Lab 7 - Mike Jacobs
pdf
keyboard_arrow_up
School
Collin County Community College District *
*We aren’t endorsed by this school
Course
1403
Subject
Astronomy
Date
Oct 30, 2023
Type
Pages
14
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: _______________________________________________________________
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
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
6 3) Review your friend’s hypothesis and analyze Graph #1. a. Name two stars with very similar apparent magnitudes that are at very different distances from the Earth. ________________________________________________________ b. If your friend’s hypothesis was correct, would you expect the more distant star to look brighter or fainter in our sky? ________________________________________________________ c. Both stars have very similar apparent magnitudes. What does this tell you about how bright they look in our sky (
one complete sentence
)? ________________________________________________________ d. Based on your answers to b and c, what can you conclude about your friend’s hypothesis (
one complete sentence
)? ________________________________________________________ Part B –
Manipulate, graph, and analyze data. Use analysis to evaluate a hypothesis. To teach your friend some astronomy, you present another hypothesis, opposite the one he suggested. Your hypothesis: “Stars do not all have the same intrinsic brightness. The reason why they appear to have different magnitudes is because they are at different distances from the Earth and have different intrinsic brightness. Therefore, in order to determine the distance a star is from the Earth you need to know both the absolute visual magnitude (
M
v
) and the apparent visual magnitude (
m
v
) of that star.” To test this hypothesis, we will calculate m
V
– M
V
for each star. This value is called the Distance Modulus
.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
7 1) Use the data that you collected in Data Table 1 to complete Data Table 2. Data Table 2 Star m
V
– M
V Star m
V
– M
V Sirius -2.89 Altair Canopus Acrux Rigil Kentaurus Aldebaran Arcturus Spica 4.42 Vega Antares Capella Pollux Rigel Fomalhaut Procyon Deneb Betelgeuse Mimosa Achernar Regulus Hadar Adhara 2) We will now plot a graph of our data to test your hypothesis. Using the graph paper provided for Graph #2
, for each of the stars, plot distance modulus (
m
V
- M
V
) (y-axis) vs. distance (pc) (x-axis). Again, it may be helpful in your analysis to label the data points with the name of the star they belong to. (Note, the two furthest stars, Deneb and Rigel cannot be plotted on this graph.) 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
8 3) Review your hypothesis and Graph #2. In a paragraph discuss the validity of your hypothesis given what Graph #2 shows you. Use two stars plotted on Graph #2 to prove the validity of your hypothesis (i.e. cite actual distance
and distance modulus
values that support your hypothesis). Hint: Follow the pattern outlined in 1a-1d above when composing the paragraph to answer this question, but remember now that you are discussing the relationship between distance and distance modulus, not
distance and apparent magnitude (apparent magnitude/brightness does not
factor into this discussion!). Part C –
Graph data and use graph (interpolation) to analyze other stars.
