2. 6 Jul 2005AST 2010: Chapter 31 Earth, Moon, and Sky

3. AST 2010: Chapter 326 Jul 2005 Locating Places on Earth In order to be able to locate places, we need to establish a reference frame or system of coordinates Chances are you are already familiar with the notions of north, south, east, and west which help orient oneself while traveling through the country

4. AST 2010: Chapter 336 Jul 2005 North, South, East, West The Earth's axis of rotation defines the North and South Poles East is the direction towards which the Earth rotates West is the opposite of east The four directions (north, south, east, and west) are well defined at almost all locations on Earth despite the fact that it is round rather than flat The only exceptions are exactly at the North and South Poles where east and west are ambiguous The Earth’s equator is a circle on the Earth’s surface, halfway between the North and South Poles

5. AST 2010: Chapter 346 Jul 2005 Coordinates on a Sphere On a flat surface it is sufficient to have a rectangular grid and the cardinal directions (north, south, east,...) to orient oneself and specify the location of places On a sphere, such as our planet, one requires a slightly more complex system of coordinates We need some new definitions and notions that will help us orient ourselves and specify places on the surface of the Earth

6. AST 2010: Chapter 356 Jul 2005 Great Circles A great circle is any circle on the surface of a sphere whose center is at the center of the sphere Examples: The Earth's equator is a great circle on the Earth's surface One can also imagine great circles that pass through the North and South Poles

7. AST 2010: Chapter 366 Jul 2005 Meridian and Longitude A meridian is a great circle that passes through the North and South Poles Any place on Earth’s surface will have a meridian passing through it, and this specifies the east-west location, or longitude, of that place By international agreement, your longitude is defined as the number of degrees of arc along the equator between your meridian and the one passing through Greenwich, England Thus, the longitude of Greenwich is zero degrees, or 0° The meridian passing through Greenwich is called the prime meridian

8. AST 2010: Chapter 376 Jul 2005 Longitudes Greenwich, England, was selected as the 0°-longitude location, after many international negotiations, because it lies between continental Europe and the United States, and because it was the site for much of the development of a way to measure longitude at sea Longitudes are measured either to the east or to the west of the Greenwich meridian from 0° to 180°

9. AST 2010: Chapter 386 Jul 2005 Latitudes The latitude of a point on the Earth’s surface is the number of degrees of arc that point is away from the equator along the meridian passing through the point Latitudes are measured either north or south of the equator from 0° to 90°

10. AST 2010: Chapter 396 Jul 2005 Example of Latitude and Longitude The latitude and longitude of the U.S. Naval Observatory in Washington, D.C., are 38.921° N and 77.066° W, respectively

11. AST 2010: Chapter 3106 Jul 2005 Celestial Sphere Revisited To specify the positions of objects in the sky, it is useful to adopt the notion of celestial sphere It was introduced by ancient astronomers, who thought that the Earth was surrounded by a solid dome, on which luminous objects were attached The celestial sphere is imaginary sphere surrounding the Earth and having its center at the center of the Earth

12. AST 2010: Chapter 3116 Jul 2005 Declination Declination on the celestial sphere is measured the same way that latitude is measured on the Earth's surface In other words, declination is measured from the celestial equator toward the north (positive) or south (negative) For example, the star Polaris, located near the north celestial pole, has a declination of about +90°

13. AST 2010: Chapter 3126 Jul 2005 Right Ascension (1) Right ascension (RA) on the celestial sphere is measured the same way that longitude is measured on the Earth's surface However, RA is different from longitude in that its starting point has been (arbitrarily) chosen to be the vernal equinox The vernal equinox is the point on the celestial sphere where the ecliptic (the Sun’s path) crosses the celestial equator

14. AST 2010: Chapter 3136 Jul 2005 Right Ascension (2) Right ascension can be expressed either in units of angle (degrees) or in units of time This is because the celestial sphere appears to turn around the Earth once a day as the planet spins on its axis Thus the 360° of RA that it takes to go once around the celestial sphere can just as well be set to 24 hours This implies that 15° (=360°/24) of arc corresponds to 1 hour of time The hour can be further subdivided into minutes

15. AST 2010: Chapter 3146 Jul 2005 Foucault’s Pendulum Experiment In 1851, French physicist Jean Foucault suspended a 60-m pendulum weighing about 25 kg from the domed ceiling of the Pantheon in Paris and started the pendulum swinging evenly In the absence of Earth’s rotation, the pendulum would have oscillated back and forth in the same exact direction However, it became clear after a few minutes of oscillations that the direction of oscillation was changing due to the rotation of the Earth, thereby providing the first direct observation of the Earth's rotation

16. AST 2010: Chapter 3156 Jul 2005 Seasonal Question Why is it hotter in summer and colder in winter here?

17. AST 2010: Chapter 3166 Jul 2005 Seasons You are no doubt familiar with the fact that at mid-latitudes, such as the United States, there are significant variations in the amount of heat we receive from the Sun in the course of the year For centuries now, the year has thus been divided into seasons to reflect the fact that some periods of the year are either warmer or colder The difference between seasons gets more pronounced the closer one gets to the poles The seasons in the Southern Hemisphere are the opposite of those in the Northern Hemisphere

