# Astronomy 291. Professor Bradley M. Peterson

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1 Astronomy 291 Professor Bradley M. Peterson

2 The Sky As a first step, we need to understand the appearance of the sky. Important points (to be explained): The relative positions of stars remain the same (on human time scales). The Sun moves eastward relative to the stars (about 1 per day). Relative to the Sun, stars rise 4 min earlier each day. The Moon moves eastward relative to the stars (about 13 per day). 2

3 The Celestial Sphere To understand the appearance of the sky, it is useful to imagine it as a sphere with Earth at the center. Observer can see only sky above the horizon (an imaginary plane tangent to Earth at the observer). Observer 3

4 Suppose Earth is stationary; then sky revolves around axis that is extension of the Earth s rotation axis. Rotation axis intersects celestial sphere at north and south celestial poles. The Celestial Sphere 4

5 Rotation of the sky is apparently westward as seen by the observer. Stars near celestial pole never drop below horizon. These are circumpolar stars. The Celestial Sphere 5

6 North Circumpolar Stars in Time Exposure 6

7 Rotation of the sky is apparently westward as seen by the observer. Stars near celestial pole never drop below horizon. These are circumpolar stars. Now let s expand the view of the Earth in this diagram. The Celestial Sphere 7

8 Projection of equator on to sky is the celestial equator. 8

9 The zenith is the point on the celestial sphere directly above the observer. 9

10 The meridian passes through the celestial poles and the zenith, bisecting the sky into east and west. 10

11 Apparent Paths of Stars To see the motion of the stars, let s zoom back outside the celestial sphere. 11

12 Apparent Paths of Stars During the course of the day, stars move in circles at a fixed distance from the celestial equator. This diurnal motion is really due to the rotation of the Earth, not the sky. 12

13 From mid-northern latitudes: Vega passes nearly overhead Mizar is a circumpolar star All stars north of the celestial equator are above the horizon more than 12 hours Southern stars are above the horizon less than 12 hours Stars on the celestial equator are above the horizon exactly 12 hours every day 13

14 Motion of the Sun The Sun also appears to rise in the east and set in the west due to the Earth s rotation. However, the Sun moves relative to the stars: The Sun moves eastward relative to the stars by about 1 per day. The Sun oscillates north/south (within 23.5 of the celestial equator) over a period of one year. 14

15 Sun s Motion in the Sky North Sun moves 1 /day along the ecliptic East celestial equator West ecliptic South 15

16 Sun s Motion in the Sky North Vernal equinox (first day of Spring) East celestial equator West ecliptic South 16

17 Sun s Motion in the Sky North Summer solstice (first day of Summer) East celestial equator West ecliptic South 17

18 Sun s Motion in the Sky North Autumnal equinox (first day of Autumn) East celestial equator West ecliptic South 18

19 Sun s Motion in the Sky North Winter solstice (first day of Winter) East celestial equator West ecliptic South 19

20 The ecliptic is the Sun s path among the stars. It is simply the projection of the Earth s orbital plane onto the celestial sphere. The Ecliptic September November January Ecliptic April July 20

21 Diurnal Path of the Sun The Sun s diurnal path varies during the year. Time above horizon depends on where it is relative to the celestial equator. 21

22 Equinoxes Equinoxes occur when the Sun crosses the equator (about 21 March and 21 September). Days and nights have equal length, exactly 12 hours. midnight 6 am 6 pm 9 am noon 22

23 Solstices noon Dates known as the solstices occur when Sun is farthest from the celestial equator. Summer solstice (about 21 June) 6 am 4 am 6 pm 8 pm 23

24 Solstices Dates known as the solstices occur when Sun is farthest from the celestial equator. Winter solstice (about 21 December) 8 am 6 am 4 pm 6 pm noon 24

25 The Zodiac March June Apparent eastward motion of Sun The Sun s motion on the ecliptic carries it through a group of constellations called the zodiac. 25

26 Measurement of Time Study of astronomy originally motivated by need for accurate calendars. Calendars are necessary for successful agriculture. 26