You may have noticed that several of your data points, at small distances, in Graph #2 were very close together even after scaling the graph to leave off the two most distance stars from our data set. The distances of the stars we plotted covered a very large range and as a result some of the detail at small distances is difficult to discern. 1) To better analyze the relationship between distance and distance modulus for all distances in this range, you will now plot the data from Graph #2 again, but this time on semi-logarithmic axes, Graph #3
. On our graph paper, the y-axis is still linear and the interval between markings is still 0.5. However, the intervals along the x-axis are now logarithmic. Between the markings 1 and 10, each interval is 1, but between 10 and 100 each interval is 10, and between 100 and 1000 each interval is 100. a. Label each line on the x-axis with the appropriate number. b. For each of the stars in our data set, plot distance modulus (
m
V
- M
V
) (y-
axis) vs. distance (pc) (x-axis). This time, do not label your data points with the name of the star they belong to. Sirius and Spica have been plotted for you as examples. c. Using a ruler or straight edge, draw a “best fit” line through your data points on Graph #3. d. 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
9 Some Practice Problems: Keep in mind that depending on how you’ve drawn your Graph #3, you might get slightly different answers than what I get. That’s okay – in the answers to these practice problems, I will even tell you about what range
of answers is appropriate. In this part, you must record your answers to the Practice Problems! 1) Suppose a star is known to be 60 pc from Earth, and its apparent visual magnitude m
v
=
4. Using Graph #3, estimate the distance modulus m
v
– M
v
for the star, and then determine M
v
. m
V
- M
V
= _____________________________________________ M
V
= _________________________________________________ 2) A star is known to have an apparent magnitude of 2.5. Based on its spectrum, it is known to be a very old form of star called a “horizontal branch” star, with an absolute magnitude of 0.5. Determine the distance modulus for this star, and from that figure out the distance to the star. m
V
- M
V
= _____________________________________________ d
= __________________________________________________ Answers to Practice Problems: 1) On graph #3, distance is along the x-axis. Notice that 60 pc is the 5
th
line after 10. Using a ruler or straight edge, go straight up from this line until you intersect your “best fit” line on Graph #3. Make a very light mark on your line, and then use the mark and your ruler to read off the corresponding value on the y-axis. My ruler, placed horizontally, was just below 4.0, so I’d call it a distance modulus of 3.9. Therefore: m
v
– M
v
= 3.9 (Depending on your line, really anything between 3.5 and 4.3 is pretty reasonable) The value for m
v
is given (4), and the distance modulus is literally
a subtraction problem, so 4 – M
v
= 3.9. If you solve that equation for M
v
(add M
v
to both sides and subtract 3.9 from both) you get:
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
10 M
v
= 0.1
(Depending on your distance modulus, between 0.5 and -0.3 is fine) 2) You’re given both m
v
and M
v
, making the distance modulus nothing but a direct subtraction problem: m
v
– M
v
= 2.5 – 0.5 = 2.0 (This is a math problem using given values, so there’s really no leeway here.) Now, using a ruler, start at the y-axis at 2.0, and read horizontally across to your best fit line. Then, from the line, read down to the x-axis (and the distances). On my graph, that put me a little over halfway between 20 and 30 pc, implying a distance of about 25 pc. d = 25 pc
(Realistically your line would likely give you between 20 pc and about 30 pc, depending on how it’s drawn. Values outside of that probably indicate your data points are not plotted correctly or your line isn’t that well drawn…) Final Calculations: 1) Let us use Graph #3 to determine some absolute visual magnitudes. Suppose a star is known to be 3 pc from Earth and its apparent visual magnitude m
V
= 2. From the graph, draw a vertical line from the 3 pc point on the x-axis up to the curve, and read the distance modulus m
V
- M
V
. Then determine M
V
. m
V
- M
V
= _____________________________________________ M
V
= _________________________________________________ 2) Denebola in the constellation Leo lies at a distance of 13 pc and has m
V
= 2.1. Find its M
V
. m
V
- M
V
= _____________________________________________ M
V
= _________________________________________________
