Orientation to the Sky: Apparent Motions

Transcription

1 Chapter 2 Orientation to the Sky: Apparent Motions 2.1 Purpose The main goal of this lab is for you to gain an understanding of how the sky changes during the night and over the course of a year. We will see how the stars move on a daily to yearly basis. We will explore the altitude-azimuth and RA-declination coordinate systems and the advantages and disadvantages of each. 2.2 Introduction As a first orientation to the sky and the motions of celestial objects, we will be using a computer planetarium. Such programs are very powerful and can display the positions and trajectories of celestial objects observed from any place and time on Earth, as well as from other planets. They also allow one to step forward and backward in time and make it easy to view how the sky changes over periods of a few minutes to hundreds or thousands of years Coordinate Systems To pinpoint any location on Earth, you must specify two coordinates (i.e., latitude and longitude). Similarly, two coordinates are required to locate an object on the celestial sphere. There are actually two different coordinate systems commonly used by astronomers. We will examine both of these systems. 3

2 Figure 2.1: The Local Coordinate System The Local Coordinate System The local (a.k.a. altitude-azimuth) coordinate system is based on two perpendicular coordinates: the azimuth angle, or the angle along the horizon from North, and the altitude angle, which is the angle above the horizon. Refer to Figure 2.1. An azimuth of 0 corresponds to due North. East has an azimuth of 90, South has an azimuth of 180, and so forth, just like a compass. The altitude can range from an angle of 0 (along the horizon) to 90 (right above your head, your zenith point). Using these two coordinates, you can locate any object above the horizon. The local coordinate system is easy, but it has its flaws As objects appear to move, their alt-az coordinates change. Furthermore, these coordinates are related to your position on Earth. So while they re useful for finding objects when you re standing outside, they re not useful for collaborating with your astronomy friends who live in different cities. Fortunately, there s another coordinate system that astronomers employ The Celestial (a.k.a. Equatorial) Coordinate System For the Equatorial coordinate system, imagine that Earth s latitude and longitude lines have been projected onto the celestial sphere. This coordinate system is measured in units of Right Ascension (RA) and declination (decl). RA corresponds to lines of longitude; declination corresponds to lines of latitude. This coordinate system is based on the Celestial Equator and the Celestial Poles, and thus doesn t depend on your location on Earth. In a sense, this coordinate system is attached to the stars. Each star has a unique Right Ascension and a unique declination. These coordinates can be used to determine when a star will be above your horizon, no matter where you are on Earth. To understand the Celestial coordinate system, take our picture of the Earth at the center of the Celestial Spherical shell. Extend the Earth s equator to the stars and call it the Celestial 4

3 Equator. Extend the Earth s polar axis to the stars and call the points of intersection the North and South Celestial Poles. As the Earth orbits the Sun over the course of a year, the Sun appears to live in different constellations (i.e., the zodiac) on the Celestial Sphere. We ll add in the path that the Sun takes: This figure provides a lot of insight into this coordinate system. Notice its features: the Sun s path intersects the Celestial Equator on the equinoxes. The sun is farthest away from the Celestial Equator on the solstices. Now, we ll introduce some nomenclature: add lines of celestial latitude and call it declination. Add lines of celestial longitude and call it Right Ascension. Notice how these coordinates are measured. Declination is measured in units of degrees. A degree can be broken up into arcminutes ( ), which can be broken up into arcseconds ( ). 5

4 There are 60 arcseconds in an arcminute and 60 arcminutes in a degree. Declination ranges from 90 at the South Celestial Pole to +90 at the North Celestial Pole. A declination of 0 corresponds to the Celestial Equator. Right Ascension is measured in units of hours, not degrees, and runs around the Equator. As a convention, an RA of 0 hours corresponds to the point in the sky where the Sun crosses the Celestial Equator at the Vernal Equinox. RA increases going East. An RA of 12 hours corresponds to the point in the sky where the Sun crosses the Celestial Equator at the Autumnal Equinox. An RA of 24 hours is the same as an RA of 0 hours. The following figure shows the entire Celestial Sphere filled in with lines of RA and declination: Measuring an angle in units of time may seem counter-intuitive at first, but there s a reason for it that we will learn shortly. We can always convert back to units of degrees: From the above figures, we can see that the entire Celestial Equator occupies 24 hours of Right Ascension. You should also know that a circle occupies 360. Therefore: 6

5 24 hr = hr = 15 This simple conversion tells us an important piece of information: in 1 hour of time, the stars appear to move 15 because of the Earth s rotation. It s essential to notice that the coordinate system is now fixed with respect to the fixed stars. In this system, a star s RA and declination do not change. What does change is the rotation of the coordinate system with respect to the local observer (you). In other words, as the Earth turns, you see the fixed stars move. The point directly above your head is called the zenith. The imaginary line connecting the poles, which passes through the zenith, is called the meridian. What changes throughout the night, in a very regular way, is the value of the RA that corresponds to your local meridian. This is why RA is measured in units of time! If your meridian currently has an RA value of 5 hours, then a star with a RA of 6 hours will lie on your meridian in one hour. 2.3 Procedure After we have looked at the Local and Celestial coordinate systems in a more detail with the Rotating Sky Explorer, we will install and use the digital planetarium program, Stellarium, to view the night sky in Williamsburg as it appears at various times Rotating Sky Explorer Start a web browser on your laptop, go to the astronomy class web page labs/astro/ and click on the software menu option. Select the Rotating Sky Explorer link. The Rotating Sky Explorer is shown in the figure below. 7

