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Is Parallax an Accurate Measure of Distance?

based on 3 ratings
Author: Barry Eitel

Grade Level:

High School

Type:

Astronomy, Mathematics

Objective:

This experiment will determine if motion parallax is an accurate measure of distance for small, faraway objects.

Research Questions:

-Is “motion parallax” an accurate form of measurement?

-Could we use “motion parallax” to measure distance in outer space?

Introduction:

“Motion parallax” is easily demonstrable by closing one eye, staring at a pencil, and then opening the closed eye and closing the other. The pencil appears to move because the eyes have different locations. With some advanced geometry, astronomers can use this principle to measure the distance to certain stars using the movement of the earth. Although on paper the idea seems sound, but is it accurate in reality?

Materials:

  • Easel
  • Large piece of paper marked with a regular grid, or graph paper
  • Tape measure that can measure 100+ yards
  • 2 washers
  • Several wire hangers
  • Fishing line
  • Telescope
  • Access to a football field
  • Metal or wood stakes
  • Journal

Experimental Procedure:

  1. Undo the hangers and straighten them into lengths of wire.
  2. Twist several of them together to create two lengths of wire about a meter long each.
  3. Head to the football field, and place the easel at one end. Place the large piece of grid paper on the easel.
  4. Draw a line down the the center vertical line of the grid.
  5. String a length of fishing line through each washer.
  6. Bend one end of each length of wire at a 90 degree angle. Tie the end of each fishing line to the crook you created.
  7. Stake the straight end of each wire segment into the ground so that the washers hang freely directly in front of the center line of the grid, but at different distances from the easel. Measure the distance of each washer to the easel. You can call these numbers X (first washer) and Y (second washer).
  8. Move to the other end of the football field with the telescope.
  9. Standing directly in front of the center line, view the objects. Move the telescope until they match up exactly with the center line of the grid (at this point it should look like only one object). Mark the position of the telescope by putting a stake in the ground.
  10. Move the telescope exactly two meters to the right, ensuring that the telescope’s height stays the same. Center the washer closest to the easel in the telescope. Using the regular spacing of the squares of the grid, measure how far from the center line the washer appears to be. Note this down. Repeat for the other washer.
  11. Repeat Step 10, but moving two meters to the left (of the center position, i.e. four meters from where you are now).
  12. For each object, average the numbers you got in Step 10 and 11. Let’s call these numbers A (first washer) and B (second washer).
  13. Using the properties of ratio, calculate the distance D between the telescope and the washers: X/A = D/2 (the amount the telescope was moved from the center point). Ensure everything is in meters. Repeat for the other washer’s numbers.
  14. With the tape measure, measure the actual distance between the telescope and the washers.
  15. Analyze this data. How accurate were your parallax calculations compared to reality?

 Concepts: motion parallax, angles, ratios

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