Understanding Parallax: A Lab Guide for Astronomy Students

21 st Century Physics & Astronomy Lab Names:___________________________ ___________________________ ___________________________ Section: __________________________ Date: ____________________________ Parallax - 1

21st Century Physics & Astronomy Lab Parallax Purpose of the Experiment  To understand what parallax is and why it is important in astronomy.  To use parallax to determine the distances to various astronomical bodies. Parallax - 2

Table of Contents Prelab ................................................................................................................................... 4 The Lab ................................................................................................................................ 7 Purpose of the Experiment ............................................................................................... 7 Apparatus ......................................................................................................................... 7 Files .................................................................................................................................. 8 Procedure ......................................................................................................................... 9 Part A: Parallax of the Moon ....................................................................................... 9 Part B: Geocentric Parallax ....................................................................................... 11 Part C: Geocentric Parallax of Vesta ......................................................................... 13 Part D: Parallax of Other Solar System Objects ........................................................ 15 Calculations Page ........................................................................................................... 16 Parallax - 3

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Prelab Prelab 1: Read the introduction to Chapter 20 on Parallax in “Observing Projects Using Starry Night College”. Perform the experiment discussed in the second paragraph. a.) Close your right eye and note the position of your outstretched hand against a distant background when observed along the line of sight from your left eye. Now close your left eye and open your right eye. What happens to the apparent position of your outstretched hand compared to the distant background and which direction does it appear to go? b.) Repeat Part (a) with your hand just a few inches from your nose. What happens to the apparent position of your hand in this case compared to the distant background and which direction does it appear to go? Is the angle your hand appears to jump through larger or smaller than in Part (a)? Why? Parallax - 4

Prelab 2: Again, refer to the introduction to Chapter 20 on Parallax in “Observing Projects Using Starry Night College”. Looking at Equation 1 in Chapter 20, complete the following statements in reference to the situation in Prelab 1: a.) The observational baseline X is the distance between ________ and ________. b.) The distance d corresponds to the distance between ________ and _________. c.) The angle θ corresponds to what angle in Prelab 1? d.) Draw a diagram of the situation in Prelab 1 and label the variables X , d , and θ on the diagram. e.) Carefully explain how you could use Equation 1 to determine how far away from your face your hand is in the situation in Prelab 1. Parallax - 5

Prelab 3: Again, consider Equation 1 from Chapter 20. Assume that you have a very distant object that you want to determine the distance to. Using Equation 1 for your justification, describe two things you must do in order to determine how far away this very distant object is to very high accuracy. Parallax - 6

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The Lab Purpose of the Experiment : To understand what parallax is and why it is important in astronomy. To use parallax to determine the distances to various astronomical bodies. Apparatus  Windows PC  Starry Night College 7 Freeman Edition  “Observing Projects Using Starry Night College” by Bergman, Clark and Wilson Parallax - 7

Files  W.H Freeman Observing Projects Starry Night Files Parallax - 8

Procedure Part A: Parallax of the Moon Question 1: When you flip the view from the location at longitude 90 ° E to the view from the location at 90 ° W, in which compass direction (east or west) does the Moon appear to move? [HINT: North is at the top and east is to the left.] Question 2: As seen from longitude 90 ° E, is the Moon rising or setting? [HINT: The horizon is hidden in these views but can be displayed by clicking the Horizon button in the buttonbar. Also, you can check the Rises and Sets times for the Moon in the HUD.] Question 3: At this same instant of time, if you were standing on the equator of the Earth at the prime meridian, longitude 0 ° : a.) What would by your local time? b.) At which specific point in the sky would you see the Moon? Parallax - 9

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Question 4: What angle does the observational baseline (AB in Figure 1) make with the line from the center of the Earth to the center of the Moon (CM in Figure 1)? Question 5: What is the parallax shift of the Moon on this date, produced by observing it from these two opposite locations, in arcseconds? Question 6: Using Equation 2 and the parallax shift you measured, what is the distance to the Moon, in kilometers? Question 7: How does your calculation for the distance to the Moon compare to that given in the HUD? Parallax - 10

Part B: Geocentric Parallax Question 8: What is the geocentric parallax, in arcseconds, of the Moon on the date observed in the previous sequences? Question 9: You used the Angular Separation tool to measure the angular radius of the Earth. a.) What is the measured angular radius, in arcseconds, of the Earth as seen from the Moon at this point in time? b.) How well does your measurement of the radius of the Earth agree with your answer to the previous question? Parallax - 11

Question 10: Assume that you are using equipment for measuring parallax that can detect angular displacements as small as one-half of an arcsecond (0.5”) and that the observational baseline you will use is equal to the diameter of the Earth (12,756 km). a.) What is the distance, in kilometers, to the farthest object for which you could measure a parallax shift? b.) What is the distance expressed in AU? [HINT: 1 AU = 1.496 × 10 8 km.] c.) What is the furthest planet in the solar system for which you could measure parallax, using this Earth baseline? [HINT: Pluto is no longer considered a planet.] Parallax - 12

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Part C: Geocentric Parallax of Vesta Question 11: What is the distance between the two viewing locations? [HINT: Draw a diagram of the cross-section of the Earth at the equator similar to Figure 1 and put on the two observing positions to help you answer this question.] Question 12: At what longitude would you need to be to see Vesta transit the meridian at this time on this date? [HINT: Look at Figure 1.] Question 13: Where is Vesta relative to the celestial equator in these views? (Hint: Select View ≫ Celestial Guides ≫ Equator from the menu to help you answer this question.) Question 14: Which of the objects in the view show a parallax shift as you move from one viewing location to the other? Question 15: Do any of the stars in the view shift their relative position as you move from one viewing location to the other? Why do you think this is so? Parallax - 13

Question 16: Looking at the above measurements: a.) What is the parallax shift of Vesta from the above measurements? b.) What is the geocentric parallax of Vesta? Question 17: What distance, in AU, did you calculate for Vesta based on your measurements of its parallax? Question 18: How does your result compare with the value for the distance to Vesta given in Starry Night ? Parallax - 14

Part D: Parallax of Other Solar System Objects View Suggested FOV Circle Diameter FOV Radius, R Measured Angle to Circle,  (“) Parallax Shift, R +  (“) Calculated Distance (AU) Actual Distance from Info Pane (AU) Europa 5” 2.5” Iapetus 3” 1.5” Miranda 1” 0.5” Nereid 0.5” 0.25” Data Table 1 : Parallax and Distance from Earth of Several Solar System Bodies Question 19: What distance did you calculate from the parallax shift of: a.) Europa b.) Iapetus c.) Miranda d.) Nereid Parallax - 15

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Parallax - 16

Calculations Page : Parallax - 17

21st Parallax

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