ChamberlainC ALAB1

AstroLab #1 Celestial Coordinate Systems and the Use of the Star Chart By James R. Westlake, Jr., M.S. Latest Revision Date: 08/18/2018 Chandler Chamberlain Experiment Summary: One of the goals of any astronomy course is to help you learn to find your way around the night sky with the use of a star chart. Once this skill is mastered, the universe is yours to explore! Using a star chart is not difficult, but understanding it requires setting up a framework and developing a number of concepts. This lab exercise is designed to assist you in learning to use the provided SC001 and SC002 constellation charts. You will also learn about the equatorial and ecliptic coordinate systems that astronomers use to pinpoint the locations of objects in the sky. Time Allocation: 2 hours Objectives To learn the proper use of the SC001 and SC002 star charts To use the equatorial coordinate system to locate objects on the celestial sphere To use ecliptic longitude to plot the positions of solar system bodies To estimate the sidereal time on a given date and time Materials materials From: QTY Item description Student Provides 1 Pencil From AstroLab Kit 1 SC001 Equatorial Constellation Chart 1 SC002 North Polar Constellation Chart 1 Metric ruler discussion and review To a person standing beneath the star-filled sky, it appears that the stars are all the same distance away, as if attached to the inside of a distant, hollow sphere with the Earth located at its center. Ancient sky-watchers concluded that this was, quite literally, the case. This illusion led to the idea of a celestial sphere that surrounds the Earth and to which the stars are permanently attached. We know today that there is no such sphere, however, the concept of a celestial sphere is still a useful model for setting up a coordinate grid to use for locating the positions of objects in the night sky. Imagine the Earth centered inside of a great sphere, a celestial sphere. The rotation of the Earth on its axis defines its two poles, one north and one south, as well as the equator that girdles the Earth midway between the two poles. Extending the Earth’s north and south poles out to the celestial sphere defines two points in the sky called the north and south celestial poles, respectively (NCP and SCP for short). Similarly, stretching the Earth’s equator out to the celestial sphere defines the celestial equator. Just as the surface of the Earth can be unwrapped and represented on a flat map, so, too, can the celestial sphere. Your SC001 constellation chart represents the unwrapped mid-section of the celestial sphere, centered on the celestial equator. The celestial equator is the straight line that runs horizontally across the middle of the chart. The left and right edges of the chart wrap around and connect. The area surrounding the NCP is shown on the SC002 chart. Because the stars surrounding the SCP are not visible from North America, no chart is included for that region. All of the constellations visible from mid-northern latitudes are covered on the SC001 and SC002 star charts. Take a closer look at your SC001 and SC002 charts. To avoid confusion, constellation names are written with all upper case letters, for example, LYRA. Proper names of individual stars are written with lower case letters, for example, Vega. Most of the stars shown on your charts also have Greek letter designations (GLDs) such that the brightest star in any given constellation is labeled with the lower case Greek letter Alpha (?), the second brightest Beta (?), then Gamma (?), Delta (?), and so on through the Greek alphabet, followed by the possessive form of the constellation name. For example, the star named Vega also has the Greek letter designation Alpha Lyrae, which means that it is the brightest star belonging to the constellation of Lyra. Think of the Greek letter as being the star’s first name and the possessive form of the constellation name as being the star’s last name. The legend at the bottom right of the SC001 chart shows how the size of the star’s image is related to its magnitude class, or apparent brightness. The brighter the star, the bigger the dot used to represent it. It is important to remember that the size of the black dot has nothing to do with the actual size of the star, only its apparent magnitude. 