21 st Century Physics & Astronomy Lab Names:

Transcription

1 21 st Century Physics & Astronomy Lab Names: Section: Date: Identifying Stars and Constellations - 1

2 21st Century Physics & Astronomy Lab Identifying Stars and Constellations Authors: T. Wolfe, A. Fullard, L. Huk, P. Hallam Purpose of the Experiment To identify stars and constellations in the Autumn night sky. To understand the Horizon coordinate system and make measurements of the positions of stars, in order to calculate the Earth s diurnal motion. Identifying Stars and Constellations - 2

3 Table of Contents Background Information... 4 Stars and Constellations... 4 Horizon and Celestial Coordinate Systems... 5 Prelab... 8 The Lab... 9 Purpose of the Experiment... 9 Apparatus... 9 Files Procedure Part Ia: Setting Up for Outdoor Observations Part Ib: Setting Up for Indoor Observations Part II: Selected Stellar Measurements Part III: Finding Constellations Analysis Calculations Page Identifying Stars and Constellations - 3

4 Background Information Stars and Constellations To begin learning about astronomy, it is often best to start by studying the night sky. On a clear evening, the stars visible appear to trace out patterns against the background of space. These patterns have been studied by people of various cultures for millennia, often serving as a source of inspiration for science, theology, and art. Referred to as constellations and asterisms, the patterns do not imply any physical relationships between the stars within them. Rather, they are useful in organizing the night sky into zones by which stars can be named according to this visual association. A necessary skill for any astronomer is to be able to orient oneself with respect to these patterns, as they can help you find specific stars or other celestial bodies associated with them. The difference between asterisms and constellations is simply an organizational one. Constellations are groupings of stars, based on historical definitions, that have been adopted as official designations of star patterns by the International Astronomical Union (IAU). Asterisms, on the other hand, are colloquially-defined patterns, and used for convenience as they can sometimes be identified more easily than some official constellations. A common example of the difference between an asterism and constellation can be found by looking for The Big Dipper in the night sky. The Big Dipper, an asterism, is a relatively easy-to-identify pattern comprised of the brighter stars in the constellation Ursa Major (the big bear). This is shown in Figure 1. Asterisms are also not always confined to a single constellation. The Summer Triangle, for example, is an asterism that extends across three constellations: Cygnus (the swan), Aquila (the Eagle), and Lyra (the Lyre). Figure 1 The Big Dipper asterism within the constellation Ursa Major Identifying Stars and Constellations - 4

5 In addition to organizing stars by constellations and coordinates, astronomers use naming conventions for stars in order to help categorize them further. While many bright stars have historic Arabic names, astronomers also refer to stars by Greek letters, such as alpha (α), beta (β), or gamma (γ), according to that star's brightness rank in the constellation (the brightest usually being α). This is followed by a three-letter shorthand of the constellation name. For example, the North Star referred to as Polaris is also known as α UMi, for being the brightest (alpha-star) in the constellation Ursa Minor. You will need to identify some stars in various constellations by their Greek letter throughout this lab. Horizon and Celestial Coordinate Systems While organizing stars into groups is convenient for astronomers, it is also necessary to record an individual star's position using a coordinate system that we can map to the sky. One example is the Horizon system, which uses coordinates called altitude, the angle of a star above the horizon, and azimuth, the angle of the star along the horizon from North, measured to the East. A visual example of this system is depicted in Figures 2 and 3. Note that the astronomer, or observer, is located at the center of the reference plane (the plane from which each coordinate is measured) of this coordinate system Figure 2: Selected Altitudes Identifying Stars and Constellations - 5

