Name:The Rotating Sky – Student GuideI. Background InformationAll materials for this lab and the Rotating Sky Explorer can be found at Work through the explanatory materialon The Observer, Two Systems – Celestial, Horizon, the Paths of Stars, and Bands in theSky. All of the concepts that are covered in these pages are used in the Rotating SkyExplorer and will be explored more fully there.II. Introduction to the Rotating Sky Simulator Open the Rotating Sky ExplorerThe Rotating Sky Explorer consists of a flat map of the Earth, Celestial Sphere, and aHorizon Diagram that are linked together. The explanations below will help you fullyexplore the capabilities of the simulator. You may click and drag either the celestial sphere or the horizon diagram tochange your perspective. A flat map of the earth is found in the lower left which allows one to control thelocation of the observer on the Earth. You may either drag the map cursor tospecify a location, type in values for the latitude and longitude directly, or use thearrow keys to make adjustments in 5 increments. You should practice draggingthe observer to a few locations (North Pole, intersection of the Prime Meridianand the Tropic of Capricorn, etc.). Note how the Earth Map, Celestial Sphere, and Horizon Diagram are linkedtogether. Grab the map cursor and slowly drag it back and forth verticallychanging the observer’s latitude. Note how the observer’s location is reflected onthe Earth at the center of the Celestial Sphere (this may occur on the back side ofthe earth out of view). Continue changing the observer’s latitude and note how this is reflected on thehorizon diagram. When the observer is in the northern hemisphere the NCP isseen above the north point on the horizon at an altitude equal to the observer’slatitude. When the observer is in the southern hemisphere the SCP is seen abovethe south point at an altitude equal to the observer’s latitude. The Celestial Sphere and Horizon Diagram are also linked in that any stars areadded to the simulation are shown on both. There are many features related tostars.o A star will be randomly created by clicking the add star randomlybutton.o A star may be created at a specific location on either sphere by shiftclicking at that location. (Hold down the shift key on the keyboard whileclicking at that spot.)NAAP – The Rotating Sky 1/12

o You may move a star to any location by clicking on it and dragging it.Note that it moves on both spheres as you do this.o Note that the celestial equatorial and horizon coordinates are provided forthe “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 otherlocation to make no star active.o If you wish to delete a star, you should delete-click on it. (Hold down thedelete 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 vehicle by which you make coordinatemeasurements. If you want to make a measurement in either diagram –you 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 isanimating, the animation will cease. Once you release the mouse buttonthe present animation mode will continue. This simulator has the power to create star trails on the horizon diagram.o A series of check boxes set the star trails option. No star trails is selfexplanatory. Short star trails creates a trail behind a star illustrating itsposition for the past 3 hours. Long trails will trace out a parallel ofdeclination in 1 sidereal day.o Stars are created without trails regardless of the trail option checked. Ifeither short or long trails is checked, the trail will be drawn once thesimulator is animated.o Existing star trails will be redrawn in response to changes – the star beingdragged 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 ofthis simulator as showing the Earth isolated in space as opposed torevolving around the sun.III. Horizon CoordinatesQuestion 1: Complete the following table involving the horizon coordinate system. Youshould predict the answers and then use the simulator to check them. Remember that youcan measure coordinates by dragging the active star to that location.NAAP – The Rotating Sky 2/12

DescriptionLatitudeWest point of the ic ofCapricornIntersection of CE and Meridian40ºNAzimuthAltitudeAnyIntersection of CE and Meridian0ºQuestion 2: The next page contains a diagram known as a35ºStarAzimuthAltitudeA0 20 B90 0 C180 -5 “fish-eye” view of the sky. Note that it is drawn like a skychart which is held up above your head and mimics the skyin that perspective. You should convince yourself that theeast and west directions are shown correctly.Assume that you are at a northern mid-latitude of 40 N.create stars at specified azimuths and altitudes.You will be asked toYou will then be asked to makepredictions about the locations and motions of the stars as time advances. After drawingin your predictions you should use the simulator to check your answer. If your originalprediction was in error, redraw your star paths to reflect the correct motion.a) Draw in the location of the North Celestial Pole. Note that since this location isdirectly above the Earth's North Pole it will not move in the sky as Earth rotates.b) Draw in star A at the specified coordinates and assume that this is time t 0 hrs.What will be the coordinates of star A at t 6 hours?At t 12 hours?At t 24 hours?Draw in each of these locations and connect the path between the stars. For whatfraction of the day is star A visible?c) Draw in B at the specified coordinates and assume that this is time t 0 hrs.NAAP – The Rotating Sky 3/12

What will be the location of star B at t 3 hours?At t 6 hours?At t 12 hours?Draw in each of these locations and connect the path between the stars. For whatfraction of the day is star B visible?d) Draw in C at the specified coordinates (as best you can) and assume that this istime t 0 hrs. Estimate the coordinates of the star at t 6 hours?At t 12 hours?At t 24 hours?For what fraction of the day is star C visible?NAAP – The Rotating Sky 4/12

