DONE Lesson 6_lab_cosmic_distance_ladder_PDF
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Astronomy
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Dec 6, 2023
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Lesson 6 Lab - The Cosmic Distance Ladder
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: (2 points) 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 DON’T
BELIEVE THIS PLAN WOULD BE SUCCESSFUL BECAUSE THE KUIPER BELT IS SO
FAR AWAY AND TYPICALLY RADAR RANGING IS USED FOR CLOSE PLANETARY
BODIES, SO WHEN THE SIGNAL IS SENT OUT IT WOULD BE VERY WEAK COMING
BACK
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 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
NAAP – Cosmic Distance Ladder 1/7
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: (2 points) Enter your perpendicular distance to the boat in map units.
7.5 (20M)=150 METERS
Show your calculation of the distance to the boat in meters
in the box below.
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: (2 points) 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?
130 M
What is the greatest distance to the boat that is still consistent with your observations?
150 M
What is the smallest distance to the boat that is still consistent with your observations?
120 M
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: (2 points) 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. THE DISTANCE OF THE BOAT COULD
BE ANYWHERE GREATER THAN 50M, YOU CANNOT ACCURATELY
DETERMINE THE DISTANCE OF THIS BOAD BECAUSE THE
OVERLAPPING OF THE TWO POINTS IS TWO SIGNIFICANT
Distance Modulus
Question 5: (2 points) 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
6.02
5
1.02
16
Star C
10
8.01
1.99
25
Star D
8.5
0.5
8
398.1
Question 6: (2 points) Could one of the stars listed in the table above be an RR Lyrae
star? Explain why or why not STAR D COULD BE AN RR LYRAE STAR BECAUSE
IT HAS AN ABSOLUTE MAGNITUDE OF 0.5
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Let’s
first
find
the Question 7: (2 points)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
Question 8: (2 points) 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? THESE
STARS HAVE A HIGH MASS AND LUMINOSITY MAKING THEM FARTHER AWAY FROM
THE CLUSTER Question 9: (2 points) 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?
THESE STARS ARE DINNER THAN THE CLUSTER AND HAVE MOST LIKELY RUN OUT OF HELIUM
Question 10: (2 points) Determine the distance to the Hyades cluster.
Apparent magnitude m
Absolute Magnitude M
Distance (pc)
9.9 M
6.8 M
41.7 PC
Question 11: (2 points) Determine the distance to the M67
cluster.
Apparent magnitude m
Absolute Magnitude M
Distance (pc)
13.6 M
6.8 M
229 PC
Cepheids
Question 12: (1 points) 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 = -1 M m-M = 12- (-1) =-5+5log10D = 3981 PC
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Question 13: (1 points) 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: (1 points) Load the data for Supernova 1987A. Explain why it is not possible to determine the distance to this supernova? SUPERNOVA 1987 IS NOT A TYOE 1 SUPERNOVA THERFORE IS IT NOT POSSIBLE TO CALCULATE THE DISTANCE ON THIS PLOT