6 N (0 ) E (90 ) W (270 ) Figure 3: How azimuth relates to the cardinal compass directions S (180 ) At a casual glance, stars in the night sky may appear static. However, each point of light in the night sky--stars, satellites, planets, etc.--are actually in motion. While within a few hours the intrinsic motion of some of these objects may not be perceptible to the human eye, they will still appear to move due to the motion of the Earth. This is referred to as diurnal motion, and can be witnessed by recording a group of stars' positions and then comparing these to another measurement of the same stars made a couple hours later. Of course, this change becomes more obvious with time. Because diurnal motion is caused by the rotation of the Earth and not motion of the stars themselves, the motion appears orbital. Most stars rise in the East and set in the West, while stars that are close to the points on the sky that the Earth's poles pass through--called Celestial Poles, imagining them extended to the sky--will appear to orbit these points and never set below the horizon. These stars are called circumpolar stars. During your observations, you will notice that stars closer to the North Celestial Pole will exhibit a different amount of diurnal motion compared to that of stars further away. These reference points comprise the Celestial Coordinate System. This system s coordinates are fixed to the sky, meaning that as the Earth rotates, the coordinates of each star do not change, even though their position appears to. Figure 4 shows the Celestial Sphere, which is a visual representation of this system. While you will not make measurements in these coordinates during this lab, you will need to use the ideas behind this sky-fixed, Earth-oriented coordinate system in order to calculate the speed of Earth s diurnal motion with your Horizon coordinate measurements of stars. Identifying Stars and Constellations - 6

7 23 h Celestial Meridian (0 h) +90 North Celestial Pole 1 h Celestial Sphere + Dec North Pole 0 Earth Equator Celestial Equator - Dec South Pole Vernal Equinox South Celestial Pole 90 Figure 4: The Celestial Sphere Identifying Stars and Constellations - 7

8 Prelab There is currently no on-paper prelab for this lab. Identifying Stars and Constellations - 8

9 The Lab Purpose of the Experiment: Identify stars and constellations, and measure their positions in horizon coordinates using an astrolabe. Some of these measurements will be used to calculate the diurnal motion of Earth. Apparatus Tripod Astrolabe Bubble-level Double-sided adhesive pad Flashlight or headlamp with red cellophane Windows PC (if indoors) Starry Night College (if indoors) Identifying Stars and Constellations - 9

10 Files None required Identifying Stars and Constellations - 10

11 Procedure Part Ia: Setting Up for Outdoor Observations Skip to Part Ib if performing the lab indoors (page 15) The astrolabes used in this lab (shown in Figure 5) are simplified versions of ones used throughout history to make measurements of stellar positions. While historical astrolabes were designed to measure both the Horizon and Celestial coordinates of stars, as well as provide a simple map of the sky for any time of the year, the ones used in this lab only provide Horizon coordinate measurements, but do so in a very simple and robust way. Each astrolabe has two rotational axes and two dials that provide angular measurements on the planes associated with those rotations. Acquiring any star through the astrolabe's sights will allow you to read the azimuth (the base's scale) and altitude (the tilting scale) coordinates of the star simply by looking at the where the indicators are pointed with respect to the dials on both parts of the astrolabe. However, the astrolabe must be calibrated for these measurements to be true. For true altitude, the astrolabe must be level with the ground, and for true azimuth, the base aligned such that its 0 mark is pointed due North (or an azimuth offset from North must be known for data calibration later). Figure 5: The astrolabe that will be used for taking measurements throughout the lab The tripods you ll be using are fairly simple. Each tripod has adjustable legs (in length and separation from each other) that can be locked in place using the three leg-locks on each leg. These leg-locks are indicated in Figure 6 Additionally, the camera mount on the top of the tripod can be locked in its orientation using an altitude lock, azimuth lock, and tilt lock. Each of these locks are indicated in Figure 7. Identifying Stars and Constellations - 11

12 Figure 6: The simple camera tripod that will serve as a mount for the astrolabe Figure 7: The camera mount that attaches to the top of the tripod While the directions for using the astrolabe is printed on the instrument itself, acquiring stars with its sights can be somewhat tricky, due to the narrow field of view of the instrument. Addition-ally, the plastic that the instrument is made out of is flexible, and if you aren't careful in keeping the instrument straight and stable, your readings will be imprecise. Use the following directions to ensure you collect good data during your observations. Identifying Stars and Constellations - 12

