Lab3_Rotating_Sky

NAAP – The Rotating Sky 1/11 Name: Lab 3: The Rotating Sky – Worksheet I. Background Information Work through the explanatory material on The Observer , Two Systems – Celestial, Horizon , the Paths of Stars, and Bands in the Sky . All of the concepts that are covered in these pages are used in the Rotating Sky Explorer and will be explored more fully there. Enter your answers to each question in the data tables and yellow highlighted areas below. When completed, please save and upload this file to the assignment submission link in Canvas. 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 in that any stars are 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.

NAAP – The Rotating Sky 2/11 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.) 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 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 vehicle by which you make coordinate measurements. 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 is animating, the animation will cease. Once you release the mouse button the 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 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

Description Latitude Azimuth Altitude West point of the horizon Any 270 º 0 º Zenith Any Any 90 º NCP 30ºN 0 º 30 º NCP 71ºN 0 º 71 º SCP 52ºS 180 º 52 º SCP Tropic of Capricorn 180 º 23.5 º Intersection of CE and Meridian 40ºN 180 º 50 º Intersection of CE and Meridian 55 ºN 0º 35º Question 2: The next page contains a diagram known as a “fish-eye” view of the sky. Note that it is drawn like a sky- chart which is held up above your head and mimics the sky in that perspective. You should convince yourself that the east and west directions are shown correctly. Assume that you are at a northern mid-latitude of 40° N. You will be asked to create stars at specified azimuths and altitudes. You will then be asked to make predictions about the locations and motions of the stars as time advances. After drawing in your predictions you should use the simulator to check your answer. If your original prediction 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 is directly 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. To draw a point, click the "Insert" tab, click "Shape", and then pick a shape from "Basic Shapes".What will be the coordinates of star A at t = 6 hours? 37.2° altitude and 25.4° azimuth At t = 12 hours? 60.0° altitude and 0.0° azimuth At t = 24 hours? 20.0° altitude and 0.0° azimuth Draw in each of these locations and connect the path between the stars. To draw the path, click the "Insert" tab, click "Shape", and then select the "squiggle" from "Lines". For what fraction of the day is star A visible? Visible all day c) Draw in B at the specified coordinates and assume that this is time t = 0 hrs. What will be the location of star B at t = 3 hours? 32.8 ° altitude and 122.7° azimuth Star Azimuth Altitude A 0° 20° B 90° 0° C 180° -5°

At t = 6 hours? 50.0 ° altitude and 180.0° azimuth At t = 12 hours? 0.0 ° altitude and 270.0° azimuth Draw in each of these locations and connect the path between the stars. For what fraction of the day is star B visible? ½ of the day d) Draw in C at the specified coordinates (as best you can) and assume that this is time t = 0 hrs. Estimate the coordinates of the star at t = 6 hours? -31.8° altitude and 222.4° azimuth At t = 12 hours? -75.0° altitude and 180.0° azimuth At t = 24 hours? -5.0° altitude and 180.0° azimuth For what fraction of the day is star C visible ? Never visible NAAP – The Rotating Sky 4/11

Question 5: 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 : circumpolar Star B : rise and set Star C : never rise Question 6: Let’s explore the boundaries of these 3 regions. 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 of declination is made for the star. Now drag this active star so that it is at the north point of the horizon. (Make sure the star is active so you can read off its coordinates.) Note that a star with a slightly smaller declination would dip below the north point while a star that is closer to the NCP would obviously be circumpolar. Thus, this star’s declination is a limiting value for the circumpolar declination range. Complete columns 2 and 3 for each of the given latitudes. Latitude North Point Declination Circumpolar Range South Point Declination Rise & Set Range 10º N +80° +80° to +90° -80° -80° to +80° 25º N +65° +65° to +90° -65° -65° to +65° 40º N +50º +50º to +90º -50° -50° to +50° 55º N +35° +35° to +90° -35° -35° to +35° 70º N +20° +20° to +90° -20° -20° to +20° Now 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 to complete columns four and five in the table above. Star Azimuth Altitude A 0° 20° B 90° 0° C 180° -5°

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 from the equator. None of the stars are actually circumpolar from the equator because every star can be seen at some point and cannot be seen at some point. Question 8: Set the simulator up for an observer at the south pole. Make sure that there are still stars (~20) in the simulator and click animate continuously. Describe the circumpolar stars seen from the south pole. Any stars located below the celestial equator appear to be circumpolar while any star located above the celestial equator never appears to rise. Question 9: Use your experiences from questions 6, 7, and 8 to help you state a general rule for identifying the three declination ranges given the observer’s latitude. When closer to the celestial equator, stars tend to mostly appear rising and setting. However, when you go towards the poles, stars begin to more frequently be either circumpolar or never rising. At the poles stars are only either circumpolar or never rising, while at the equator all stars are rising and setting. V. Star Trails Visualizing star trails is an important skill that is very closely related to declination ranges. Again set up the simulator for a latitude of 40º N, create about 20 stars randomly in the sky, turn on long star trails, and click 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.