Lab 7 - Mike Jacobs

.pdf

School

Collin County Community College District *

*We aren’t endorsed by this school

Course

1403

Subject

Astronomy

Date

Oct 30, 2023

Type

pdf

Pages

Uploaded by AgentLightning8462

1 Lab 7: APPARENT & ABSOLUTE MAGNITUDE Worksheet Name: _________________________________________________________ CWID: _________________________________________________________ Enter you answers to each question in the data tables and indicated spaces below (this document is form-fillable). When completed, please upload this file using the lab submission link in Canvas (please submit this file in .pdf format only). Please be sure that all data tables and all questions are completed. Introduction The apparent visual magnitude of a star is a brightness scale established by early astronomers. It's since been refined by modern day astronomers and continues to be used even in professional research. It is an inverted scale… the smaller the apparent visual magnitude ( m v ), the brighter the star (with negative magnitudes indicating a brighter star than positive magnitudes). For example, a very faint star might have an m v of 5.0 whereas a bright star might have an m v of -1.0. The human eye can detect faint stars with an m v of 6.0 assuming you're out in the country far away from city lights and the Moon is not visible. A typical amateur telescope can detect stars with an m v of 13.0. Large professional telescopes can detect stars with an m v of 22.0. According to the tables attached to this lab, Barnard's star has an m v of 9.54. This means you cannot see this star with the naked eye even in the best of viewing conditions but you can easily see it with an amateur telescope. According to the same table the star 61 Cygni has an m v of 5.22. This means you can probably see this star with the naked eye but it's near the limit. You'll probably have to go out in the country to see it. When modern day astronomers refined the apparent visual magnitude scale for professional use they introduced negative values for m v . For example, the tables attached to this lab indicate that the star Sirius has an m v of -1.46. Compared to Luyten 789-6 with an m v of 12.18, Sirius is very bright. Luyten 789-6 requires an amateur telescope to observe whereas Sirius is easily visible to the naked eye even in a large city or during a moonlit sky - in fact, Sirius is the brightest star in the night sky.

2 The Sun has an m v of -26.72. This makes the Sun much brighter than Sirius from our perspective on Earth. But Sirius is 8.6 light-years from us, meaning it takes light 8.6 years to travel from Sirius to Earth. However, light from the sun reaches us in only 8 minutes! Whereas the Sun is 93 million miles from us, Sirius is 50 trillion miles away. How bright would the Sun appear if it were as far away as Sirius? Compared to some other stars, Sirius is actually among the closer stars. Is its brightness due to its closeness or is it really and truly an intrinsically bright star? To answer questions like this, astronomers have defined another term called the Absolute Visual Magnitude, M v . This is the brightness of a star if it were at a distance of 10 parsecs from earth. (One parsec = 3.04 x 10 13 km = 3.26 light years). Since Absolute and Apparent Visual magnitude have the same initials, astronomers now denote Apparent Visual magnitude with a lower case “m” and Absolute Visual Magnitude with an upper case “M.” The advantage of knowing M v is that since all stars are assumed to be at the same distance, it allows us to figure out how truly bright the star is. In effect, it “levels the playing field” by putting all stars at the same distance. Practice Questions (you don’t have to submit answers to these questions): 1. Polaris (the North Star) has an apparent magnitude of 2. 61 Cygni’s is 6. a. Can either (or both) stars be seen with the naked eye? b. Which of the two is brighter? 2. Alpha Centauri is 1.7 pc away. If you moved it to 10 pc away, would its apparent magnitude become a lower or a higher number? 3. Same question as #2, but would the absolute magnitude become a lower or higher number? 4. The star HR 551 is 10 pc from the sun and has an absolute magnitude of 5.6. What is the star’s apparent magnitude? Answers to Practice Questions 1. a. A magnitude of 6 or less can be seen with the naked eye, so both stars would be visible to the naked eye. b. Magnitude is an inverse scale – lower numbers mean brighter objects. Since 2 is less than 6, that means Polaris looks brighter than 61 Cygni. 2. Moving it from 1.7 pc to 10 pc is moving it further away. Moving something further away makes it look dimmer. Dimmer magnitudes are higher numbers, so the star’s apparent magnitude would become a higher number. 3. A star’s absolute magnitude is its actual brightness. How bright something really

