naap_distance_sg_08
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Northern Virginia Community College *
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May 6, 2024
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Name: The Cosmic Distance Ladder – Student Guide Exercises The Cosmic Distance Ladder Module consists of material on seven different distance
determination techniques. Four of the techniques have external simulators in addition to
the background pages. You are encouraged to work through the material for each
technique before moving on to the next technique. Radar Ranging Question 1:
Over the last 10 years, a large number of iceballs have been found in the
outer solar system out beyond Pluto. These objects are collectively known as the Kuiper
Belt. An amateur astronomer suggests using the radar ranging technique to learn the
rotation periods of Kuiper Belt Objects. Do you think that this plan would be successful?
Explain why or why not?
I personally do not think it will work because radar ranging it is used to find range, angle, and radial velocity of a nearby object. It has no way of aiding in finding the rotational period. Parallax In addition to astronomical applications, parallax is used for measuring distances in many
other disciplines such as surveying. Open the Parallax Explorer
where techniques very
similar to those used by surveyors are applied to the problem of finding the distance to a
boat out in the middle of a large lake by finding its position on a small scale drawing of
the real world. The simulator consists of a map providing a scaled overhead view of the
lake and a road along the bottom edge where our surveyor represented by a red X may be
located. The surveyor is equipped with a theodolite (a combination of a small telescope
and a large protractor so that the angle of the telescope orientation can be precisely
measured) mounted on a tripod that can be moved along the road to establish a baseline.
An Observer’s View
panel shows the appearance of the boat relative to trees on the far
shore through the theodolite. Configure the simulator to preset A
which allows us to see the location of the boat on the
map. (This is a helpful simplification to help us get started with this technique – normally
the main goal of the process is to learn the position of the boat on the scaled map.) Drag
the position of the surveyor around and note how the apparent position of the boat relative
to background objects changes. Position the surveyor to the far left of the road and click
take measurement
which causes the surveyor to sight the boat through the theodolite and
NAAP – Cosmic Distance Ladder 1/7
measure the angle between the line of sight to the boat and the road. Now position the
surveyor to the far right of the road and click take measurement again.
The distance
between these two positions defines the baseline of our observations and the intersection
of the two red lines of sight indicates the position of the boat. We now need to make a measurement on our scaled map and convert it back to a
distance in the real world. Check show ruler
and use this ruler to measure the distance
from the baseline to the boat in an arbitrary unit. Then use the map scale factor to
calculate the perpendicular distance from the baseline to the boat. Question 2:
Enter your perpendicular distance to the boat in map units. ______________
Show your calculation of the distance to the boat in meters in the box below. Distance =7.5 map units
D= (7.5 map units)(20 meters/1 map units)
D=150 meters
Configure the simulator to preset B
. The parallax explorer now assumes that our
surveyor can make angular observations with a typical error of 3
°
. Due to this error we
will now describe an area where the boat must be located as the overlap of two cones as
opposed to a definite location that was the intersection of two lines. This preset is more
realistic in that it does not illustrate the position of the boat on the map. Question 3:
Repeat the process of applying triangulation to determine the distance to the
boat and then answer the following: What is your best estimate for the
perpendicular distance to the boat? 130m
What is the greatest distance to the boat
that is still consistent with your
observations? 150m
What is the smallest distance to the boat
that is still consistent with your
observations? 120m
Configure the simulator to preset C
which limits the size of the baseline and has an error
of 5
°
in each angular measurement. Question 4:
Repeat the process of applying triangulation to determine the distance to the
boat and then explain how accurately you can determine this distance and the factors
contributing to that accuracy. There is little to no accuracy for this distance. NAAP – Cosmic Distance Ladder 2/7
Distance Modulus Question 5:
Complete the following table concerning the distance modulus for several
objects. Object Apparent Magnitude m Absolute Magnitude M Distance Modulus m-
M Distance (pc) Star A 2.4 2.4 0 10 Star B 6 5 1 16 Star C 10 8
2 25 Star D 8.5 0.5 8 400 Question 6:
Could one of the stars listed in the table above be an RR Lyrae star? Explain
why or why not. Yes. RR Lyrae stars have an absolute magnitude between 0.6 and
0.1 and an apparent magnitude between 7 to 8.5. Star D has an absolute magnitude of 0.5
and an apparent magnitude of 8.5. Spectroscopic Parallax Open up the Spectroscopic Parallax Simulator
. There is a panel in the upper left
entitled Absorption Line Intensities
– this is where we can use information on the types
of lines in a star’s spectrum to determine its spectral type. There is a panel in the lower
right entitled Star Attributes
where one can enter the luminosity class based upon
information on the thickness of line in a star’s spectrum. This is enough information to
position the star on the HR Diagram in the upper right and read off its absolute
magnitude. Let’s work through an example. Imagine that an astronomer observes a star to have an
apparent magnitude of 4.2 and collects a spectrum that has very strong helium and
moderately strong ionized helium lines – all very thick. Find the distance to the star using
spectroscopic parallax. NAAP – Cosmic Distance Ladder 3/7
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Let’s first find the
spectral type. We can see in the
Absorption Line Intensities panel
that for the star to have any
helium lines it must be a very hot
blue star. By dragging the
vertical cursor we can see that for
the star to have very strong
helium and moderate ionized
helium lines it must either be O6
or O7. Since the spectral lines
are all very thick, we can assume
that it is a main sequence star.