27 Seasonal Variations Seasonal variations in temperature are due to two factors: Amount of time Sun spends above horizon Maximum elevation of Sun in sky 27

28 Basic Measures of Time Measure Day Month Year Phenomenon Rotation of the Earth Revolution of the Moon Revolution of the Earth Day, month, and year are of astronomical origin. 28

29 Prehistoric Astronomy The week is also tied to astronomy: Weeks are an invention of the Babylonians, loosely based on quarter of lunar cycle. Number of days in week equals number of planets (non-stationary celestial objects) Seven objects in the sky move relative to the stars: Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn. English names for the days of the week are based on these. 29

30 Names of the Days of the Week Day (English) Teutonic God Planet Day (French/Italian) (equivalent) Sunday Sun dimanche/domenica Monday Moon lundi/lunedi Tuesday Tiw Mars mardi/martedi Wednesday Woden Mercury mercredi/mercoledi Thursday Thor Jupiter jeudi/giovedi Friday Frigg Venus vendredi/venerdi Saturday Saturn samedi/sabato 30

31 Motions of the Earth and Measures of Time The major motions of the Earth determine how we measure time Rotation days, hours, minutes, seconds Revolution and Precession years 31

32 Motions of the Earth 1 Rotation (P = 23 h 56 m ) Earth rotates eastward (i.e., west to east) on its axis. Solar Day = 24 h 00 m Sidereal Day = 23 h 56 m 32

33 Rotation of the Earth Sidereal Day Solar Day Earth one day later 23 h 56 m 1 24 h 00 m Sidereal day: one full rotation with respect to the stars. Solar day: one full rotation with respect to the Sun. 33

34 Rotation of the Earth It takes the Earth about 4 minutes to rotate the extra 1. Because of difference in sidereal and solar time, stars rise 4 minutes earlier each day. 34

35 Rotation of the Earth Proof of rotation: The Foucault Pendulum A large mass suspended by a wire oscillates in a single plane (Newton s First Law). The Earth rotates underneath the Foucault Pendulum 35

36 Major Motions of the Earth 1 Rotation (P = 23 h 56 m ) 2 Revolution (P = 1 year) The Earth revolves around the Sun, counterclockwise as seen from above the North Pole. 36

37 Revolution of the Earth Proof of revolution: Stellar parallax Parallax is the apparent motion of nearby stars due to the motion of the Earth around the Sun. 37

38 Stellar Parallax Apparent motion of nearby stars Earth three months later 1 AU " Star Sun Earth Parallax angle " 38

39 39

40 Stellar Parallax Parallax is inversely proportional to distance: = 1/ d Largest observed parallax is for Centauri = 0.75 arcseconds d = m = 270,000 AU Because stellar parallaxes are so small, they were not measured until

41 Precession Equator Earth s rotation axis Ecliptic 41

42 Precession Sun and Moon pull Earth s equatorial bulges towards ecliptic This results in westward precession of the Earth s rotation axis 42

43 Precession The line of intersection of the ecliptic and celestial equator also precesses westward. Precession causes the vernal equinox to move westward. This makes the calendar year (called the tropical year) shorter than the sidereal (or orbital) year. 43

44 Tropical Year One tropical year Vernal equinox 2000 Vernal equinox 1999 Direction of Earth s Motion Motion of the Equinoxes Sun 44

45 Tropical Year Tropical Year: days Sidereal Year: days Sun 45

46 Period of Precession Sidereal year: 365 d Tropical year: 365 d Difference: 0 d.0142 = 20 m 24 s days year N (years) 365 d.256 N 25,772 years 46

47 Time and Calendars Civil time: Based on the solar day (defined by successive transits of the Sun) Though Earth s rotation speed remains (nearly) constant, length of solar day is variable. 47

48 Time and Calendars Why is the length of the solar day variable? 1 Tilt of the Earth s axis (astronomers call this the obliquity of the ecliptic ) 48

49 Obliquity of the Ecliptic Solstice N +20º Equator W -20º Equinox Ecliptic 12 h 6 h 0 h 18 h 12 h 49

50 Qbliquity of the Ecliptic Motion of the Sun along the equator is greater at solstice than at equinox; length of the solar day is longer at solstice. 50