3 is does not depend on how far away it is from us (a 100 W light bulb is still 100 W regardless of whether or not it is 2 m away, or 10 miles away). So Alpha Centauri’s absolute magnitude would not change if you moved it from 1.7 pc to 10 pc further away. (It’s kind of a trick question.) 4. By definition, a star’s absolute magnitude is what its apparent magnitude would be if it were exactly 10 pc away from the sun. Since this star is 10 pc away, that means its absolute magnitude must be equal to its apparent magnitude, by definition. So the apparent magnitude would be 5.6 Prelab Questions Question 1 . The apparent visual magnitude of Canopus is –0.6 and that of Hadar is +0.6. Which star is brighter? How do you know? Answer: _______________________________________________________________ Question 2 . What is the absolute visual magnitude of a star? Answer: _______________________________________________________________ Question 3 . Epsilon Eridani has an apparent visual magnitude of + 3.7. Will it will be visible with the naked eye? How do you know? Answer: _______________________________________________________________ Question 4 . Ross 128 has an apparent visual magnitude of +11.1. Will it will be visible with the naked eye? How do you know? Answer: _______________________________________________________________ Question 5 . Ross 128 is 3.4 parsecs from us. If it were moved to 10 parsecs, would it appear brighter or dimmer? Why? Answer: _______________________________________________________________

4 Exercise In this lab, we will use Stellarium find information about individual stars. First, you will need to start the program. After the program has started, move your cursor to the left side of your screen to bring up the vertical menu, and click the “Sky and viewing options window” icon. Click the “Sky” tab, and un-check the box that says “Show atmosphere”. Daylight should fade and stars should now be visible (although the sun may still be displayed in the sky). You can move around by simply clicking on the screen and moving the mouse. We also need to remove the ground from the screen. To do this, open the Sky and viewing options window again, and click on the “Landscape” tab. Now, un-check the boxes labeled “Show ground” and “Show fog”. This should remove the ground from the screen. Close the Sky and viewing options window, and now you are ready to start the exercise. Part A – Collect, manipulate, graph, and analyze data. Use analysis to evaluate a hypothesis. Let’s test a hypothesis suggested by a know-it-all friend. You know from your studies in Astronomy that this hypothesis is not correct, but you have the task of convincing your friend. Your friend insists on the Hypothesis that: “A star is a star. All stars have the same intrinsic brightness. The reason why they appear to have different magnitudes is because they are at different distances from the Earth. This means a star close to the Earth will always be brighter than a star far away. Therefore, knowing the apparent visual magnitude of a star tells you the distance that star is from the Earth.” 1) Below in Data Table 1 is a list of 22 of the brightest stars in the night sky. To test your friend’s hypothesis, we will use Stellarium to gather information on this group of stars. First, open the “Search window” from the vertical menu on the left side of the screen. To find an object, simple type the name of the object in the box, and press “Enter” on your keyboard. Stellarium will automatically move your view over to that object. The first star in Data Table 1 is Sirius. Type this star name in the box in the Search window and press “Enter”. Stellarium should now move to Sirius. Information on this object is displayed in the upper left corner of the screen. Use this method to find and record the distance, apparent magnitude mv (Stellarium refers to this as just “Magnitude”), and absolute magnitude Mv for each star in Data Table 1 – stars Sirius and Spica have been entered and calculated for you as examples. Calculate the distance in Parsecs (pc) using the conversion: 1 pc = 3.26 ly.

5 Data Table 1 Star Distance (ly) Distance (pc) m V M V Sirius 8.6 2.64 -1.45 1.44 Canopus Rigil Kentaurus Arcturus Vega Capella Rigel Procyon Betelgeuse Achernar Hadar Altair Acrux Aldebaran Spica 249.74 76.61 0.95 -3.47 Antares Pollux Fomalhaut Deneb Mimosa Regulus Adhara 2) We will now plot a graph of our data to test your friend’s hypothesis. Using the graph paper provided for Graph #1 , for each of the stars in the data set, plot m V (y-axis) vs. distance (pc) (x-axis). It may be helpful in your analysis to label the data points with the name of the star they belong to. The stars Sirius and Spica have been plotted for you. Use a digital camera (or your phone) to take a picture of your graph, and paste it in the space below. Upload a picture of your graph with this worksheet in Canvas

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version