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Part 1: Finding the Distance to Stars Using the Parallax Angle

Instructions:

Read Chapter 15 and Appendix D (pp. 543-545) in the textbook and the background information below.

Answer the three questions at the bottom directly in this lab worksheet. 

This NASA web page provides additional explanation and allows you to check your answer:

http://imagine.gsfc.nasa.gov/features/yba/HTCas-size/parallax3.html

Background:

Stellar Parallax is the apparent shift in the location of a star due to the orbit of the Earth.  In other words, the star will appear to be in a different place depending on the line of sight from the Earth. By knowing the diameter of Earth’s orbit and by measuring the angle of apparent shift (the parallax angle), astronomers can calculate the distance to the nearby stars using trigonometry. This method has been used for centuries. The ancient Greeks were able to measure some of the closest stars this way. Today, sophisticated telescopes have greatly enhanced this method. Figure 1 is a graphic from your textbook showing how this works:

Assignment:

For this assignment, you will determine the distance to a star, “HT Cas”, using the method of stellar parallax. Figure 2 and 3 below are photos of HT Case, taken six months apart:

When we super-impose these photos, we get the following image (figure 4):

You can see that the position of the star appears to have changed over the six-month time period. However, it is actually the angle from which the photos were taken that has changed.  During that 6-month period, the Earth moved from one side of the sun to the other.

Using a stellar astrometric catalog, we find that the two stars closest to HT Cas are a distance of 0.01 arcseconds apart. Based on this information, we can estimate that the angle of shift of HT Cas (the parallax angle) to be approximately 0.015 arcseconds apart.

We also know that the radius of the Earth’s orbit is 1.0 A.U. (astronomical units).

Using these two measurements, we can then determine the approximate distance to HT Cas using the following equation:

d= distance to HT Cas

a=radius of the Earth’s orbit

p=parallax angle

1.     (10 points) Given the above equation and information provided, about how far away is HT Cas? 

a.     133 parsecs

b.    67 parsecs

c.     33 parsecs

d.