# lab for astronomy AST 111 (Parallax Lab) DUE TODAY !!

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ParallaxLabActivity.docx

First, gather your materials:

· Tape measure (or meter stick).

· Provided data sheet. Parallax Lab Data Sheet.docx   or  Parallax Lab Data Sheet.pdf

· Glue. (A glue stick works best)

· Manila folder (or cardboard, or very stiff paper)

· String

· Small weight (a small roll of tape or hex nut would work).

· Masking tape

· Calculator

· Scotch tape to tape straw to astrolabe template (optional).

Fig1: Lab Materials

Lab Procedure Part One: Demonstrating Parallax Hold your thumb close to your nose. Look at an object on the far side of the room, first with your right eye closed, then with your left eye closed. (Select a particular object such as map or picture, not a blank wall.) What happened to your thumb? It should have appeared to move from one side of the distant object to the other. This effect is called parallax. Now, hold your thumb at arm’s length.  How far did the thumb move  compared to what happened when you held your thumb nearer to your face? The farther you hold your thumb from your eye, the less it jumps from side to side. The amount of this shift indicates how far away the object is. This is how your eyes judge distances. When objects are too far away, however, they do not "move" at all. This demonstrates the limitations in the use of parallax for determining distance.

Astronomers use parallax to judge the distances to stars. To get two different perspectives of the star, they compare two pictures taken from distant viewpoints (nearly186 million miles apart!). The amount the star seems to jump indicates its distance. Parallax can only be used to judge the distance to nearby stars. For stars extremely far away, having two viewpoints separated by 186 million miles is still not enough to make a star appear to change location.

Part Two: Making the Astrolabe

Important: Download and print:  astrolabe.pdf

1. Now, you'll need your astrolabe template, a half of a manila folder (or cardboard or other very stiff paper), a straw, a 20-cm piece of string, and a small weight. You will also need glue, tape, and scissors.

2. Cut out the template and glue it to the folder to make it firm, then cut out your astrolabe.

3. Tape a straw along the diagonal edge of the astrolabe.

4. Poke a hole in the circle marked on the astrolabe. Place a string through the hole so that the string hangs down in front of the astrolabe. Tape the other end securely to the back of astrolabe.

5. Tie a weight to the bottom of the string. You can now use your astrolabe to measure angles.

Fig. 2: Completed astrolabe

Part Three: Measuring the Angle and Baseline You'll now need the data sheet provided in this module. You will determine the height of a doorway using the astrolabe, and then compare this to the "known" value of the doorway. For the "known" height, you can directly measure the height of the doorway using a tape measure (or meter stick).

1. In parallax there is always a “baseline” distance that we know. Astronomers use the distance from one side of Earth’s orbit to the other to measure stellar parallax, a baseline of about 186 million miles! Now, stand on the ground and extend the tape measure from the top of the doorway to the floor. Record this "known" height (in either cm or inches - make sure to record the units you use!)

2. Next, measure a distance of about 10-15 feet, horizontally along the ground from the doorway with your tape measure. You can record the distance you select in cm or inches, but make sure that you use the same units you used in (1.) above for the height of the doorway. You may wish to mark this location with masking tape.

3. You will now measure the distance to the top of the doorway using the same mathematical principles astronomers use to calculate the distance to stars. Imagine that the highest point on the doorway is a distant star, and that you are going to measure the distance to it from Earth.

4. Stand at the location you measured in (2.) and look through the straw of your astrolabe so that you can see the top of the doorway. Make sure that the string and the weight hang freely from the device. When you tilt the astrolabe up to view the top of the doorway, the hanging string marks the angle at which you are viewing the doorway. Once you have sighted the top of the doorway, hold the string against the astrolabe and read the angle to the nearest five degrees. This is the parallax angle. You should record this angle on your data sheet. Perform this three times and record the angle each time.

Fig. 3: Our helpful assistant demonstrating the use of the astrolabe.

1. Find the average of these three angles and record the average value.

2. Take a look at the right triangle below. The distance you measured from the doorway to the tape represents the base of a triangle. The angle that you measured using the astrolabe represents the angle connecting the base to the diagonal side (the hypotenuse). The angle shown is the (average) parallax angle you measured with your astrolabe and recorded in (5.). The side of the triangle opposite the angle is the height of the doorway that you'll calculate using the equation below. Calculate the doorway height using the equation and record the value.

3. Since you did not lie on the ground to measure the angle, you will have to add the height to your eye level to the calculation in Step (6.) to get the actual height of the doorway. Do this, then record your final experimental value for the doorway height.

4. Lastly, calculate the percent difference between this value and the value calculated in (7.)

tan⁡(θ)=oppadj=doorwayheighthorizontaldistancefromdoorway

%error=∣knownvalue−experimentalvalueknownvalue∣×100