 23 hours, 56 minutes, 4.1 seconds

23 Why is the Solar Day Longer? The reason: Earth rotation on its axis + orbital motion around the Sun The Earth has to travel an additional angle to have the Sun at the same position each day. 1 orbit = 1 full circle = 360 degrees Earth takes 1 year = 365 days to complete 1 orbit. additional angle Earth has to rotate: 360 degrees/365 days = degrees/day How long does it take the Earth to cover ~ 1 degree? It takes 1 day to rotate 360 degrees on its axis 1 day = 24 hrs = 1440 minutes 1440 minutes/360 degrees = 4 min/degree Solar day is 4 minutes longer

24 Apparent Annual Motion of the Sun Because of Earth orbital motion, the Sun position relative to the stars is different every night.

25 Apparent Annual Motion of the Sun The Sun apparent path relative to the stars is called the ECLIPTIC The Sun moves eastward relative to the stars on celestial sphere It moves ~ 1 degree per day. Why? The 12 constellations through which the Sun moves are the constellations of the ZODIAC What is a constellation? A constellation is a region of the sky limited by lines of RA and Dec. The ancients attached a figure to a constellation. The IAU defined 88 constellations that cover the celestial sphere

26 An example of a constellation: Orion the Hunter The stars form the figure of a Hunter but the stars are located a different distances. The stars in a constellation are not physical related to each other

27 The Zodiac constellations (All the Zodiac constellations lie along the ecliptic)

28 ZODIAC CONSTELLATIONS

29 There are actually 13 (NOT 12) zodiac constellations (Ophiuchus) Sky has changed since Babylonians came up with the signs of the zodiac (Earth precession later) For example: August 4 th is not Leo anymore, but Cancer The Sun spends different times in different constellations (they are not all the same size!) Scorpius only 7 days Virgo 47 days

30

31 The seasons Chapter 2 Section 2.2

32 Why do we have seasons?

33 Question TRUE OR FALSE? We have seasons because the Earth is closer to the Sun in summer and farther from the Sun in winter.

34 Question TRUE OR FALSE? We have season because the Earth is closer to the Sun in summer and farther from the Sun in winter. Hint: When it is summer in America, it is winter in Australia.

35 TRUE OR FALSE! Earth is closer to the Sun in summer and farther from the Sun in winter. Actually it is the opposite: Earth is closer to the Sun during the north hemisphere winter and farter during the north hemisphere summer (see another slide later) Seasons are opposite in the N and S hemispheres, so distance cannot be the reason. The real reason for seasons involves Earth s axis tilt.

36 What causes the seasons? Seasons depend on how Earth s axis affects the directness of sunlight.

37 Earth s rotation axis is tilted by 23.5 degrees compared to the direction perpendicular to the Earth s orbital plane 23.5

38 The sun crosses the meridian higher during the summer. In the winter the sun crosses the meridian lower in the sky.

39 Seasons

40 Summary: The Real Reason for Seasons Earth s axis points in the same direction (to Polaris) all year round, so its orientation relative to the Sun changes as Earth orbits the Sun. Summer occurs in an hemisphere when sunlight hits it more directly; winter occurs when the sunlight is less direct. AXIS TILT is the key to the seasons; without it, we would not have seasons on Earth.

41 Why doesn t distance matter? Is there a change in distance from the Sun during the year? Yes, but the variation of Earth Sun distance is small about 3%; this small variation is overwhelmed by the effects of axis tilt.

42 How do we mark the progression of the seasons? We define four special points: summer (June) solstice winter (December) solstice spring (March) equinox fall (September) equinox

43 We can recognize solstices and equinoxes by Sun s path across sky: Summer (June) solstice: highest path; rise and set at most extreme north of due east Winter (December) solstice: lowest path; rise and set at most extreme south of due east Equinoxes: Sun rises precisely due east and sets precisely due west.

44 How does the orientation of Earth s axis change with time? The effect is called precession. Although the axis seems fixed on human time scales, it actually precesses over about 26,000 years. Polaris won t always be the North Star. Positions of equinoxes shift around orbit; e.g., spring equinox, once in Aries, is now in Pisces!

45 Long-Term Changes: Climatic Changes In about 13,000 years the Earth North Pole will be closer to the Sun in December. The Earth is at its shortest distance from the Sun in January. How will this affect our seasons?

46 Moon phases and eclipses Chapter 2. section 2.3

47 Motion of the Moon The Moon rises in the east and sets in the west moving across the sky in an arc The Moon moves slowly eastward against the stars (half a degree per hour) The Moon returns to the same position among the stars every 27.3 days (its orbital period or sidereal period)

48 Why do we see phases of the Moon? Lunar phases are a consequence of the Moon s 27.3-day orbit around Earth Pearson Education, Inc.

49 Differences in angular diameter of the moon when it is at apogee (farthest from Earth) and perigee (closest from Earth ) This is caused by the elliptical orbit of the moon Pearson Education, Inc.

50 Phases of the Moon

51 Why do we see phases? The Moon emits no light of its own shines by reflecting light from the Sun The half of the Moon facing the Sun is always lit We see a combination of lit and dark areas

52 Phases of the Moon Half of Moon is illuminated by Sun and half is dark. We see a changing combination of the bright and dark faces as the Moon orbits the Earth Depending on the angle between the Moon and the Sun as seen from Earth, is the combination of bright and dark areas that we see. Examples: At new moon, the moon rises at sunrise and sets at sunset At full moon, the moon rises at sunset and set at sunrise 2010 Pearson Education, Inc.

