Lab 1 The Rotating Sky

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Eastern Washington University *

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Astronomy

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Feb 20, 2024

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The Rotating Sky Remember to type your answers in blue text I. Background Information Work through the Main Content pages on The Observer , Two Systems – Celestial, Horizon , Paths of the Stars, and Bands in the Sky . All the concepts covered in these pages are used in the Rotating Sky Explorer simulator and will be explored more fully there. II. Introduction to the Rotating Sky Simulator  Open the Rotating Sky Explorer The Rotating Sky Explorer consists of a flat map of the Earth, Celestial Sphere, and a Horizon Diagram that are linked together. The explanations below will help you fully explore the capabilities of the simulator.  You may click and drag either the celestial sphere or the horizon diagram to change your perspective.  A flat map of the earth is found in the lower left which allows one to control the location of the observer on the Earth. You may either drag the map cursor to specify a location, type in values for the latitude and longitude directly, or use the arrow keys to make adjustments in 5 ° increments. You should practice dragging the observer to a few locations (North Pole, intersection of the Prime Meridian and the Tropic of Capricorn, etc.).  Note how the Earth Map, Celestial Sphere, and Horizon Diagram are linked together. Grab the map cursor and slowly drag it back and forth vertically, changing the observer’s latitude. Note how the observer’s location is reflected on the Earth at the center of the Celestial Sphere (this may occur on the back side of the earth out of view).  Continue changing the observer’s latitude and note how this is reflected on the horizon diagram. When the observer is in the northern hemisphere the NCP is seen above the north point on the horizon at an altitude equal to the observer’s latitude. When the observer is in the southern hemisphere the SCP is seen above the south point at an altitude equal to the observer’s latitude.  The Celestial Sphere and Horizon Diagram are also linked such that any stars added to the simulation are shown on both. There are many features related to stars. o A star will be randomly created by clicking the add star randomly button. o A star may be created at a specific location on either sphere by shift- clicking at that location. (Hold down the shift key on the keyboard while clicking at that spot.) NAAP – The Rotating Sky 1/9

o You may move a star to any location by clicking and dragging on it. Note that it moves on both spheres as you do this. o Note that the celestial equatorial and horizon coordinates are provided for the “active” star. Only one star (or none) may be active at a given time. Simply click on a star to make it the active star. Click on any other location to make no star active. o If you wish to delete a star, you should delete-click on it. (Hold down the delete key on the keyboard while clicking on the star.) o You may remove all stars by clicking the remove all stars button. o Note that stars are the means by which you make coordinate measurements. If you want to make a measurement in either diagram, place the active star at that location.  There are several modes of animation as well as a slider to control speed. o You may turn on animate continuously or for preset time intervals: 1 hour, 3 hours, 6 hours, and 12 hours. o If you click-drag a sphere to change its perspective while the simulator is animating, the animation will cease. Once you release the mouse button the present animation mode will continue.  This simulator has the ability to create star trails on the horizon diagram. o A series of check boxes set the star trails option. No star trails is self- explanatory. Short star trails creates a trail behind a star illustrating its position for the past 3 hours. Long trails will trace out a parallel of declination in 1 sidereal day. o Stars are created without trails regardless of the trail option checked. If either short or long trails is checked, the trail will be drawn once the simulator is animated. o Existing star trails will be redrawn in response to changes – the star being dragged on either sphere or changing the observer’s location. o What’s not in this simulation? – the revolution of the Earth around the sun. This simulator animates in sidereal time. One sidereal day (one 360° rotation of the earth) is 23 hours and 56 minutes long. You should think of this simulator as showing the Earth isolated in space as opposed to revolving around the sun. III. Horizon Coordinates Question 1: The first column in the following table lists the description of a point in the sky, as seen from an observer on Earth. The second column lists the observer’s latitude on Earth. From these two pieces of information, you should be able to determine the azimuth and altitude of that point in the sky. Try to predict the answers first, and then NAAP – The Rotating Sky 2/9

use the simulator to check them. You can check (and correct) your answer by creating an active star and entering the altitude and azimuth you think is correct. Description Latitude Azimuth Altitude East point on the horizon Any 90 0 Zenith Any Any 90 NCP (North Celestial Pole) 15ºN 0 15ºN NCP 48ºN 0 48ºN SCP (South Celestial Pole) 45ºS 180 45ºS SCP 50ºS 180 50ºS Intersection of CE (Celestial Equator) and Meridian 48ºN 180 42ºN Intersection of CE and Meridian 35ºS 180 35ºS Question 2: Assume that you are at latitude 48° N, which is the approximate latitude of Spokane. When making predictions about the future locations of stars A, B, and C, use the diagram on the top of the next page that depicts a “fish-eye” view of the sky. Remember that the sky appears to rotate around the NCP, which is a point at altitude = 48°, azimuth = 0° in the diagram (as seen from Spokane). Try making your predictions first, and then use an active star within the horizon diagram view simulator to check (and correct) your answers. a) Assume star A is at the specified coordinates at time t = 0 hrs. What will be the alt/az coordinates of star A at t = 12 hours? At t = 24 hours? For what fraction of the day is star A visible (above the horizon)? b) Assume star B is at the specified coordinates at time t = 0 hrs. What will be the coordinates of star B at t = 6 hours? At t = 12 hours? For what fraction of the day is star B visible? c) Assume star C is at the specified coordinates at time t = 0 hrs. What will be the coordinates of the star at t =12 hours? At t = 24 hours? NAAP – The Rotating Sky 3/9 Question 1: Approx. Az.15°/ Alt.270° Question 2: Az.15°/ Alt.0° Question 3: 0 hours to 12 hours Question 4: Az.180°/ Alt.40.6 Question 5: Az.270°/ Approx. Alt.0 Question 7: It’s never visible from 48° N Question 8: Approx. Az.309°/Approx. Alt.89° Question 10: Az.180°/Approx. Alt.-10° Star Azimuth Altitude A 0° 15° B 90° 0° C 180° -10°