13 1.) Once at Observatory Park, begin by finding the directions of North, South, East, and West (hint: the University of Denver is due West of Observatory Park). Once you've oriented yourself with the cardinal directions, set up your tripod with one leg pointing approximately North. You can set up your tripod either on the ground, with the legs fully extended, or on a nearby table if you have access to one. Note that you can adjust the length of the tripod s legs by clipping or unclipping the three locks along the legs and extending or collapsing the legs to the desired length. Remember to relock each leg lock once you are satisfied with your tripod setup. 2.) Next, using a double-sided adhesive pad, attach the astrolabe to the camera mount atop the tripod (see Figure 8 for an example of this setup). Figure 8: Tripod and astrolabe assembled together 3.) Then place the bull's eye level on top of the astrolabe s azimuth dial. Adjust the length of the tripod legs and make the surface of the mount level by observing the bubble inside the level until it is within its circle marking. Lock down the tripod's legs at this Identifying Stars and Constellations - 13

14 point and try not to bump the tripod for the rest of the observing session. If you do, you will have to double-check that the tripod is level and re-level it if necessary. 4.) To determine the calibration offset (from due North) of astrolabe's azimuth dial, you will need to acquire Polaris (α UMi, the North Star) in the astrolabe's sights. In order to find Polaris, first find The Big Dipper, the asterism depicted in Figure 9. This asterism is located slightly West of North. If you cannot find it on your own, ask your TA for assistance. The portion of The Big Dipper that is currently lowest in the sky may be hard to see due to Denver's light pollution. 5.) Once you can identify The Big Dipper, note the two stars that form the edge of the cup portion of the dipper. The lower of these two stars will be the lowest star in the asterism. Facing the asterism, the upper of the two, called Dubhe, will be brighter, a little higher and to the right of the lower. These two stars are referred to as the pointer stars, as you can use them to envision a line that points approximately to Polaris, which will be the next obviously bright stars along that line. Use this method to find Polaris now. 6.) Polaris is referred to as the North Star since it is at a point in the sky nearly in-line with where the Earth's North Pole points, if the North Pole were considered to be an imaginary line pointing from its location on Earth into space. In other words, finding Polaris allows you to find due North form your location. At this time, sight Polaris by crouch or kneel behind the astrolabe and begin tilting the altitude axis of the instrument toward the star's position in the sky. Once at the approximately correct altitude, use both your eyes, looking along the astrolabe's sights, and adjust the astrolabe so it is pointed directly towards the star you wish to measure. 7.) Have a group member make sure that the astrolabe is stable and that it's vertical portion is straight up and down during this next step. Close one eye and with the other, look through the astrolabe's sights and try to acquire the target star in the instrument's field of view. A good methodology for this is to look through the sight closest to your eye at an angle so that you can see the star you wish to acquire, but outside of the sight farthest from your eye. Next, while continuing to look through the sight closest to your eye, move the astrolabe in small amounts so that you begin to eclipse the target star with the sight farthest from your eye. Once the star is eclipsed by the other sight, keep moving the astrolabe in the correct direction to get the star exactly in the field of view of the further sight. 8.) Once sighted on Polaris, record the azimuth reading of the astrolabe to the nearest 2.5 in the field provided below. This will be your azimuth offset for all of your measurements for the rest of the lab. Azimuth of Polaris ( ) Identifying Stars and Constellations - 14

