Name: ______________________________ Class: ______________________________ Date: ______________________________

Assignment # 2: Mapping The Sky Ever tried to give someone directions to a friend's house without knowing the exact address? It’s hard! Just as buildings have addresses to help us find them, astronomers need ways to locate things in the sky. Ideally, there should be a precise way to map the sky, just as we have a map of the surface of the Earth. To locate any point on the surface of the Earth, we specify the point’s LATITUDE and LONGITUDE, two angles that measure a spot's position relative to the center of the Earth. For example, Los Angeles (at least the center of it) is located at 34º North, and 118º West. Similarly, we need a way to tell other astronomers where to look for things in the sky. We can’t just say “Look to the left of that bright red star and then go up a little.” In this assignment, we’ll study the two ways of locating objects in the sky using angles – one called Altitude & Azimuth (Alt/Az), and the other called Right Ascension & Declination (RA/Dec) - and their relative advantages & disadvantages. PART A Start Stellarium. Make sure your location is Los Angeles. If it is not, open the Location window, enter Los Angeles in the search box and then click on Los Angeles, United States. Turn off the Atmosphere and Fog if they're on, by pressing the A and F keys. Put the horizon at the center of the screen by dragging it until it's at the center. It doesn't matter which part of the horizon – N, S, E or W, you choose. Pick a star that is as close to the horizon as possible. Click on it. Information on your star will appear in the upper left-hand corner of the screen. •

What is the common name of your star? __________________________________

In the information, look for the line that starts Az/Alt. It should be the 6th line of information on the screen in the upper left-hand corner. Az/Alt stands for Azimuth/Altitude, and the numbers on this line list the angles that are the star's Azimuth and Altitude, as discussed in class. The first number listed is the Azimuth, and the second number, after the slash, is the Altitude. •

What are the Altitude and Azimuth of your star? ROUND OFF ALL YOUR ALTITUDE AND AZIMUTH READINGS TO THE NEAREST DEGREE – IN OTHER WORDS, IGNORE EVERYTHING AFTER THE ° SYMBOL!

Az __________ Alt ____________

Try a few other stars along the horizon. Click on them. Look at their altitudes. Compare the answers to what you saw for your first star. Do you notice a pattern? •

What is the value of altitude for any star on the horizon? _________________°

Now find a star that is straight above one of the stars you just chose. In other words, look a little higher in the sky. Click on the new star. Note its altitude and azimuth, and compare them to the values for the stars on the horizon. One of the numbers will have changed, and the other will be (approximately) unchanged. •

As you move the cursor straight up from the horizon (in other words, as you look up from the horizon, toward the zenith), which angle changes, Altitude or Azimuth? ___________________________

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Zoom out and re-center the sky until you are looking at the entire sky at once. Click as close as you can to the zenith (the point at the center of the screen). Remember, the zenith is the point directly over your head in the sky. •

What is the value of altitude at the zenith? _________________°

Altitude is an angle that tells you where a star is above the horizon. Picture two rays coming from your head – one pointing at the horizon directly below the star, and the other pointing at the star you're looking at. The angle between those rays is the altitude of a star. Click the cursor on a star that is below the horizon – in other words, click on the ground. Notice the value of the altitude here. •

How can you tell by looking at a star’s altitude whether it is above or below the horizon? __________________________________________________________________________ Go back and click on a few more stars on the horizon.

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As you click left or right along the horizon, which angle changes, Alt or Azm? ____________

Click around the entire horizon (you may have to move the horizon by grabbing it with the cursor and dragging it), and watch the Azimuth change. Drag the sky around so you're looking at the Northern horizon. Click on various places on the horizon just to the left and right of North, and look at the values of altitude and azimuth for various points on the horizon. •

What is the maximum value of azimuth? ______________°

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What is the azimuth of E? ___________° W? ____________° S? ___________° NW? ___________°

Azimuth measures the angle along the horizon in degrees, to your chosen star, starting at North and going clockwise. Find the star Polaris, using Stellarium's Search window (or by using CTRL-F or the F3 key). •

What are the altitude and azimuth of the star Polaris? Alt_____________° Az _____________°

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What is the latitude here in L.A., where you are observing from? (To find your latitude, open the Location window – your latitude and longitude are listed there) _________________________°

