naap_distance_sg_08

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Northern Virginia Community College *

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150

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Astronomy

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May 6, 2024

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docx

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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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