0248285 Greek letter designations for stars do not date back to the time of the ancient Greek civilization. They were first introduced by German astronomer Johann Bayer in his 1603 star atlas, Uranometria. 00 Greek letter designations for stars do not date back to the time of the ancient Greek civilization. They were first introduced by German astronomer Johann Bayer in his 1603 star atlas, Uranometria. Exercise 1: Celestial Scavenger Hunt Procedure Look over your SC001 star chart and, using a pencil (not ink), circle the biggest star dot that you can find. This is the brightest star visible in our night sky. Next, find the second biggest star dot and circle it. Continue with this process until you have circled 10 stars. These are the 10 brightest stars visible in our night sky, called 1st magnitude stars. NOTE: The symbol keys located at the bottom right and top left corners of each star chart will prove helpful. SPELLING COUNTS, so read carefully. The ONLY references you are allowed to use on this exercise are your SC001 and SC002 star charts and this document. No Googling -- it defeats the purpose of the exercise! Beginning at the left edge of your chart and working toward the right, list in Table 1 the proper name (if any), the complete Greek letter designation (including the possessive form of the constellation name), and the constellation name for each of the 10 stars that you circled. You may write out the Greek letters as Alpha, Beta, Gamma, Delta, etc. The complete Greek alphabet is provided in Appendix A. The possessive forms of the constellation names can be found in Appendix B. NOTE: DO NOT list your stars in order of brightness, but in the order that they appear from left to right across your star chart. Data Table 1: Celestial Scavenger Hunt - The Ten Brightest Stars Star No. Proper Name (if any) Complete Greek Letter Designation Constellation Name Example Deneb Alpha Cygni Cygnus, the Swan 1 Procyon Alpha Canis Minoris Canis Minor, the Little Dog 2 Sirius Alpha Canis Majoris Canis Major, the Big Dog 3 Caponus Alpha Carinae Carina, the Keel 4 Betelgeuse Alpha Orionis Orion, the Hunter 5 Capella Alpha Aurigae Auriga, the Charioteer 6 Rigel Beta Orionis Orion, the Hunter 7 Achernar Alpha Eridani Eridanus, the River 8 Altalr Alpha Aquilae Aquila, the Eagle 9 Vega Alpha Lyrae Lyra, the Harp 10 Arcturus Alpha Bootes Bootes Find the proper name and complete Greek letter designation (GLD), including the possessive form of the constellation name, of the brightest star in the constellation of HYDRA, the Female Water Snake. Enter your answers in Data Table 2. Find the proper name of the star designated ? Persei in the constellation of PERSEUS, the Hero. Enter your answers in Data Table 2. Find the Messier numbers (the “M” numbers) of two nebulae found near the constellation of SAGITTARIUS, the Archer. Enter your answers in Data Table 2. Find the proper name and Messier number of the star cluster found in the constellation of CANCER, the Crab. Enter your answers in Data Table 2. Find the Messier number of the galaxy found in the constellation of ANDROMEDA, the Chained Maiden. Enter your answers in Data Table 2. Find the proper name and the complete Greek letter designation of the brightest variable star in the constellation of CETUS, the Sea Monster. Enter your answers in Data Table 2. Find the proper name and the complete Greek letter designation of the brightest double star in the constellation of CYGNUS, the Swan. Enter your answers in Data Table 2. On your SC002 polar constellation chart, find the proper name, the complete Greek letter designation, and constellation name for the bright star located closest to the North Celestial Pole (the bulls-eye of the chart). Enter your answers in Data Table 2. Data Table 2: Celestial Scavenger Hunt Answers Item No. Answers 3 Alphard Alpha Hydrae 4 Algol 5 M20 M8 6 Beehive M44 7 M31 8 Mira Omicron Ceti 9 Albireo Beta Cygni 10 Polaris Alpha Ursae Minoris discussion and review The Equatorial