15 NOTE: If the tripod or Astrolabe get knocked out of alignment during the lab, you record a new azimuth offset by re-sighting Polaris using the procedure above. Be sure to make note of what measurements the re-recorded offset corresponds to. 9.) Once your astrolabe is North-aligned, you may rotate your astrolabe about its azimuthal axis (and not the base itself) toward the next star you wish to observe. Proceed to Part II of this lab (page 16). Part Ib: Setting Up for Indoor Observations Due to the unpredictable nature of weather, it is an unfortunate reality that your GTA may have decided to take you to the lab room to perform your measurements indoors using the Starry Night College software. 1.) Skip this step if you began your observations outdoors but had to move inside to finish the lab due to a change in weather. On your desk you will find a tripod and an astrolabe. Perform steps 2-3 of Part Ia to assemble the astrolabe and tripod, and practice taking measurements of altitude and azimuth of different objects around the room. This just to get acquainted with the equipment, as you may use them for other labs later on. 2.) Open Starry Night College on your group s computer, and make the following changes using the menus a. Go to the File menu, and select Preferences. In the Preferences menu, go to Brightness/Contrast and change the Range to 5.5. Additionally, change the Min/Max Star Size setting to 0.1 to 11 b. Also in the Preferences menu, go to Cursor Tracking (HUD), and uncheck all boxes except the one for name c. Go to the View menu, and turn on the following features under Alt/Az (Altitude/Azimuth) Guide: Grid, and Zenith/Nadir. Then, still under the Alt/Az Guide, select Options, and set the spacing to fine. 3.) At no point in this lab should you turn on the constellations or use the info panel. Use the instructions in the rest of the lab manual to find the stars and constellations listed. Use the Alt/Az grid in Starry Night to determine the altitude and azimuth coordinates for each measurement you need to make. Record all azimuth measurements in the corrected azimuth columns of the data tables in Parts II and III. Since you are doing the lab indoors, the azimuth measurements you make will already be calibrated. 4.) When you get to part IV, before making your second set of stellar measurements, stop time in Starry Night and change the time to 8:30pm. Then proceed to measure the positions of the selected stars in Part II a second time. NOTE: The orientation of the stars on-screen may not always match the orientation of the constellations in Part III, depending on how you ve used the computer mouse to change what direction of the sky you are looking at. Identifying Stars and Constellations - 15

16 Part II: Selected Stellar Measurements Now that the Astrolabe is aligned, you may begin taking making measurements of each of the stars in Table 1, beginning with Polaris. Use the directions below to find each star and use the astrolabe to sight them and record their altitudes and azimuths as your first measurement (the columns labeled 1 for each measurement). Additionally, record the current time during each measurement in the appropriate column of the table. NOTES: Have a lab partner hold the astrolabe stable and vertical, and read the azimuth and altitude measurements provided by the instrument with the help of a flashlight. Note that due to the how the dials of the astrolabe are labeled, the azimuth reading is accurate to the nearest 2.5 and altitude to the nearest 0.5. Double-check the alignment of the azimuth scale of the astrolabe with the mark you made on the mount before recording each measurement. Realign the astrolabe as needed, and if the tripod is moved accidentally during your observations, re-check its level and level it again if necessary before proceeding with your measurements. 1.) To find Dubhe, recall that this is currently the upper of the two pointer stars in The Big Dipper. 2.) To find Caph, use the pointer stars in The Big Dipper again to form an arc upward and to the East, through Polaris until you find a W shape in the sky (it will appear to be tipped on its side). Caph is currently the star highest in the sky of this W. 3.) To find Altair, first find Vega, which is the brightest star in the Autumnal night sky, and will be located near zenith. Once you find this star, face South and follow a line downward from Vega toward the Southern horizon. 4.) Altair will be the next obviously bright star along this line. Notice: At this time, you are not being asked to measure Vega's position in the sky. Why can't you? Star Name Polaris Dubhe Caph Altair Time 1 (hh:mm) Altitude 1 ( ) Table 1: Selected stellar measurements Azimuth 1 ( ) Corrected Azimuth 1 ( ) Time 2 (hh:mm) Altitude 2 ( ) Azimuth 2 ( ) Corrected Azimuth 2 ( ) Identifying Stars and Constellations - 16