6 1. Enter the latitude and longitude of Williamsburg in the lower left section. The latitude of Williamsburg is 37.3 o (37 o 16 ) North and the longitude is 76.7 o (76 o 47 ) West. In the lower middle of the panel, check the boxes for show labels, show 0h circle, show celestial equator and show angle between the celestial equator and the horizon. You may click and drag either the celestial sphere or the horizon diagram sphere to change your perspective. 2. 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.) You maymoveastartoanylocationbyclickingonitanddraggingit. Notethatitmoveson both spheres as you do this. You can also enter the star s local or celestial coordinates in the appropriate boxes on the celestial view or the Horizon (local) view. The help button at the upper right of the panel provides more detailed information on using the Rotating Sky Explorer. 3. Create a star on the Horizon (local) view. You can click and drag the star around to measure its position. Complete Table about the local coordinate system. Description Latitude Azimuth Altitude Zenith 37.3 o any West point of the horizon 37.3 o North Celestial Pole 37.3 o 0 o Intersection of Celestial Equator and Meridian 37.3 o 180 o 4. The two end stars of the Big Dipper are known as the pointer stars since a line drawn through them points toward Polaris (a very important marker in the sky since it is located very near the North Celestial Pole). Click the remove all star button. Use the star patterns pull down menu to add the Big Dipper to the celestial sphere. Check the long star trails box. Click the animate button. 5. Do the pointer stars always point at the the North Celestial Pole? Describe the path of the stars of the Big Dipper. For a given latitude, a circumpolar star is a star that never disappears below the horizon, due to its proximity to the celestial poles. Check the show circumpolar region box. Are all of the Big Dipper stars always visible from Williamsburg? Answer below: 6. The group of stars known as Orion and the Southern Cross can also be selected from the star pattern menu. Is Orion visible from Williamsburg? Is the Southern Cross visible from Williamsburg? 8

7 2.3.2 Installing Stellarium on your Laptop If you did not install Stellarium at the first meeting of the your lab section, please do it now. Go the the class web site and select software from the main menu. Download the appropriate file (Mac or MS Windows) for your laptop. You should also download the Users Guide for future reference. Once you have downloaded the appropriate file and saved it on your desktop, run that file (double-click on it) to install Stellarium on your computer. (Note to Windows 7 and Vista users: right click on the downloaded file and select install as administrator.) After you have installed the program, start Stellarium by double clicking on the icon Stellarium Controls Stellarium has many controls. You should explore the program in more detail outside of class. For now, we will investigate the basic features. If you move the cursor to the lower edge of the window the main control menu will appear. The figure below show the main controls and the number below each icon gives its function in the table. Number Description Number Discription 1 Draw Constellation lines 12 Center on Object 2 Constellation labels 13 Night Mode 3 Draw Constellation art 14 Full screen mode 4 Equatorial Grid 15 Ocular View 5 Azimuthal Grid 16 Satellite hints 6 Ground 17 Decrease time speed 7 Cardinal Points 18 Set normal time (pause) 8 Atmosphere 18 Set time to now 9 Nebulas 20 Increase time speed 10 Planet Labels 21 Quit program 11 Equatorial/Azimuthal Mount Move the mouse cursor to the lower left and the windows menu will appear. The function of the various window options is shown in the figure below. 9

8 2.3.4 Setting the Location and Observation Time Open the Location window on the window (side) menu. A figure of the Location window is show below. The default location is Paris and Stellarium does not have Williamsburg in its extensive list of location. Enter the latitude (37 o 16 North) and longitude (76 o 43 West) for Williamsburg. Use 20 meters for the Alitude Select United States for the country and Earth for the Planet. Enter Williamsbug for the Name/City. Click the add to list button. Check the use as default box and close the window. Select the Date/Time window. Set it to the current time and date if it is not already set to the correct time and date. Close the Date/Time window Locating Stars You should now see the stars as they appear in the night sky. 10

9 1. Click on the Cardinal Points, Planets Labels, Equatorial Grid button on the bottom control menu if the icons are not already highlighted. Advance the time to approximately 10 pm (22:00) tonight using the Increase time speed button. You can more around the sky by clicking and dragging the sky or using the left, right, up and down keys. Move so that you are pointed toward due north. 2. At the North Celestial Pole (90 o declination where all the right ascension lines meet on the Equatorial grid) you should see a bright star which is Polaris. Click on the star and information about the star will be displayed in the upper left of the screen. Fill in the appropriate data below. Use the RA/DE (of date) for the Celestial coordinate system data. Polaris Right Ascension Declination Azimuth Altitude 3. The two pointer stars of the Big Dipper are known as Merak(β UMa) and Dubhe(α UMa). Find the Big dipper and record their information below. Merak Right Ascension Declination Azimuth Altitude Dubhe Right Ascension Declination Azimuth Altitude 4. Find three other bright stars and record their data below. Right Ascension Declination Azimuth Altitude Right Ascension Declination Azimuth Altitude Right Ascension Declination Azimuth Altitude Questions 1. Describe how the stars move during the night in Williamsburg. 2. What do you think the motion of the stars would look like at the north pole? Where would Polaris be located? 11

10 3. If you were on the equator, what would be the altitude of Polaris? What would be declination of Polaris? 4. How long will it take a star to return to it initial position? 2.4 Conclusion Write a conclusion about what you have learned. 12