Coordinate System (RA and Dec) In pinpointing the locations of places on the Earth’s surface, we use a system of latitude and longitude. Latitude is defined as the number of degrees away from the equator, either north (N) or south (S). For example, the latitude of Denver, Colorado is 39.7º N, which means that Denver is 39.7º north of the Earth’s equator. Longitude is defined as the number of degrees east (E) or west (W) of the prime meridian that runs north to south through the Royal Observatory in Greenwich, England. For example, the longitude of Denver, Colorado is 105.0º W, which means that Denver is located 105.0º west of the prime meridian. Locating the positions of objects on the celestial sphere is done in a very similar manner using a system of celestial latitude and longitude called the equatorial coordinate system. Celestial latitude, called declination (Dec), is defined as the number of degrees away from the celestial equator, either north (+) or south (-). Declination specifies the north/south position of a star and will always be a number between 0º and 90º. Referring to your SC001 chart, you’ll see that the declination of the star Betelgeuse in ORION is +7.5º, and the declination of the star Antares in SCORPIUS is -26º. Declination scales are located along the right and left edges of your star chart, as well as in several intermediate places. The small divisions on each declination scale represent one degree, except on the scale located along the lower right edge of your chart. This scale is subdivided into one-half degree intervals. Just be aware of it. Celestial longitude is called right ascension (RA). Just as the prime meridian on the Earth’s surface is defined as running through the Royal Observatory in Greenwich, England, the “prime meridian” of the sky is defined as running through a point in the sky called the vernal equinox. Referring to your SC001 chart, you will find the vernal equinox at the very center of your chart, and the “prime meridian” of the sky is the line that runs vertically through it. Unlike longitude on the Earth’s surface that is measured in degrees, however, right ascension is measured in hours and minutes. The entire celestial sphere is divided into 24 equal slices, each one called one hour of RA. Similarly, each hour of RA is chopped into 60 pieces, each one called one minute of RA. Each minute of RA is then chopped into 60 seconds of RA. You will notice that the top and bottom margins of your SC001 chart show the RA scale marked off in hours. Also notice that the “prime meridian” is labeled with 0h. Right ascensions of stars are measured from the 0h line eastward, or, to the left on your SC001 chart. Each small division on the RA scale represents 5 minutes of RA. For example, the RA of the star Betelgeuse in ORION is just shy of the 6h circle at about 5h 55 min (written as 5:55). This means that Betelgeuse is located 5h and 55 min east of the vernal equinox. Another example: The RA of the Alpha (?) star in CORONA BOREALIS is 15:35. DO NOT make the mistake of trying to relate the hours and minutes of RA to the hours and minutes of time on your watch. They do not correlate in any simple way. Although measured in hours and minutes, RA gives the position of an object on the celestial sphere, not the time. Exercise 2: The Equatorial Coordinate System Procedure To get some practice reading the equatorial coordinates on your SC001 and SC002 star charts, fill in all of the blanks in Data Table 3. Locate each star (or object) listed in the table and identify the constellation to which it belongs and its complete Greek letter designation, if it has one. Then, measure its right ascension (RA) and declination (Dec) and fill in the table. If the RA and Dec are already given, then go to those coordinates to find the name of the star (or object), its complete Greek letter designation (if any), and its constellation. SPELLING COUNTS, so be careful. NOTE: For the Greek letter designation, you must include the Greek letter from the star chart plus the possessive form of the constellation name, like in the examples provided in the table. Data Table 3: The Equatorial Coordinates