lab 11

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University of Nebraska, Omaha *

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001

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Astronomy

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Feb 20, 2024

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Name: NAME______________________ CLASS_________ Radar Ranging Question 1: Over the last 10 years, a large number of ice balls 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 do not think this plan would work. Radar becomes more difficult the farther the object is. Pluto is too far for this, Kniper is not large enough. Question 2: Enter your perpendicular distance to the boat in map units. _7.5 map units____ 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: 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? What is the greatest distance to the boat that is still consistent with your observations? What is the smallest distance to the boat that is still consistent with your observations? NAAP – Cosmic Distance Ladder 1/5 Question 1:

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. Theres almost no accuracy for this distance. The surveyor was able to move but limited to pinpoint an area. 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 10 Star B 5 16 Star C 10 25 Star D 8.5 0.5 Question 6: Could one of the stars listed in the table above be an RR Lyrae star? Explain why or why not. Star D could because RR Lyrae have absolute magnitudes near .5 Spectroscopic Parallax 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 NAAP – Cosmic Distance Ladder 2/5

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 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 13.1 strong molecular lines very thick 7.2 strong ionized metal lines moderate hydrogen lines very thick 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 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. NAAP – Cosmic Distance Ladder 3/5

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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 ran out of hydrogen fuel in their cores. 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 received mass from their companion. Question 10: Determine the distance to the Hyades cluster. Apparent magnitude m Absolute Magnitude M Distance (pc) Question 11: Determine the distance to the M67 cluster. Apparent magnitude m Absolute Magnitude M Distance (pc) 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? Supernovae NAAP – Cosmic Distance Ladder 4/5 Question 2:

Question 13: Determine the distance to Supernovae 1994ae and explain your method in the box below? Question 14: Load the data for Supernova 1987A. Explain why it is not possible to determine the distance to this supernova? It does not fit the red line. NAAP – Cosmic Distance Ladder 5/5 Question 3:

lab 11

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