Lab 8_ Parallax

Stellar Parallax Lab Learning Objectives: ● Learn how parallax is used ● Use stellar parallax to measure the distance to stars ● Use publicly available databases of star information ● Use spreadsheets to calculate values and create graphs Introduction Parallax: Parallax is a simple way to measure the distance to far away objects by not really measuring them. Look at the diagram. This is how we first figured out the distances to far away astronomical objects. Our varying view makes a triangle and we can then use a little math to calculate other parts of the triangle. In the case above, the earth (the dot at June & December) moves around the sun. In June, we see that red star at a specific angle ‘downward’, but in December, we see it at another angle ‘upward’. The distant stars are so far away they don’t change enough to notice. So, this makes a triangle. Apparent magnitude: Shown to the right 1 is the constellation Hercules, outlined in red with some stars in its asterism connected with blue lines. Apparent magnitude is a numerical way to describe the brightness of stars that we can see from Earth. Bright stars have small values for their apparent magnitude and dimmer stars have larger values for their apparent magnitude. Rank the brightness of these stars in Hercules from dimmest to brightest. The values listed with the star names are their apparent magnitudes. ● Beta Herculis, 2.78 ● Epsilon Herculis, 3.92 ● Eta Herculis, 3.48 ● Gamma Herculis, 3.74 ● Zeta Herculus, 2.81 1. Would you expect the bright stars to be closer to the Earth than the dimmer stars, or are the bright stars farther from the Earth? Explain your answer. 1 Image modified from screenshot from Stellarium used with permission , Hercules artwork by Johan Meuris licensed under CC BY - SA 3.0 Based on “Stellar Parallax Lab“ by Andrea Goering and Richard Wagner licensed under CC BY - NC - SA 4.0

Part 1: Parallax Hold your index finger at arm’s length in front of you and close your left eye. Have a member place a small piece of masking tape on the far wall to indicate where the tip of your finger appears in ‘projection’ against the wall. Now, DO NOT MOVE YOUR FINGER and open your left eye and close your right, and have your partner places a new mark on the wall where your finger tip appears. Measure the distance between the marks, P . Measure the distance from your finger to your eyeballs (basic arm length), A . Measure CAREFULLY the distance between your pupils, B . Perform the math calculations indicated below. You just made a big “X”. Since both triangles share an angle at the cross ( ? ), they are called “similar triangles”. That means a ratio of one is the same for the other. So, 𝐴 ? = 𝐵 ? So, you measured ‘A’, ‘B’, & ‘P’. Now calculate ‘W’. 2. Now measure ‘W’. How accurate is this measurement compared to your calculations? State both calculated and measured value. Show all calculations.

Make a scatter plot graph with Distance on the x-axis and apparent brightness on the y-axis. Make sure to label you axis. 3. Add the graph below. Working with Google Sheets and Google Docs, we can add our graph directly into this document. Click on your graph in Google Sheets, copy it (Control+C or Command+C) it in a document. 2.6 2.8 3 3.2 3.4 3.6 3.8 4 0 10 20 30 40 50 60 70 80 90 100 Parallax (milli-arcseconds) Parallax (arcseconds) Distance (parsecs) Distance (light years) 4. Based on the graph you just made, how are distance and brightness related? They are very close to each other on the scatter plot. 5. Was your prediction in question number 1 correct? If you were not correct, explain what else you think might matter when talking about the brightness of stars.