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Comparing the answers to the previous two questions, what might you guess is the relationship between an observer’s latitude and the altitude of Polaris above his or her horizon? _______________________

Stellarium can superimpose a grid on the sky that allows you to easily measure Altitude and Azimuth. To show this grid, press the “Z” button on your keyboard (or go to the toolbar at the bottom of the screen and click on Azimuthal Grid). The lines in the grid that run parallel to the horizon are lines of altitude, measuring from the horizon to the zenith, and the lines that are perpendicular to the horizon, and which all meet at the 2

zenith like the spokes of a wheel, are lines of azimuth, measuring along the horizon, from North. The grid lines are labeled, in degrees where they hit the edge of the screen. Set the time for 8 PM tonight by changing the time in the Date/Time window. Label the brightest stars by opening the View window and putting a check next to Stars in the Labels and Markers section of the Sky sub-menu. Also, move the slider next to Stars to about half way from the left. Close the View window. It's in the end of the bowl of the Big Dipper in the constellation Ursa Major. Look for Ursa Major, and then click on the end star in the bowl of the Big Dipper to make sure you've found Dubhe. Don't forget, if you want to see the constellation outlines and names on the screen, press C and then V. •

What is Dubhe’s Alt and Az at 8 PM (Remember, if you click on a star, its data will be shown onscreen!)? Alt ________________° Az___________________°

Change your location to New York City (Lat=41º N, Lon=74º W) in the Location window by entering New York in the search box and then scrolling down until you find New York, United States in the resulting list and clicking on it. •

Find Dubhe's altitude and azimuth in New York AT THE SAME TIME AS THE PREVIOUS QUESTION. Alt ____________° Az _______________°

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Are Dubhe's Altitude and Azimuth the same in New York and L.A. at the same time? Why or why not? ___________________________________________________________________________

Change your location back to Los Angeles, and the date back to today's date, at 9 PM. •

Back in L.A., what is Dubhe’s alt and azm at 9 PM? Alt __________° Az ___________°

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Do a star's altitude and azimuth stay constant as the night goes on? ____________________

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What is Polaris' altitude and azimuth at 8 PM? Alt __________° Az__________°

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What about at 9 PM? Alt _________° Az __________°

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Why does Dubhe behave differently from Polaris? ___________________________________________________________________________________ ___________________________________________________________________

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If someone told you they saw a satellite at 85 degrees altitude, where would you look (circle one)? a) Near the horizon b) Near the Zenith c) Halfway up the sky d) None of the above

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If you wanted to tell someone to look at a star halfway up the sky in the Southwest, what Alt and Az would you give? Alt _______________° Az ________________________°

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PART B As we have seen, altitude and azimuth have one large drawback - they are observer dependent – they change, depending on both where the observer is, and what time he or she is observing. We need a set of coordinates that are observer independent, that never change, like Latitude and Longitude on the Earth! The coordinates we have developed that fit the bill are called Right Ascension and Declination, together known as the Equatorial System. As we have discussed in class, Right Ascension and Declination (RA and Dec), are the two numbers we use to specify a star’s location, using a grid fixed on the sky. To display that grid, first turn off the Azimuthal grid by pressing the Z key, and turn on the Equatorial grid by pressing the E key. You can also turn these grids on and off using their buttons in the toolbar at the bottom of the screen. Drag the sky around and zoom out until the Southern horizon is at the bottom of the screen and you can see the whole sky at once. You should see a different grid pasted over the sky – this one in blue. The lines that shoot out like curved spokes from the North Celestial Pole are lines of Right Ascension. The circular lines perpendicular to these Right Ascension lines are lines of Declination. Again, the lines are labeled with their units at the edge of the screen. These lines are the grid that we use to measure fixed address locations in the sky. The Right Ascension and Declination of any star's position are listed in the information that appears when you click on that star. Click on any star. The information about that star appears in the upper left-hand corner of the screen. Look for the line that reads RA/DE (J2000). The two sets of numbers separated by a slash are the star's Right Ascension and Declination. Let's look at Declination first. •

What units is declination measured in? ________________________________________

Press the “.” (the period) key on your keyboard. This will highlight the Celestial Equator in brighter blue. Pick a star lying right along the Celestial Equator. Click on it. Look at the star's Declination. Do this for a few more stars along the Celestial Equator. •