of Selected Objects Object Name Greek Letter Designation (if any) Constellation Name RA Dec Arcturus Alpha Bootis Bootes 14:15 +19º Deneb Alpha Cygni Cygnus 20:45 +45º Kochab Beta Ursae Minoris Ursa Minor 14:50 +74º Vega Alpha Lyrae Lyra 18:40 +49º M13 Hercules 16:40 +36.5º Fomalhaut Alpha Piscis Austrinus Piscis Austrinus 22:55 -29.5º Antares Alpha Scorpii Scorpius 16:30 -26.5º Altair Alpha Aquilae Aquila 19:50 +9º Dubhe Alpha Ursae Majoris Ursa Major 11:05 +62º Alpheratz Alpha Andromedae Andromeda 00:10 -29º discussion and review Geocentric Ecliptic Longitude (GEL) Another important feature on your SC001 star chart is the ecliptic. The ecliptic is the curved line that crosses your chart from left to right. You will notice that it crosses the celestial equator at two points, at the 0h circle and at the 12h circle. The significance of the ecliptic is that it marks the path that the Sun follows across the sky during the course of one year. In fact, if you look closely, you will see that the ecliptic is marked off with the dates of the year in ten-day intervals. Thus, you can see exactly where the Sun is located on any given day of the year. For example, on July 4th each year, the Sun sits in the heart of the constellation of GEMINI, the Twins. Every Groundhog Day (Feb 2), the Sun is in the constellation of CAPRICORNUS, the Sea Goat. During the course of one year, the Sun passes in front of twelve different constellations. Starting at the right edge of your SC001 star chart, they are: VIRGO, LIBRA, SCORPIUS, SAGITTARIUS, CAPRICORNUS, AQUARIUS, PISCES, ARIES, TAURUS, GEMINI, CANCER, and LEO. These are the twelve constellations of the zodiac. Zodiac is a word that means “circle of animals.” The Sun is not the only object that follows the ecliptic and passes through the twelve constellations of the zodiac. The Moon and all of the planets closely follow the ecliptic, although, not exactly on it like the Sun. This is due to the fact that our solar system is flat, like a pancake. The planets all orbit the Sun in nearly the same plane. The Moon is never more than 5.5º off the ecliptic and the naked eye planets never stray more than 9º off the ecliptic. It is often convenient, when dealing with the position of a solar system body, to indicate its geocentric ecliptic longitude (GEL). This specifies where the body is located along the ecliptic, as seen from Earth. Notice that the ecliptic on your chart is also labeled with degree markings at 10-degree intervals. The 0º point is located at the vernal equinox, at the center of your chart, where the ecliptic crosses the celestial equator and the 0h circle. Ecliptic longitudes are measured eastward from this point. For example, notice that the EL of the Sun on July 4th each year is about 103º. Exercise 3: Ecliptic Longitude Procedure Look up, in Appendix C, the geocentric ecliptic longitude (GEL) of the seven major solar system bodies that are easily visible to the unaided eye - Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn - for the closest first day of the month. For example, if today is Jan 15, 2018, then look up the GELs for Jan 1, 2018. If today is Jan 16, 2018, then look up the GELs for Feb 1, 2018. Record today’s date and the date of your GELs for the listed bodies in Data Table 4. Plot the GELs of the seven bodies directly on your SC001 star chart (in pencil only). Circle and label each position with the name of the appropriate body. Once you have plotted and labeled the positions of the seven solar system bodies, answer the following questions and record your answers in Data Table 4. SPELLING COUNTS, so be careful. In which zodiacal constellation is the Sun seen on the given date? NOTE: If the body is on the border between two zodiacal constellations, list both. In which zodiacal constellation is the Moon seen on the given date? In which zodiacal constellation is the planet Mercury seen on the given date? In which zodiacal constellation is the planet Venus seen on the given date? In which zodiacal constellation is the planet Mars seen on the given date? In which zodiacal constellation is the planet Jupiter seen on the given date? In which zodiacal