ASTR 110L                                                                                                                          Name:

Spring 2009

# Parallax Worksheet

Read: Ridpath, pp. 12-14 (star distances and parallax); related sections of your ASTR 110 textbook.

Our formula that relates parallactic shift, q, of a nearby target to its distance, D, from the observer is:

1. (2 pts.)  On the parallax diagram below, clearly label the distances or angles that b, D, and q represent:

2.  FIRST TARGET: Use red light on tripod as target, and use very distant streetlamp as background landmark.

a. (5 pts.)  Measure b and q for three different values of b.  Note: Taking and averaging together repeated measurements of q (at each value of b) will improve your value for q!  (Thought question: Why?)  Finally, calculate D using a calculator for each case.  Include units on all your values of b, q, and D.

 Measure: b Measure: q Calculate: D First b Second b Third b Estimated uncertainty in your measured values of b and q

b. (1 pt.)  Use your values in the table above to arrive at a value for the distance to your target.  Did you just average all three of your above values for D, or did you decide to exclude one or more of them for some reason?  Explain.

c. (1 pt.)  Calculate the percent uncertainties in your measurements of b and in your measurements of q, based on your estimated uncertainty listed above.  Which is greater?  (We will assume that our percent uncertainty in D will be comparable.)

d. (1 pt.)  Go out and physically measure the distance to your target.  Does your calculated value above in part (b) “agree” with your physically measured value of D?  Explain the source of any possible errors.

3.  SECOND TARGET:  Choose a more distant target (and even more distant “landmark”) than you did in part (2).  In this case, you cannot go out and physically measure the distance to your target… parallax is the only convenient way to determine its distance!

Target used:                                                                                Distant landmark used:

a. (5 pts.)  Measure b and q for three different values of b.  Taking and averaging repeated measurements of q (at each value of b) will improve your value for q!  (Thought question: Why?)  Then calculate D using a calculator for each case.  Include units on all your values of b, q, and D.

 Measure:  b Measure: q Calculate:  D First b Second b Third b Estimated uncertainty in your measured values of b and q

b. (1 pt.)  Use your values in the table above to arrive at a value for the distance to your target.  Did you just average all three of your above values for D, or did you decide to exclude one or more of them for some reason?  Explain.

4. (4 pts.)  In order to determine distances to nearby objects, astronomers use the “annual parallax” of the Earth: over the course of 6 months, the Earth travels halfway around its orbit, creating a “baseline” of 2.00 AU.  Suppose the “target” is the nearest star to the Sun, a Centauri, and very distant stars or galaxies are used as the “background” objects.  How large of a parallactic shift, q, in degrees, would we expect a Centauri to undergo?  (Be sure to convert 2.00 AU to either meters or kilometers, and also to convert the distance of a Centauri to the same units, before plugging them into our parallax formula.)  [Your answer will be a tiny fraction of a degree.  The ancient Greeks understood the idea of parallax, and tried but could not measure such a tiny angle.  So they logically concluded that the Earth is at rest, and that the Sun, planets, and stars all moved around the Earth!  The parallax of a Centauri, the star with the greatest and most obvious annual parallactic shift, is still so small of a shift that it was not successfully measured until 1839.]  [Further note: Astronomers tend to use the angle: π = ½q for the parallactic shift of a star… but don’t worry about that.  Just answer my question as I have posed it here, and solve for q using our formula.]