53 Phases of the Moon Phases change in a regular sequence over a 29.5 day period (synodic period). It is the time required for a complete cycle of lunar phases

54 Question The time at which the moon rises depends on its phase (phase of the moon depends on the relative positions of the Sun, Moon & Earth) If the Sun sets at 6pm, when does a full Moon rise? At 6 pm. The side of the Moon we see is facing the Sun, so when the Sun is setting, the Moon is rising. Another way of looking at it: The Sun and the Moon are ~ 180 degrees apart. The moon and Sun rising times are 12 hrs apart. Sun rose at 6 am Moon at 6pm.

55 Another question If the Sun sets at 6pm, when does a 1 st quarter Moon rise? The Moon and Sun rising times are now 6 hrs apart (~90 degrees). If the Sun rose at 6 am, the Moon will rise 6 hours later (noon). How about New Moon and 3 rd quarter Moon?

56 Phases of the Moon: 29.5-day cycle Waxing Moon visible in afternoon/evening Gets fuller and rises later each day Waning Moon visible in late night/early morning Gets less full and sets later each day 2010 Pearson Education, Inc.

57 Question It s 9 a.m. You look up in the sky and see a moon with half its face bright and half dark. What phase is it? A. first quarter B. waxing gibbous C. third quarter D. half moon 2010 Pearson Education, Inc.

58 Question It s 9 a.m. You look up in the sky and see a moon with half its face bright and half dark. What phase is it? A. first quarter B. waxing gibbous C. third quarter D. half moon 2010 Pearson Education, Inc.

59 Phases of the Moon Why do we always see the same face of the moon? The Moon and Earth are tidally locked Moon keeps the same side towards Earth at all times. A consequence of this is that : Moon rotation period = Moon orbital period As a person walks around you, in order for you to always see her face She must be slowly spinning around ( rotating on her axis )

60 Lunar and Solar Eclipses Chapter 2

61 What causes eclipses? The Earth and the Moon cast shadows. When either passes through the other s shadow, we have an eclipse. Umbra: the dark central region of the shadow Penumbra: The lighter, outlying region of the shadow 2010 Pearson Education, Inc.

62 Lunar and solar eclipses A lunar eclipse occurs when the Earth lies directly between the Sun and the Moon, so that the Earth s shadow falls on the Moon A solar eclipse occurs when the Moon lies directly between the Sun and the Earth so that the Moon s shadow falls on Earth 2010 Pearson Education, Inc.

63 Lunar and solar eclipses Full Moon, a condition for lunar eclipse New Moon, a condition for a solar eclipse 2010 Pearson Education, Inc.

64 2010 Pearson Education, Inc. Lunar Eclipse

65 When can lunar eclipses occur? Lunar eclipses can occur only at full moon. Lunar eclipses can be Total: The moon passes through Earth s umbra Partial: If the alignment is not perfect, only part of the full Moon passes through the umbra Penumbral: The Moon passes through the Earth s penumbra 2010 Pearson Education, Inc.

66 2010 Pearson Education, Inc. Solar Eclipse

67 When can solar eclipses occur? Solar eclipses can occur only at new moon. Solar eclipses can be partial, total, or annular Pearson Education, Inc.

68 Types of solar eclipses Total eclipse: The Moon s umbra touches a small area of Earth s surface, no more than 270 km diameter. Because the Earth and the Moon are moving, this area drift across the Earth s surface and may cover a total of 7,000 km. An observer located inside this strip will see a total solar eclipse. Partial solar eclipse: If the observer is located in the penumbral part of the shadow, only part of the Sun will be covered and the observer will see a partial solar eclipse Annular solar eclipse: If the Moon is relatively far from Earth in its orbit (Or the Earth closer to the Sun or a combination of both effects), the Moon disk will not completely cover the disk of the Sun. It leaves a ring around the Sun. In that case, the umbra of the Moon s shadow will not touch the surface of Earth. The observer will see a bright ring (the Sun) around the Moon. The Earth and the Moon orbits are elliptical. Because of that, the distances between the two bodies can varies. The Sun-Earth distance can change from 147 x10^6 to 152 x 10^6 km The Earth-Moon distance can change from 357,000 to 406,000 km 2010 Pearson Education, Inc.

69 2010 Pearson Education, Inc. Types of solar eclipses

70 Why don t we have an eclipse at every new and full moon? The Moon s orbit is tilted 5 to ecliptic plane. So we have about two eclipse seasons each year, with a lunar eclipse at new moon and solar eclipse at full moon Pearson Education, Inc.

71 Summary: Two conditions must be met to have an eclipse: 1. It must be full moon (for a lunar eclipse) or new moon (for a solar eclipse). AND 2. The Moon must be at or near one of the two points in its orbit where it crosses the ecliptic plane (its nodes) Pearson Education, Inc.

72 Predicting Eclipses Eclipses recur with the 18-year, 11 1/3-day saros cycle, but type (e.g., partial, total) and location may vary. When will be the next total solar eclipse seen from the continental US? August 21, 2017 (about 4 years and 7 month from now) 2010 Pearson Education, Inc.

73 What have we learned? Why do we see phases of the Moon? Half the Moon is lit by the Sun; half is in shadow, and its appearance to us is determined by the relative positions of Sun, Moon and Earth. What causes eclipses? Lunar eclipse: Earth s shadow on the Moon Solar eclipse: Moon s shadow on Earth Tilt of Moon s orbit means eclipses do not occur for every new or full Moon. They occur during two periods each year Pearson Education, Inc.

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