constellation is the planet Saturn seen on the given date? Which of the bodies (if any) are located within 15º of the Sun’s position and are, therefore, lost in the Sun’s glare and not observable on the given date? Data Table 4: Geocentric Ecliptic Longitudes (GEL) of the Sun, Moon, and Planets Today’s Date: 9/9/18 Closest first day of a month: 9/1/18 Object Name GEL Constellation Name Observable? (Y/N) Sun 159 Leo N/A Moon 42 Aries yes Mercury 142 Leo yes Venus 203 Scorpius yes Mars 299 Capricornus/ Sagittarius yes Jupiter 227 Libra yes Saturn 273 Sagittarius yes discussion and review Sidereal Time and Using the SC001 and SC002 Constellation Charts In order to use the SC001 and SC002 constellation charts to find your way around the sky, you first have to determine which half of the sky shown on your chart is actually above your horizon and visible at the date and time that you are outside observing. Imagine a line drawn in the night sky that runs exactly north to south, through the NCP and the SCP, and passes through your overhead point, or zenith. This imaginary line is called your meridian. When a star rises above your eastern horizon, it moves higher and higher until it crosses your meridian, then it sinks lower and lower, finally setting below your western horizon. A star’s meridian crossing marks its high point for the day. For example, when the Sun crosses your meridian, it is high noon. Sidereal time, or “star time,” is defined as being the RA line that is crossing your meridian at any given moment. Thus, your stationary meridian is like the hand of a clock that tells you the sidereal time. If the 6:00 RA line is crossing your meridian, then the sidereal time is 6:00. Looking at your SC001 star chart, you will notice that when 6:00 RA is crossing your meridian, the constellations of ORION, LEPUS, and AURIGA are near their high point for the day and are well placed for observing. Determining the sidereal time that you are outside observing is crucial to knowing which constellations are well placed for observing at that hour. To assist you with this, your SC001 star chart is labeled along the bottom margin with the dates of the year at roughly 15-day intervals. Your SC002 polar chart is labeled similarly around the edge of outermost circle. The date listed underneath each hour of RA tells you the date on which that RA line is crossing your meridian at 8:00 pm by your watch (or 9:00 pm by your watch during Daylight Savings Time). Read this last statement over and over until it makes sense. NOTE: We are on Daylight Savings Time (DST) between the second Saturday in March and the first Sunday in November. All other dates are on Standard Time. As an example, let’s determine the sidereal time on July 10, if you are outside observing at 10:00pm by your watch. Follow these steps: Look along the bottom margin of your SC001 star chart and find the date closest to July 10. That would be the date marked “July 6.” No need to interpolate between dates – just go with the closest one. Notice the RA hour line that corresponds to your chosen date. In this case, “July 6” corresponds to the 15 hour RA line. Because DST is in effect in July, this tells us that the 15:00 RA line is on your meridian at 9:00pm on July 6 and, by default, on our chosen date of July 10. So, the sidereal time at 9:00pm on July 10 is 15:00 RA. But we are not outside observing at 9:00pm, we are outside at 10:00pm. That just means that we need to add one more hour to our sidereal time, making it 16:00 RA. Therefore, at 10:00pm on July 10, the stars and constellations along the 16:00 RA line are positioned right along your celestial meridian. You can see that this includes the constellations of LUPUS, LIBRA, and BOOTES, to name a few. What other constellations are in view at 10:00pm on July 10? Because only one-half of the sky is visible at any given moment (that’s 12 hours of RA), you can see constellations within about 6 hours either side of your meridian. So, on July 10 at 10:00 pm, you would be able to see the constellations between the 10:00 RA line (that’s 16:00 minus 6:00) and the 22:00 RA line (that’s 16:00 plus 6:00). To use the