11 3) In the Big Dipper, marking the junction of the bowl to the handle, lies the star Megrez. Its distance is 20 pc and it is the faintest of all the Big Dipper stars with m
V
= 3.3. Find its M
V
. m
V
- M
V
= _____________________________________________ M
V
= _________________________________________________ 4) Sometimes a star’s distance is not known but its absolute visual magnitude can be calculated by other means. We can then use the distance modulus and graph 2 to find its distance. The star Sigma Libra has an apparent visual magnitude of +3.31 and an absolute visual magnitude of +1.9. Calculate the distance modulus and use Graph #3 to determine the distance to this star. m
V
- M
V
= _____________________________________________ d
= __________________________________________________ 5) The star Iota Ursa Major (sometimes called "Talita") has an apparent visual magnitude of +3.12. Its absolute visual magnitude is +2.22. Calculate the distance modulus and use Graph #3 to determine the distance to this star. m
V
- M
V
= _____________________________________________ d
= __________________________________________________ 6) Suppose a star is known to be 10 pc from the Earth and its apparent visual magnitude has been measured to be +4.30. Use Graph #3 to determine the absolute visual magnitude of the star. m
V
- M
V
= _____________________________________________ M
V
= _________________________________________________
12 7) Suppose a star is known to be 3 pc from the Earth and its absolute visual magnitude is +8.70. Use Graph #3 to determine the apparent visual magnitude of the star. m
V
- M
V
= _____________________________________________ m
V
= _________________________________________________
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Sirius
Spica
‐
1.5
‐
1.0
‐
0.5
0.0
0.5
1.0
1.5
0
50
100
150
200
250
300
350
400
450
Apparent Magnitude (m
v
)
Distance (pc)
Graph #1
Distance vs. Apparent Magnitude
Sirius
Spica
‐
5
‐
4
‐
3
‐
2
‐
1
0
1
2
3
4
5
6
7
8
9
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
Distance Modulus (m
v
‐
M
v
)
Distance (pc)
Graph #2
Distance vs. Distance Modulus
Related Documents
Browse Popular Homework Q&A
Q: Whats your thoughts about In U.S., Decline of Christianity Continues at Rapid Pace?
Q: 2Mg(s)+O2(g)→2MgO(s)2Mg(s)+O2(g)→2MgO(s)
When 13.2 gg MgMg reacts with 14.0 gg O2O2, 12.3 gg MgOMgO…
Q: Which of following is the first line of defense for plants?
Systemic acquired resistance
Secondary…
Q: Two bodies P and Q on a smooth horizontal surface are connected by a light cord. The mass of P is…
Q: 10
0
1
0
Derive the Boolean equation(s) from the following truth table (only d, e, f are inputs).…
Q: 5. Help me selecting the right answer. Thank you
Q: Determine AH, q, w, and AE at 298 K and 1 atm pressure for the reaction of 9.211 g of NH3(g) with…
Q: Find an expression for the Fourier
coefficients of the ramp waveform shown
in Figure 1.
V(t)
1v+
T…
Q: A 1.0-kg block and a 2.0-kg block are pressed together on a horizontal frictionless surface with a…
Q: A nonuniform horizontal bar of mass m is supported by two
massless wires against gravity. The left…
Q: Determine is the given series is a p
sin(4x) x(3+5)
Select the correct answer below:
n=0
O a) Yes,…
Q: Provide the abbreviation of the following nucleotide.
0 0
11
O-P-O-P-O-P-O-
O
O O
ок
H
0.
OH
N
TH
OH…
Q: |. The QR factorization of the matrix A is given by:
-10
A =
2
and b =
2
5/2
[5
1
2
5/2
[o 2/2
2…
Q: What are the annual payments for years 1 to 30?
What is remaining balance at the end of each year?…
Q: watch help video
Find the distance between the two points in simplest radical form.
Answer:
✓
O
O…
Q: For what values of p does the series below converge?
Select the correct answer below:
O p > 2
O p =…
Q: This problem set deals with the problem of non-constant acceleration. Two researchers from
Fly By…
Q: Problem 2. Sketch the set of points x = (₁, ₂) in R² such that
(i) ||x||2 = 1,
(ii) ||x||₁ = 1,…
Q: Let T : R² → R² by T(x) = A˜, where
1. Find ker T
2. Find a basis for im T.
A-[¹₁2]
Α
=
-3 -6
Q: By the end of the High Middle Ages was healthcare more about providing care from trained…
Q: 17) In an accelerating Universe, the scale factor a. grows at an ever-decreasing rate over time. b.…
Q: Complete the following operations and write your answer with the correct number of significant…
Q: Suppose that there were no previous studies in the medical literature indicating that the population…
Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xy2 dx…
Q: 10. How far will a hockey puck with mass of 0.5 kg and initial velocity of 30 m/s travel on ice, if…