Parallax Lab
Nature of Science
September 16th, 2015
Introduction
This lab will help you to understand how distances in the universe can be
measured by the parallax method. This method, like several other methods to
determine distances, is based on the principle that a triangle is completely known
with only three elements. Therefore those methods are called triangulation
methods. They are used by surveyors to make a map of a region. To understand
those methods it is not necessary to make calculations or to know about
trigonometry. We have only to measure angles and the length of a basis line that is
within our reach, then we make a scale drawing. So we need two instruments for
measuring (an angle-measure tool and a tape measure) and a ruler, a protractor,
paper and a pen for drawing, that's all!
We will start with an outdoor activity, measuring the distance to an object without
arriving there, like surveyors do. It will become clear that practically there are some
problems in using the same method for objects in the sky. Thus, another method is
proposed to determine a triangle, using the phenomenon of parallax.
Part A:
Standing in front of Beckman Institute, you will determine the distance to the spire in
the center of the Beckman Quad.
1. Stand several meters away from your partner in a line roughly perpendicular
to the line connecting Beckman and the spire. Measure and record the
distance between you and your partner.
2. Measure the angle from your partner to the spire. Your partner should
measure the angle from you to the spire. Record these angles in your lab
notebook.
3. Use your protractor to draw the triangle connecting you, your partner, and
the spire. Use the angles you measured to get a triangle that is similar to the
real one.
4. Measure the length of the base and sides of your triangle. Which one is
equivalent to the base of your triangle in your scale model?
5. Use your triangle to determine the distance from where you were standing to
the spire?
6. Measure the distance directly using a meter stick. How accurate was your
triangulation method?
7. Name two ways to improve the accuracy of this measurement.
8. Would your triangulation method be more or less accurate if the spire were
twice as far away (assuming the base is the same)? Could you use this
method to measure the Earth-Moon distance
Parallax Method For Measuring Distances To Near Celestial Objects
Part B:
Standing in the back of our classroom, you will determine the distance from your
face to your finger at arm’s length using the method of parallax.
9. Stand at the back of the classroom and hold your pointer finger at arm’s
length in front of you.
10. Close your left eye and note which post-it note your finger is pointing to.
11. Close your right eye and note which post-it note your finger is pointing to
now.
12. Measure the angular distance between the two post-it notes using your
fingers (see page 3). Close one eye as you do this (it does not matter which
one). This is twice your parallax angle, p.
13. Have your partner measure the distance between your eyes in centimeters.
14. Construct a scaled down version of the triangle between your two eyes and
your finger using the angle you measured, the distance between your eyes,
and the knowledge that this is an isosceles triangle.
15. What is the distance between your face and finger at arm’s length using this
method?
16. Measure the actual distance from your finger to your face. How accurate is
this method?
17. Describe two ways you could improve the accuracy of this measurement.
Post-Lab Questions
To measure the annual parallax of stars parallax, photos of a small part of the
starry sky are made by a telescope. Below there are drawings made from two
photos taken from the same part of the starry sky 6 months apart.
The whole photographic plate has a dimension of 1/3 arc second, so about
0.0001°.
a) Which star is the nearest to the earth? What is its annual parallax?
b) Which star is the most remote? What is its annual parallax?
c) When star D is at 18 light-years distance from the earth, what are the
distances of the stars A, B and E in light-years?
d) Determine the parallax for Alpha Centauri by using the formula: p = 1/d,
where p is the parallax angle in arcseconds and d is the distance in parsecs.