SC002 polar chart, determine the sidereal time on the date and time that you are observing, then, rotate the chart until the corresponding date and RA line are positioned at the TOP as you hold it in front of you. The SC002 chart will then match the real sky at that moment. Here’s one more example. See if you can determine the sidereal time on November 30 at 11:00 pm, the constellations visible along your meridian at that time, and the 12-hour range of sky visible at that time. You can check your answers by scrolling down to the very end of this lab. Did you get the correct answers? Great! Then you’re ready to move on to the next exercise. -10160175260 Most major observatories have two different clocks on the wall. One is a clock that shows the civil time. The other one shows the sidereal time. The civil clock runs on a 24-hour mean solar day and the sidereal clock runs on a 23 hour 56 minute sidereal day, the true rotation rate of the Earth. The two clocks display the same time on only one day each year. Can you figure out on which day that happens? 00 Most major observatories have two different clocks on the wall. One is a clock that shows the civil time. The other one shows the sidereal time. The civil clock runs on a 24-hour mean solar day and the sidereal clock runs on a 23 hour 56 minute sidereal day, the true rotation rate of the Earth. The two clocks display the same time on only one day each year. Can you figure out on which day that happens? Exercise 4: Sidereal Time and Using the Star Charts Procedure Refer to your SC001 star chart and determine the sidereal time at 9:00pm by your watch on the closest first day of the month to today’s date. For example, if today is August 15, then drop back and look up the sidereal time for August 1. If today is August 16, then jump ahead and look up the sidereal time for September 1. Record this chosen date, watch time, and sidereal time in Data Table 5. List in Table 5 the names of SIX constellations located on or near your meridian and, thus, best placed for observing on your chosen date at 9:00pm. Use BOTH the SC001 and SC002 star charts. SPELLING COUNTS, so be careful. Determine the 12-hour range of RA that will be visible above your horizon on your chosen date and time. (Hint: Add and subtract 6 hours from the sidereal time you found in step 1.) Record your answer in Data Table 5. Add two more hours to your original sidereal time and determine the new sidereal time at 11:00 pm on your chosen date. Record this new sidereal time in Data Table 5. List in Data Table 5 the names of SIX constellations located on or near your meridian and, thus, best placed for observing on your chosen date at 11:00pm. Use BOTH the SC001 and SC002 star charts. SPELLING COUNTS, so be careful. Data Table 5: Sidereal Time Your Chosen Date (Closest first day of the month): September 5th 2018 Sidereal Time at 9:00pm: 19:00 RA Six constellations on the meridian at 9:00pm: Corona Australis, Sagittarius, Scutum, Aquila, Serpens, Lyran 12-hour RA range visible at this sidereal time: 13:00 RA- 1:00RA Sidereal Time at 11:00pm: 21:00 RA Six constellations on the meridian at 11:00pm: Indus, Microscopium, Capricornus, Equuleus, Delphinus, Cygnus Questions What does the Greek letter designation “Gamma Canum Venaticorum” tell you about that star? Be specific! The star is located in the constillation Canes Venatici. It is the third brigtest star in that constilation. What are the equatorial coordinates (both RA and Dec) of the Vernal Equinox? 0:0 RA 0.0º What happens to the equatorial coordinates (the RA and Dec) of a star during the night, as the Earth rotates? The coordinates stay the same. How long does it take the Sun to complete one 360º trip around the ecliptic and through all twelve constellations of the zodiac? One year What is the only day of the year that the time showing on a sidereal clock and the time showing on your watch would be the same? Explain why you chose that date. The date would be April 6th. April sixith has a sidereal time of 9:00 RA. Considering daylight savings time, our time would also be 9:00pm. ****************************************************************************** Appendix