18. AST 2010: Chapter 3176 Jul 2005 What Causes Seasons? Contrary to what most people believe, the seasons are NOT caused by the changing distance between the Earth and the Sun The distance of the Earth from the Sun varies by only about 3% during the course of the year Remember that the Earth’s orbit is nearly circular This small variation is NOT sufficient to explain the significant variations in temperature experienced throughout the year The common belief is also contradicted by the fact that the Earth is actually closest to the Sun in January, when the Northern Hemisphere is in the middle of winter

19. AST 2010: Chapter 3186 Jul 2005 Actual Cause of Seasons The seasons are caused by the 23° tilt of the Earth's axis relative to the plane in which it circles the Sun

20. AST 2010: Chapter 3196 Jul 2005 Seasons and Sunshine (1) By virtue of angular momentum conservation, the Earth's axis of rotation (tilted by 23° relative to the Earth's path around the Sun) always points in the same direction (relative to distant stars) This means that, as the Earth travels around the Sun, a given surface of the Earth receives different amounts of sunlight

21. AST 2010: Chapter 3206 Jul 2005 Seasons and Sunshine (2) Example: In June, the Northern Hemisphere leans into the Sun and is more directly illuminated In December, the situation is reversed and the Northern Hemisphere leans away from the Sun The situation is reversed in the Southern Hemisphere In September and March, the Earth leans "sideways" relative to the Sun, and the two hemispheres receive more or less the same illumination There are actually two effects to consider The angle of the illumination The duration of the illumination

22. AST 2010: Chapter 3216 Jul 2005 Angle of Illumination Since the Earth's tilt has a fixed orientation (relative to the stars), the angle of illumination from the Sun changes throughout the year, and so the amount of light received on a given region of the Earth's surface changes in time As much of the Sun’s light is transformed into heat in Earth's oceans, lakes, ground, and atmosphere, the temperature varies accordingly with the angle of illumination SummerWinter

23. AST 2010: Chapter 3226 Jul 2005 Duration of Illumination You have no doubt observed the duration of the day changes with the seasons In the summer, days are longer, and the Sun gets to shine longer: as more illumination is received, the temperature becomes much warmer The situation is reversed in the winter as the days are shorter and lesser amounts of illumination are received on the ground, the temperature gets colder This variation of the duration of the day again is caused by the tilted axis In June, the Sun spend more time above the celestial equator, the illumination of the Northern Hemisphere last longer, days are longer and warmer in the Northern Hemisphere Situation reversed in the Southern Hemisphere which sees little of the Sun in June, but gets most of it in December

24. AST 2010: Chapter 3236 Jul 2005 Keeping Time The measurement of time is based on the rotation of the Earth Throughout history, time has been determined by the positions of the Sun and stars in the sky Only recently have mechanical and electronic clocks taken over this important function of regulating our lives The most fundamental astronomical unit of time is the day, measured in terms of the rotation of the Earth There is, however, more than one way to define the day

25. AST 2010: Chapter 3246 Jul 2005 Length of Day Usually, the day is defined as the rotation period of the Earth with respect to the Sun — this is the solar day People of all countries set their clock to the solar day Astronomers also use a sidereal day, which is defined in terms of the rotation period of the Earth with respect to the stars A solar day is slightly longer than a sidereal day because the Earth moves along its path around the Sun in a day

26. AST 2010: Chapter 3256 Jul 2005 Difference between Solar Day and Sidereal Day Given that there are about 365 days in a year, the Earth moves roughly 1° (360°/365) of arc per day along its orbit This implies that each day the Earth has to rotate by an extra degree to complete a solar day In other words, the solar day is longer than the sidereal day by 1° Given that there 360° in one 24 hours, 1° corresponds to 24/360 hours, or about 4 minutes Thus, the solar day is about 4 minutes longer than the sidereal day

27. AST 2010: Chapter 3266 Jul 2005 Clocks Ordinary clocks are set to solar time This implies that stars appear to rise 4 minutes earlier each day Astronomers prefer using sidereal time because in that system a star rises at the same time every day

28. AST 2010: Chapter 3276 Jul 2005 Apparent Solar Time (1) Apparent solar time is determined from the actual position of the Sun in the sky The earliest measurements of time were accomplished with sundials and thus provided a measure of the apparent solar time Today we adopt the middle of the night as the starting point of the day and measure time in hours elapsed since midnight During the first half of the day, the Sun has not reached the meridian Those hours are referred to as before midday (ante meridiem, or A.M.) The hours of the second half of the day, after noon, are referred to as P.M. (post meridiem) The apparent solar time seems simple enough...