Setting the star to luminosity class V in the Star Attributes
panel then determines its position on the HR Diagram and identifies its absolute
magnitude as -4.1. We can complete the distance modulus calculation by setting the
apparent magnitude slider to 4.2 in the Star Attributes panel. The distance modulus is
8.3 corresponding to a distance of 449 pc. Students should keep in mind that
spectroscopic parallax is not a particularly precise technique even for professional
astronomers. In reality, the luminosity classes are much wider than they are shown in this
simulation and distances determined by this technique are probably have uncertainties of
about 20%. Question 7:
Complete the table below by applying the technique of spectroscopic
parallax. Observational Data Analysis m Description of spectral lines Description of line
thickness M m-M d (pc) 6.2 strong hydrogen lines moderate helium lines very thin .9
5.3
117
13.1 strong molecular lines very thick 14.5 -1.4
5.25
7.2 strong ionized metal lines moderate hydrogen lines very thick 3.6 3.6 52.5
Main Sequence Fitting Open up the Cluster Fitting Explorer. Note
that the main sequence data for nearby stars
whose distances are known are plotted by
absolute magnitude in red on the HR Diagram.
In the Cluster Selection Panel, choose the
NAAP – Cosmic Distance Ladder 4/7
Pleiades cluster. The Pleiades data are then added in apparent magnitude in blue. Note
that the two y-axes are aligned, but the two main sequences don’t overlap due to the
distance of the Pleiades (since it is not 10 parsecs away). If you move the cursor into the HR diagram, the cursor will change to a handle, and you
can shift the apparent magnitude scale by clicking and dragging. Grab the cluster data
and drag it until the two main sequences are best overlapped as shown to the right. We can now relate the two y-axes. Check show horizontal bar which will automate the
process of determining the offset between the m and M axes. Note that it doesn’t matter
where you compare the m and M values, at all points they will give the proper distance
modulus. One set of values gives m – M = 1.6 – (-4.0) = 5.6 which corresponds to a distance of 132 pc. Question 8:
Note that there are several stars that are above the main sequence in the upper
left. Can you explain why these stars are not on the main sequence? The stars are not in the main sequence because they are a different
luminosity class. Question 9:
Note that there are several stars below the main sequence especially near temperatures of about 5000K. Can you explain why these stars are not on the main sequence? They are not in the main sequence because they are dimmer and may have run out of helium
.
Question 10:
Determine the distance to the Hyades cluster. Apparent magnitude m Absolute Magnitude M Distance (pc) 9.9m
6.8m
41.7pc
Question 11:
Determine the distance to the M67 cluster. NAAP – Cosmic Distance Ladder 5/7
Apparent magnitude m Absolute Magnitude M Distance (pc) 13.6m
6.8m
229pc
Cepheids Question 12:
A type II Cepheid has an apparent magnitude of 12 and a pulsation period of
3 days. Determine the distance to the Cepheid variable and explain your method in the
box below? m=12
3 days=-1M
m-M=12-(-1)=-5+5log10d=3981pc
Supernovae Open up the Supernovae Light Curve Explorer
. It functions similarly to the Cluster
Fitting Explorer. The red line illustrates the expected profile for a Type I supernovae in
terms of Absolute Magnitude. Data from various supernovae can be graphed in terms of
apparent magnitude. If the data represents a Type I Supernovae it should be possible to
fit the data to the Type I profile with the appropriate shifts in time and magnitude. Once
the data fit the profile, then the difference between apparent and absolute magnitude
again gives the distance modulus. As an example load the data for 1995D. Grab and drag the data until it best matches the
Type I profile as shown. One can then use the show horizontal bar
option to help
calculate the distance modulus. One pair of values is m – M = 13-(-20) = 33 which
corresponds to a distance of 40 Mpc. NAAP – Cosmic Distance Ladder 6/7
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Question 13:
Determine the distance to Supernovae 1994ae and explain your method in
the box below? 13.1-(-19.4)=-5+5log10d
D=31.6
Question 14:
Load the data for Supernova 1987A. Explain why it is not possible to
determine the distance to this supernova? It is not possible to determine the distance of the supernova because it is a
type 2 not a type 1.
NAAP – Cosmic Distance Ladder 7/7