A: The Greek Alphabet Letter Upper Case Symbol Lower Case Symbol alpha ? ? beta ? ? gamma ? ? delta ? ? epsilon ? ? zeta ? ? eta ? ? theta ? ? iota ? ? kappa ? ? lambda ? ? mu ? ? nu ? ? xi ? ? omicron ? ? pi ? ? rho ? ? sigma ? ? tau ? ? upsilon ? ? phi ? ? chi ? ? psi ? ? omega ? ? Appendix B: The 88 Official Constellations Constellation Name English Nickname Possessive Form Andromeda The Chained Maiden Andromedae Antlia The Air Pump Antliae Apus The Bird of Paradise Apodis Aquarius The Water Carrier Aquarii Aquila The Eagle Aquilae Ara The Altar Arae Aries The Ram Arietis Auriga The Charioteer Aurigae Bootes The Herdsman Bootis Caelum The Engraving Tool Caeli Camelopardalis The Giraffe Camelopardalis Cancer The Crab Cancri Canes Venatici The Hunting Dogs Canum Venaticorum Canis Major The Big Dog Canis Majoris Canis Minor The Little Dog Canis Minoris Capricornus The Sea Goat Capricornii Carina The Keel (of the ship Argo) Carinae Cassiopeia The Queen Cassiopeiae Centaurus The Centaur Centauri Cepheus The King Cephei Cetus The Sea Monster Ceti Chamaeleon The Chameleon Chamaeleontis Circinus The Drafting Compass Circini Columba The Dove Columbae Coma Berenices Queen Berenice’s Hair Comae Berenices Corona Australis The Southern Crown Coronae Australis Corona Borealis The Northern Crown Coronae Borealis Corvus The Crow Corvi Crater The Cup Crateris Crux The Southern Cross Crucis Cygnus The Swan Cygni Delphinus The Dolphin Delphini Dorado The Dolphinfish Doradus Draco The Dragon Draconis Equuleus The Little Horse Equulei Eridanus The River Eridani Fornax The Furnace Fornacis Gemini The Twins Geminorum Grus The Crane Gruis Hercules The Strong Man Herculis Horologium The Pendulum Clock Horologii Hydra The Female Water Snake Hydrae Hydrus The Male Water Snake Hydri Indus The Indian Indi Lacerta The Lizard Lacertae Leo The Lion Leonis Leo Minor The Little Lion Leonis Minoris Lepus The Rabbit Leporum Libra The Scales Librae Lupus The Wolf Lupi Lynx The Lynx Lyncis Lyra The Harp Lyrae Mensa The Table Mensae Microscopium The Microscope Micrscopii Monoceros The Unicorn Monocerotis Musca The Fly Muscae Norma The Carpenter’s Square Normae Octans The Octant Octantis Ophiuchus The Serpent Bearer Ophiuchi Orion The Hunter Orionis Pavo The Peacock Pavonis Pegasus The Winged Horse Pegasi Perseus The Hero Persei Phoenix The Phoenix Phoenicis Pictor The Painter Pictoris Pisces The Fishes Piscium Piscis Austrinus The Southern Fish Piscis Austrini Puppis The Poop Deck (of the Ship Argo) Puppis Pyxis The Compass Pyxidis Reticulum The Reticle Reticuli Sagitta The Arrow Sagittae Sagittarius The Archer Sagittarii Scorpius The Scorpion Scorpii Sculptor The Sculptor Sculptoris Scutum The Shield Scuti Serpens The Serpent Serpentis Sextans The Sextant Sextantis Taurus The Bull Tauri Telescopium The Telescope Telescopii Triangulum The Triangle Trianguli Triangulum Australe The Southern Triangle Trianguli Australis Tucana The Toucan Tucanae Ursa Major The Big Bear Ursae Majoris Ursa Minor The Little Bear Ursae Minoris Vela The Sail (of the Ship Argo) Velorum Virgo The Maiden Virginis Volans The Flying Fish Volantis Vulpecula The Fox Vulpeculae Appendix C: Geocentric Ecliptic Longitudes* (GELs) of the Sun, Moon, and Planets Date Sun Moon Mercury Venus Mars Jupiter Saturn 01/01/2018 281 85 258 279 224 227 271 02/01/2018 312 138 301 317 243 231 275 03/01/2018 340 146 350 353 260 233 277 04/01/2018 11 197 13 31 278 232 279 05/01/2018 41 232 14 68 293 229 279 06/01/2018 70 277 64 105 305 226 278 07/01/2018 99 310 123 140 309 223 276 08/01/2018 129 354 142 174 303 224 274 09/01/2018 159 42 142 203 299 227 273 10/01/2018 188 80 195 220 306 232 273 11/01/2018 219 133 241 210 321 238 275 12/01/2018 249 171 240 209 339 245 278 * GELs are from the NASA/JPL website: http://ssd.jpl.nasa.gov/horizons.cgi#top Answers to the sidereal time example: The sidereal time at 11:00pm on November 30 is 4:00 RA. The constellations along your meridian would include HOROLOGIUM, ERIDANUS, TAURUS, PERSEUS, and CAMELOPARDALIS. The 12-hour RA range visible in the sky at that date and time would be between the 22:00 RA line and the 10:00 RA line.