Parallax (page 2)

Why?

Each eye sees the toothpick from a different point. The distance between the points is the baseline. The apparent change in position of an object when viewed from two different points is called parallax. As the distance from the toothpick increased, parallax decreased. The farther away an object, the smaller the measurement of parallax.

Try New Approaches

How does the length of the baseline affect parallax? Look in a mirror and measure the distance between the pupils of your eyes. This was the baseline for the original experiment. Make a viewer with baselines greater and less than your eye baseline. Draw a 5-inch (12.5-cm) line across the widest part of a 4-by-6-inch (10-by-15-cm) index card. Punch a hole at each end of the line. Label each hole "1." In the center of the card, punch two holes 1 inch (2.5 cm) apart and label each hole "2." Repeat the experiment twice, first looking through the number 1 holes, then through the number 2 holes. To look through the holes, begin by holding the card so that its center is in line with the end of your nose. Keeping the card in place, move your head to the right and left to look through the holes.

Design Your Own Experiment

1. Design an experiment to demonstrate how parallax effect is used to measure the distance (d) to a nearby object. One way is to use a predetermined baseline and measure the parallax shift. Then determine the distance to the object using the following equation:
   d = 57.3° (baseline distance ÷ parallax shift)

Note: This equation yields a number without a unit of measurement. When no unit of measurement is indicated in giving the measure of an angle, the angle is understood to be expressed in radians. To express the angle in degrees, the conversion 57.3° per 1 radian is used.

Mark two points on the ground exactly 10 feet (3 m) apart and about 30 paces from a tree. Label the points "A" and "B." Stand at point A and use a cross-staff to measure the angular separation between the tree and a distant object such as a telephone pole. (See Chapter 4 for more information about angular separation and using a cross-staff to measure it.) Note: The distant object (telephone pole) should be about 10 times or more distant than the near object (tree) whose distance is being measured. Move to point B and make another measurement (see Figure 9.2). For the example shown, if the angular separation measures 5° from point A and 5° from point B, then the parallax shift equals their sum, or 10°. The distance to the tree is then calculated as follows:

d = 57.3° (10 feet ÷ 10°) or 57.3° (3 m ÷ 10°)
= 57.3 feet (17.2 m)

b. Use a tape measure to measure the distance to the tree. Then use the method in Appendix 2 to



determine the relative error of your measurements. This will give you an indication of how accurate your cross-staff is.

 

2. Diagram the parallax shift of a star using the diameter of Earth's orbit as the baseline. For information as well as other parallax experiments, see Janice VanCleave's A+ Projects in Earth Science (New York: Wiley, 1999), pp. 43–50.

Get the Facts

The parallax method cannot measure the distance of most stars because they are too far away. Instead, astronomers use photometers (light meters), Cepheids (pulsating stars), and, for stars in remote galaxies, something called red shift. For information on how these methods are used to calculate distances to stars, see Terence Dickinson, Nightwatch: A Practical Guide to Viewing the Universe (Willowdale, Ontario: Firefly Books, 1998), p. 89.

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