What is the Declination anywhere on the Celestial Equator? _______________________°

Make sure you're looking at the whole sky by zooming out and centering the sky on the screen. Click on various stars and watch the information that appears for them. Notice that the Right Ascension (RA) and Declination (Dec) change in various places in the sky. Try to find the place where Declination reaches its maximum value. •

What is the maximum value of declination? ______________________________________

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What is the name of the bright star almost exactly at the point where declination reaches its maximum value? ________________________________

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What angle does declination measure? ___________________________________________________ ___________________________________________________________________________________

Now let’s look at the Right Ascension lines. Again, these are the lines that circle the celestial sphere but ALL RUN THROUGH THE NORTH AND SOUTH CELESTIAL POLES.

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Unlike Declination, which is measured in degrees (and fractions of a degree called arc-minutes and arcseconds), Right Ascension is measured in a different unit. Click on a few stars and look at their Right Ascension values. •

What are the units RA is measured in? Hint: look at the letters that appear in the RA scale __________

Click on various stars along the Celestial Equator (the brighter blue line) and note their Right Ascension. Do you see a pattern? Keep clicking on stars and try to find the maximum value of RA. You may have to let some time pass to click all the way along the entire Celestial Equator. •

What is the maximum value of RA (before it starts over again at zero)? __________________________

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What is the exact RA of Polaris? (Click on Polaris and look at its displayed information) ________

Center the whole sky on the screen, and click on a star as close as possible to the zenith to estimate the RA and Dec coordinates of the zenith itself. Don't forget to write the units for each measurement below! •

Zenith RA _______________ Dec ___________________

Now change the time to 1 hour later. Again, click on a star as close as possible to the zenith to estimate the new RA and Dec coordinates of the zenith. •

Zenith RA _______________ Dec ____________________

What would you guess the RA and Dec coordinates of the zenith would be six more hours later? •

Zenith RA _______________ Dec _____________________

The answers to the previous questions should help you understand why RA is measured in hours (and minutes and seconds). Each hour that passes causes one hour of Right Ascension to pass by any point in the sky. Right Ascension and Declination, or the Equatorial system is a much more useful way to locate stars and objects in the sky than Altitude and Azimuth. To see why in another way, turn both grids on at once by pressing Z and E until you see both grids at the same time. Press L three times to let time go by at 1000 times normal speed and watch the stars move across the sky. •

Do the stars stay fixed relative to the Alt/Az grid as time passes? _________________________

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If we use Altitude & Azimuth to measure a star's position, would the star's Altitude and Azimuth stay the same as the night went on? ____________________________________

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Do the stars stay fixed relative to the blue Equatorial grid as time passes? ________________________

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If we use Right Ascension and Declination to measure a star's position, would the star's RA and Dec stay the same as the night went on? _________________________________

Now you can see why we use Right Ascension and Declination as our “address” in the sky. RA and Dec do not change, regardless of where the observer is on Earth, or what time of day or night it is, or what day of the year it is.

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PART D We can now give every spot in the sky a unique address that won't ever change, using Right Ascension and Declination. This applies not just to stars, but to “Deep Sky” objects, like nebulae, galaxies, and star clusters. Practice looking up some of these addresses by filling in the Deep Sky Address Table on the next page. Find each object by either opening the Search window from the menu, or by typing CTRL-F or F3. Once the object is selected and in the center of the screen (you may have to hide the ground by pressing “G” to see some of the objects), then zoom in until you can see each of the objects. The object's information, including its RA and Dec address, will be displayed in the upper left-hand corner of the screen. Just list the degrees for Declination, and the hours and minutes for Right Ascension – don't bother with the fractions of a degree or the fractions of a minute. Also add two other Deep Sky Objects of your own by choosing two other NGC objects by number from the list in the Search Box.

Deep Sky Address Table Deep Sky object name

RA

Dec

Deep Sky Object name

M31 (the Andromeda Galaxy)

Pleiades

Crab Nebula

Ring Nebula

Lagoon Nebula

Sombrero Galaxy

NGC 5139 (Omega Centauri)

Triangulum Galaxy

M42 (Orion Nebula)

Whirlpool Galaxy

RA

Dec

Write a brief conclusion explaining what the advantages and disadvantages are of using Altitude & Azimuth or Right Ascension & Declination, and what you learned about them in this exercise. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________

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