51 Time and Calendars Why is the length of the solar day variable? 1 Tilt of the Earth s axis (astronomers call this the obliquity of the ecliptic ) 2 Eccentricity of the Earth s orbit (Kepler s Second Law) 51

52 Eccentricity of the Earth s Orbit Solar Day Sidereal Day 52

53 Eccentricity of the Earth s Orbit Sidereal Day Solar Day 53

54 Eccentricity of Earth s Orbit Solar days are thus longest at perihelion since the Earth must rotate farther to catch up with the rapid rate at which the Sun is moving across the sky (i.e., the rapid rate the Earth is moving in its orbit). 54

55 Time and Calendars Mean Solar Time (MST): based on the apparent motion of the Sun over a year. This is what clocks measure; it moves at a fixed rate. The Sun actually moves at a variable rate; time kept by the real Sun is called apparent solar time. 55

56 Equation of Time Apparent Solar Time is where the Sun is in the sky (time measured by sundials). The difference between MST and Apparent Solar Time is the Equation of Time. MST + Equation of Time = Apparent Solar Time 56

57 Equation of Time Apparent Solar Time and Mean Solar Time can differ by as much as 16 minutes. MST + Equation of Time = Apparent Solar Time 57

58 True Sun Behind True Sun Ahead 58

59 Equation of Time 59

60 Equation of Time We can also plot the Sun s declination (angle from the celestial equator) versus the equation of time. This gives a shape called the analemma. 60

61 The Analemma The analemma shows the equation of time and declination of the Sun. This is often found on globes. Declination Aug Mar June May Sep Nov Jan Time (min) 61

62 The Analemma If you take a photograph at the same (mean solar) time each day, you can see how the Sun moves in declination and when it is ahead and behind of the mean Sun. 62

63 63

64 Time Conventions Civil Time = Mean Solar Time in year 1900 A.D. Earth s rotation is slowing down, so Earth runs slower than clocks. Compensate by periodically adding leap seconds, which let the Earth catch up to clocks. About 29 leap seconds have been added between 1900 and

65 How s the Math on That Figure? A day in the year 2000 is longer than a day in the year 1900 by seconds. The average day in the 20th Century is thus longer than a day in the year 1900 by half this, /2 = seconds. Earth falls behind clocks by this amount every day, for all days of the century seconds/day days = 29 sec. 65

66 Calendars The difficulty with calendars is that the tropical year is not an integral number of solar days. We therefore use tropical years with a variable number of integral days to approximate the true tropical year. 66

67 Early Roman Calendar Day 730 Day 365 Day 0 Early Roman calendar of 365 days per year was too short. First day of Spring occurred later each year. 67

68 Early Roman Calendar 1 year = 365 days Vernal equinox occurs later each year. After only 128 years, vernal equinox has moved from March 21 to April

69 Julian Calendar Add an extra day every fourth year: Year 1: 365 days Year 2: 365 days Year 3: 365 days Year 4: 366 days Average length of year: days 69

70 Julian Calendar But after 100 years, the Julian calendar is in error by more than 3/4 day. After 100 years: 100 tropical (75 years+25 leap years) Difference

71 Gregorian Calendar The Julian Calendar has overcorrected by 3/4 of a day, so skip a leap year every century (1800, 1900, etc.). 400 tropical 146, (304 regular years + 146, leap years) Difference

72 Gregorian Calendar But skipping a leap year every 100 years leads to an error of near one day after 400 years. Add an extra leap year every 400 years (instead of skipping the leap year in century years). Thus, 1200, 1600, 2000, and 2400 are leap years, not skipped leap years. 72

73 Gregorian Calender 365 days per year (Early Roman) Years divisible by 4 are leap years, and have 366 days (Julian modification) If year is also divisible by 100, skip the leap year and make it a regular year If year is also divisible by 400, then don t skip the leap year, keep it! (Gregorian modifications) One day error accumulates after 3225 years 73

74 Chapter 2: Emergence of Modern Astronomy 74

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