17 Part III: Finding Constellations After completing your first round of stellar position measurements, begin finding the constellations listed in Tables 2 through 7 by using the instructions below. For each constellation, measure the altitude and azimuth of the three stars listed in those tables, with help of the constellation maps provided. Please follow these instructions in order. 1.) Find The Big Dipper again and measure the stars indicated in the associated data table according to their positions indicated in the figure. Recall that the star Dubhe is part of this constellation. Figure 9: Stars in The Big Dipper portion of Ursa Major, the big bear. Table 2: Stellar measurements in Ursa Major Star Name Time (hh:mm) Altitude ( ) Azimuth ( ) Corrected Azimuth ( ) η UMa (Alkaid) ζ UMa (Mizar) ε UMa (Alioth) Identifying Stars and Constellations - 17

18 2.) Next, find Ursa Minor by finding Polaris, using the pointer stars in The Big Dipper if you need to. Polaris is the brightest star in Ursa Minor, and marks the end of handle of The Little Dipper, which Ursa Minor is sometimes referred to as. This Little Dipper forms a pattern similar to The Big Dipper, but smaller and nearly mirrors its shape in the sky (i.e., if The Big Dipper is up-right, then The Little Dipper will be upside-down) Figure 4: Ursa Minor the little bear Table 3: Stellar measurements in Ursa Minor Star Name Time (hh:mm) Altitude ( ) Azimuth ( ) Corrected Azimuth ( ) β UMi (Kochab) γ UMi (Pherkad) Identifying Stars and Constellations - 18

19 3.) Next, measure the indicated stars in Cassiopeia, which is the W -shaped constellation you found earlier, containing the star Caph. Figure 5: Cassiopeia, the queen Table 4: Stellar measurements in Cassiopeia Star Name Time (hh:mm) Altitude ( ) Azimuth ( ) Corrected Azimuth ( ) α Cas (Shedar) γ Cas (Navi) δ Cas (Ruchbah) Identifying Stars and Constellations - 19

20 4.) Next, find the constellation Cepheus. Notice the vaguely house-shaped pattern in the constellation diagram. This currently will appear upside-down in the sky, in between Ursa Minor and Cassiopeia Figure 6: Cepheus, the king Table 5: Stellar measurements in Cepheus Star Name Time (hh:mm) Altitude ( ) Azimuth ( ) Corrected Azimuth ( ) α Cep (Aldemarin) β Cep (Alfirk) γ Cep (Er Rai) Identifying Stars and Constellations - 20

21 5.) Aquila is a kite-shaped constellation containing the star Altair, which you found earlier. Measure the indicated stars in this diagram. Figure 7: Aquila, the eagle Table 6: Stellar measurements in Aquila Star Name Time (hh:mm) Altitude ( ) Azimuth ( ) Corrected Azimuth ( ) δ Aql (Deneb Okab) ζ Aql (Deneb el Okab) λ Aql (Althalamain Prior) Identifying Stars and Constellations - 21

22 6.) Next, find Pegasus, by first looking east and finding the brightest stars above the horizon. These stars form a fairly large tilted-square (or diamond-like) pattern that is about 20 across. Use your constellation diagram Figure 8 to aid you in finding this square pattern, and once you do, you ll be able to find the rest of the constellation's stars fairly easily. Note that this is the largest constellation you will find this evening. Figure 8: Pegasus, the winged horse Table 7: Stellar measurements in Pegasus Star Name Time (hh:mm) Altitude ( ) Azimuth ( ) Corrected Azimuth ( ) α Peg (Markab) β Peg (Scheat) ε Peg (Enif) Identifying Stars and Constellations - 22

23 7.) Find the star Vega once more (again, this is the brightest star in the Autumnal sky). This is part of the constellation Lyra, noted for its parallelogram-like shape. Measure Vega's position as well as the other stars indicated. Due to how high this constellation is and how small, you are not required to make any measurements of the stars within it. Figure 9: Lyra, the lyre Identifying Stars and Constellations - 23

24 8.) Find the constellation Cygnus by identifying its brightest star, Deneb. Deneb is the third star in The Summer Triangle asterism, the other two stars being Vega and Altair. If you look straight up in the night sky towards Vega, follow a line southward from Vega to Altair, and another line Northeast from Altair towards the third of tonight s sky s brightest stars, Deneb, you should be able to map out a large trianglepattern (connecting a third line from Deneb back to Vega). Deneb is the tail of Cygnus, as shown in Figure 10. Figure 10: Cygnus, the swan Identifying Stars and Constellations - 24