29. AST 2010: Chapter 3286 Jul 2005 Apparent Solar Time (2) It is, however, not very convenient to use because the exact length of the day varies slightly during the year because the speed of the Earth changes along its orbit around the Sun Another reason is that because of the Earth's tilted axis of rotation the apparent solar time does not advance at a uniform rate Apparent solar time has long been abandoned since the advent of exact clock that runs at a uniform rate

30. AST 2010: Chapter 3296 Jul 2005 Mean Solar Time Mean solar time is based on the average value of the solar day over the course of the year A mean solar day contains exactly 24 hours and is what we use in everyday time-keeping It is inconvenient for practical purposes because it is determined by the position of the Sun Noon occurs when the Sun is located overhead This implies that noon happens at different times at different longitudes If mean solar time was strictly applied, travelers would have to continue adjusting their watches as they travel east or west

31. AST 2010: Chapter 3306 Jul 2005 Abandonment of Mean Solar Time Mean solar time was used until roughly the end of the 19th century in the United States Basically all towns had to keep their own local time The need for a standardization became evident and pressing with the development of the railroads and telegraph A first standard was established in 1883

32. AST 2010: Chapter 3316 Jul 2005 Standard Time The nation was divided into four standard time zones in 1883 Today, a fifth zone is added to include Alaska and Hawaii Within each zone, all places keep the same standard time The standard time is adjusted to correspond to the time of a meridian lying roughly at the middle of the time zone Daylight saving time is simply the local time of a location plus one hour Adopted for spring and summer use in most states in the US as well as in many other countries to prolong the sunlight into evening hours

33. AST 2010: Chapter 3326 Jul 2005 International Date Line (1) The fact that as one travels eastward time advances poses a practical problem As one travels east, one passes a new time zone approximately every 15° and thus has to add one hour to the time on one's watch This implies that if one goes around the globe, one will end up adding 24 hours to one's watch An international date line was established by international agreement along the 180° meridian of longitude The date line runs essentially across the middle of the Pacific Ocean By convention, at the date line the date of the calendar is changed by one day Crossing the line from west to east, i.e. advancing ones time, one compensates by decreasing the date Crossing from east to west, you increase the date by 1 day

34. AST 2010: Chapter 3336 Jul 2005 International Date Line (2) Note that this implies that a given event will be referred by people living in different cities as a different date and time Japan’s attack on Pearl Harbor happened on Sunday, December 7, 1941, according to people living in the US, whereas Japanese remember it as Monday, December 8, 1941

35. AST 2010: Chapter 3346 Jul 2005 The Calendar Calendars are used to keep track of time over the course of long time spans to plan, or anticipate the changes of the seasons to honor special religious or personal anniversaries For a calendar to be useful, it must used by people who agree on common units or natural time intervals The natural units of our calendar are the day, based on the period of rotation of the Earth on its axis the month, based on the period of revolution of the moon about the Earth the year, based on the period of revolution of the Earth about the Sun

36. AST 2010: Chapter 3356 Jul 2005 Calendar Maintenance Historically, difficulties arose in maintaining a sound calendar because the three reference intervals were not commensurate to one another The rotation period of the Earth is by definition 1.0000 day The period of the moon (the time to complete its cycles), called the lunar month, is 29.5306 days The period of revolution of the Earth around the Sun (the tropical year) is 365.2422 days

37. AST 2010: Chapter 3366 Jul 2005 Origins of Our Calendar Our western calendar derives from one established by the Greeks as early as during the 8th century B.C. The Greek calendar eventually evolved into the Julian calendar introduced by Julius Cesar The Julian calendar has 365.25 days fairly close to the actual value of 365.2422

38. AST 2010: Chapter 3376 Jul 2005 Julian Calendar & Gregorian Calendar The Romans implemented this calendar by declaring the normal year to have 365 days, and one year every fourth year, a leap year, to have 366 days, thus making the average year (after four years) exactly 365.25 Although the Julian calendar represented a great advance, it still differed from the true year by about 11 minutes This was an amount that accumulated over the centuries to an appreciable error To fix the problem, Pope Gregory XIII, a contemporary of Galileo, felt it necessary to institute a reform of the Julian calendar As a result, today most of the world has adopted the Gregorian calendar established in 1582

39. AST 2010: Chapter 3386 Jul 2005 The Moon The Moon is the second brightest object in the Earth's sky after the Sun However, unlike the Sun, it does not shine under its own power, but merely glows with reflected sunlight Viewed from the Earth, the Moon appears to have a cycle of phases during the course of a month The cycle begins with the Moon starting dark — the new moon phase — and getting more and more illuminated by sunlight over the course of about two weeks After the Moon’s disk becomes fully bright — the full moon phase — it begins to fade, returning to dark about two weeks later The cycle then repeats itself

40. AST 2010: Chapter 3396 Jul 2005 Phases of the Moon [Animation] Animation

41. AST 2010: Chapter 3406 Jul 2005 The Moon’s Sidereal and Rotation Periods The Moon’s sidereal period, which is the period of its revolution around the Earth with respect to the stars, is 27.3217 days The Moon rotates on its axis in exactly the same time it takes to revolve about the Earth As a consequence, although the Moon does travel around the Earth, the Moon always keeps the same face turned toward the The so-called dark side of the Moon (its back side, the side we never see from Earth) does not actually bear its name properly The back side of the Moon is actually illuminated through half of its orbit around the Earth

42. AST 2010: Chapter 3416 Jul 2005 Eclipses of the Moon A lunar eclipse occurs when the Moon enters the shadow of the Earth  This figure is not to scale