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For what fraction of the day is star C visible? Question 3: For this question, assume you are in Spokane at latitude 48° N and you want to determine the declination of a star that passes through your zenith. Try to predict the answer first, and then use the simulator to verify your answer. If you go out at any time of night in Spokane and see a star directly overhead, it will have this declination. NAAP – The Rotating Sky 4/9 Question 13: It’s never visible from 48° N Question 15: Location of NCP, as seen Question 16: from Question 17: 90° Question 18:

Remember that the declination of a star indicates how far north (or south) of the celestial equator it is located. Declination = IV. Declination Ranges The area of an observer’s sky where stars can always be seen is called the circumpolar region; the area where stars can sometimes be seen in the rise and set region; and the area where stars can never be seen is the never rise region. Note that you can select these three regions in the simulator by checking the appropriate boxes under Appearance Settings . For an observer at a specific location on Earth, it is the declination of the star that determines which of the 3 regions it is found in. In this section you will be investigating these different regions. Question 4: The two end stars of the Big Dipper are known as the “pointer stars” since a line drawn through them points toward Polaris (an important marker in the sky since it is located very near the NCP). Use the s tar patterns control to add the Big Dipper to the celestial sphere. Now manipulate the observer's location on Earth to find a point (in latitude) where the Big Dipper can always be seen (circumpolar), where it sometimes can be seen (rise and set), and where it never can be seen (never rise). It will be helpful to turn on the long star trails when running the simulation to see whether or not the stars go below the horizon. You only need to find the latitude of one location that satisfies the given conditions, and record that latitude in the table below. Star Pattern Circumpolar rise and set never rise Orion Not circumpolar Between 85N and 85S Not confined to specific latitude Big Dipper 41 Between 41-90N Above 41 Southern Cross 25 S Between 25S and the Equator North of the equator Repeat with Orion and the Southern Cross. All stars within the pattern must be visible (above the horizon) to be counted as seen . NAAP – The Rotating Sky 5/9

Question 5: In which of the 3 declination ranges (circumpolar, rise and set, or never rise) Are the stars A, B, and C from question 2 found, assuming you are at latitude 48° N? Star A Rise and set Star B Never rise Star C Never rise Question 6: Let’s explore the boundaries of these 3 regions. Set the observer at latitude 40º N, create a random star, and set the coordinates of this star so that it is on the north point of the horizon (0 Az, 0 Alt). Select the long star trails option and animate for 24 hours so that a complete circle of declination is made for the star. Note that a star with a slightly smaller declination (further from the NCP) would dip below the northern horizon while a star that is closer to the NCP would be circumpolar. Thus, the declination of the star that just touches the north point on the horizon is the outer boundary of the circumpolar range. The declination of this star is called the north point declination (+50º for an observer at 40º N). All stars from this declination up to the NCP (+50º to +90º for an observer at 40º N) would be within the circumpolar range. Now set the star to the south point on the horizon and read off the star’s declination. This is the outer boundary of the never rise range, and is called the south point declination (-50º for an observer at 40º N). The range of declinations between the north point and south point declinations is the rise and set range (+50º to -50º for an observer at 40º N). Complete the columns in the table below for each of the given latitudes. Note that the coordinates for an observer at 40º N have already been provided from the above example. Latitude North Point Declination Circumpolar Range South Point Declination Rise and Set Range NAAP – The Rotating Sky 6/9

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15º N 15N 75-90 75S 65-115 25º N 25N 65-90 25N 60-90 40º N +50º +50º to +90º -50º +50º to -50º 50º N 50N 31-90 50N 40-90 85º N 85N 5-90 90N circumpolar Question 7: Set up the simulator for an observer on the equator. Create some stars (~20) in the simulator and set it to animate continuously. Describe the motion of the stars, relative to the horizon , as seen from the equator. Question 8: Change the location of the observer to the North Pole and repeat the animation. Describe the motion of the stars, relative to the horizon , as seen from the North Pole. NAAP – The Rotating Sky 7/9 Question 19: All stars are “set and rise” declination range Question 20: All stars are moving parallel with the horizon. Question 21:

V. Star Trails Visualizing star trails is an important skill that is very closely related to declination ranges. Again, set up the simulator for latitude 48º N, create about 20 stars randomly in the sky, turn on long star trails, and set the simulator to animate continuously. The view to the right illustrates the region around the north celestial pole. Realize that we need to imagine what these trails would look like from the stick figure’s perspective. Question 9: Check the box in the simulator that shows the angle between the celestial equator and the horizon. The angle will be nearly the same for all circles of declination (i.e. star trails) near the east or west point of the horizon. Use the table below to record the star trail angles for stars that rise and set at various latitudes. Latitude Direction Star Trail Angle 12º N E 80 25º N E 65 48º N E 50 55º N E 35 73º N E 20 Question 10: Notice the pattern between the latitude and star trail angle. Describe a general rule for determining your latitude from looking at just star trail angles. Summary/Conclusion (5 points): Imagine watching the sky while taking a trip from the equator to the North Pole. Describe how the location of each of the following would NAAP – The Rotating Sky 8/9 Question 22: Latitude is found by subtracting star trail angle from 90.

change as you traveled from the equator to the North Pole: The North celestial pole , the celestial equator , the circumpolar region , and the star trail angles . NAAP – The Rotating Sky 9/9 Question 23: From the equator you see the whole sky over time, rise and set. From the North Pole, you will only ever able to see half the sky.

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Lab 1 The Rotating Sky

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