25 Part IV: Once you've measured the stars required of each constellation, by 8:45pm you should begin your repeat measurements of each star from your first list in Table 1. You should be able to finish these measurements by 9:00pm to complete the observation portion of this lab Analysis: 1.) If you did not do so during the lab, go through each data table in your lab manual and correct the azimuth values using your recorded azimuth offset. This is done by taking the absolute value of the difference between your azimuth data and the azimuth offset. Record the corrected values in the appropriate fields of each data table. 2.) Label Figure 11 with the appropriate azimuth markings. Start by holding the page upright (with respect to the figure s caption) and label the top vertical line as 0, just outside of the outer-most circle. Above this 0 mark, label that this is north. Then, along the outside of the circle, label each straight line similarly, in 10 increments, clockwise around the circle. Label the 90, 180, and 270 degree marks as East, South, and West, respectively. 3.) After labeling azimuth on Figure 11, label altitude by noting that the very center of the Figure corresponds to 90 in altitude. Each circle surrounding the center begins decreasing by 10 ; label each of these accordingly. The circle at the edge of the figure should have an altitude of 0 4.) Plot your altitude and azimuth data in Table 1 on Figure 10. The first positions of the stars you measured should be marked as X's, and the second as circles. Your GTAs provided your group with an equatorial grid transparency which serves as a projection of Earth's longitude and latitude system onto the sky. Because of this alignment, you can use this transparency to measure the change in angular position on the sky (in degrees). 5.) Once you have all of your data plotted in Figure 11, overlay the transparency and line it up so that the markings of North overlap, and that the center line of longitude on transparency overlaps exactly with the azimuth markings that go North-South on the horizon grid. The transparency s lines of longitude are separated by 10 degrees; you will need to use this information to make your measurements. Once they are properly aligned, approximate the motion of the stars you measured by judging how far the stars moved across the longitude axis of the transparency. Example: If one of your stars first position was exactly in between two lines of longitude and the second position was in exactly between the next two lines of longitude (essentially the star crossed one line), the apparent motion of the star in Identifying Stars and Constellations - 25

26 the amount of time between your two measurements would be approximately 10 degrees. If your group measured the stars' positions accurately, then the change in position as seen through the transparency should be mostly parallel to lines of latitude. Determine the approximate changes in positions for each star to the nearest degree in Table 8 below. 6.) Calculate the difference between the times of measurements 1 and measurements 2 for each star in Table 1, in units of hours with three decimal places. Divide the change in position you recorded by the time difference calculated for each star, and record the new value in the Rotation Speed column of Table 1. These are your estimates of the speed of diurnal motion of the Earth. 7.) Find the percent error between your calculations of rotation speed and that of the Earth (15 /hr), using the equation % Error = observed value accepted value accepted value and record these values in the Percent Difference column of Table % 8.) Some of your percent error values may be very large compared to others. If in a 24 hour period the diurnal motion of all stars in the night sky are functionally equal, why might some of your results be so far off from the accepted value of 360 /hr? (hint: this is not because of human error or improper technique on your part). 9.) Bonus: (5 pts): Provide your TAs some feedback about this lab: What did you like about it? Was it effective in teaching you some basic observational astronomy tools and techniques? What criticisms of this lab do you have, if any? Write your feedback on the Calculations page (29). Star Name Polaris Dubhe Altair Caph Table 8: Analysis of selected stellar measurements (from Table 1) Change in Position ( ) Time Difference (hr) Rotation Speed ( /hr) Percent Error (%) Identifying Stars and Constellations - 26

27 Figure 11: Horizon coordinate grid for plotting data from Table 1 Identifying Stars and Constellations - 27

28 Figure 12 Identifying Stars and Constellations - 28

29 Calculations Page: Identifying Stars and Constellations - 29