Question 3: Think about the characteristics of a star that passes through your zenith point(still at 40 N). Use the simulator to determine the following characteristics of this star.Rising Azimuth Setting Azimuth Declination IV. Declination RangesQuestion 4: The two end stars of the Big Dipper are known as the “pointer stars” since aline drawn through them points toward Polaris (a very important marker in the sky sinceit is located very near the NCP). Use the constellations control to add the Big Dipper tothe celestial sphere. Now manipulate the observer's location to estimate where on theEarth the Big Dipper can always be seen, where it sometimes can be seen, and where itnever can be seen. (Hint: you will need to use the start animation control since the BigDipper can be either above or below the NCP.) Repeat with Orion and the SouthernCross.Star PatternAlways CanSometimes CanNever CanBe SeenBe SeenBe SeenBig DipperOrionSouthern CrossNAAP – The Rotating Sky 5/12

Question 5: Return the simulator to 40 N latitude. In which of the 3 declination ranges(circumpolar, rise and set, or never rise) are stars A, star B,and star C found?Star A:Star B:StarAzimuthAltitudeA0 20 B90 0 C180 -5 Star C:Question 6: Let’s explore the boundaries of these 3regions. Make sure you are still at a latitude of 40º N,create a star, select the long trails option for star trails,and animate for 24 hours so that a complete parallel ofdeclination is made for the star. Now drag this activestar so that it is at the north point of the horizon.(Make sure the star is active so you can read off itscoordinates.) Note that a star with a slightly smallerdeclination would dip below the north point while astar that is closer to the NCP would obviously be circumpolar. Thus, this star’sdeclination is a limiting value for the circumpolar declination range. Complete columns 2and 3 for each of the given latitudes.LatitudeNorth PointDeclinationCircumpolarRange 50º 50º to 90ºSouth PointDeclinationRise & SetRange10º N25º N40º N55º N70º NNow drag the star to the south point on the horizon and read off the star’s declination.This is a limiting value for the never rise declination range. You should now be able tocomplete columns four and five in the table above.NAAP – The Rotating Sky 6/12

Question 7: Set the simulator up for an observer on the equator. Create some stars ( 20)in the simulator and click animate continuously. Describe the circumpolar stars seen fromthe equator.Question 8: Set the simulator up for an observer at the south pole. Make sure that thereare still stars ( 20) in the simulator and click animate continuously. Describe thecircumpolar stars seen from the south pole.Question 9: Use your experiences from questions 6, 7, and 8 to help you state a generalrule for identifying the three declination ranges given the observer’s latitude.V. Star TrailsQuestion 10: Visualizing star trails is an importantskill that is very closely related to declinationranges. Again set up the simulator for a latitude of40º N, create about 20 stars randomly in the sky,turn on long star trails, and click animatecontinuously. The view to the right illustrates theregion around the north celestial pole. Realize thatwe need to imagine what these trails would looklike from the stick figure’s perspective.NAAP – The Rotating Sky 7/12

Sketch the star trails from the observer’s perspective for each of the followinglatitudes and directions. You should indicate the position of a pole when looking N or S.Latitude Direction40 NN40 NS40 NE40 NWStar Trail DescriptionNAAP – The Rotating Sky 8/12

Pole above horizon(at zenith)90 N?0 NE0 NN (or S)NAAP – The Rotating Sky 9/12

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Question 11: Note that the simulator has a display option that illustrates the angle that thecelestial equator makes with the horizon. The angle will be nearly the same for otherparallels of declination (i.e. star trails) near the east or west point. Use the table below torecord the star trail angle for rise and set stars at various latitudes.LatitudeDirection10º NE25º NE40º NE55º NE70º NEStar Trail AngleQuestion 12: Describe a general rule for determining your latitude from looking at startrails.NAAP – The Rotating Sky 11/12

VI. Sidereal Time & Hour Angle (optional)Sidereal Time is used to describe the rotation of Earth and is needed to accuratelypoint telescopes and keep track of the positions of objects in the sky. A sidereal day isthe time needed for one complete rotation of Earth and is approximately 23 hours and 56minutes long. If Earth were rotating isolated in space and a star were on the observer'smeridian, it would take one sidereal day for it to return to the meridian again. Thesidereal time is defined as the value of right ascension of an object on the observer'smeridian.Hour angle is defined as the angular distance measured westward along thecelestial equator between the observer’s meridian and the meridian (RA value) passingthrough a celestial body. It is effectively how long until (or since) a body would (or did)travel through the observer’s meridian. If an object's hour angle is positive, then theobject has already passed through the observer's meridian.Hour angle is closely related to the sidereal time (also defined as the hour angle ofthe vernal equinox.) They are related through:This simulator displays hourangle along the parallel ofHour Angle Local Sidereal Time – Right Ascensiondeclination containing theHA LST - RAobject of interest. This isconsistent with the idea of HAThis equation effectively says: "If the rightbeing the time before/afterascension of the object of interest (RA) is greater than thetransiting the observer'sright ascension of a point on the observer's meridianmeridian. Technically it should(LST) --- then the hour angle (HA) is negative and thebe shown on the celestialobject has not yet reached the meridian."equator.Question 13: UsetheSiderealTimeandHourAngledemonstrator to answer the following questions. Assume the observer is at a mid northernlatitude of 40º N.a) A star is on the observer’s meridian. What is its hour angle?b) A star is on the celestial equator and the eastern horizon. What is its hour angle?c) On the Vernal Equinox at noon, what is the hour angle of a star with a rightascension of 2 hours?d) On the summer solstice at midnight, what is the hour angle of a star with a rightascension of 22 hours?NAAP – The Rotating Sky 12/12