Parallax
Parallax is the apparent shift of a foreground object with respect to a background object when it is viewed from two (or more) different vantage points. If you need to review the concept, look in the Prologue of the Chaisson text. You will be using one of the small laboratory telescopes to make your measurements. You will receive instructions on how to use the telescopes during one of the lab sessions. If you still have questions about using the telescope when you begin this lab, ASK! In this lab, you should keep the telescope pointing perpendicular to the direction that the scope can slide on the table.
Part 1. Calibrate Your Telescope
Because different eyepieces will show you a different field of view in a telescope, you must figure out what angle is shown with the eyepiece you will be using. The procedure for this should be done inside.
Place a meter stick across the room (at least 5 meters away) from the telescope. Turn it so you will be able to see the numbers on the meter stick through the telescope. Measure the distance from the center of the base of the telescope to the meter stick. (Use a tape measure or a second meter stick to measure the distance.)
Distance ______________________________ (cm).
You will be using a reticle eyepiece. That just means it is an eyepiece with some kind of grid or markings visible at the focal plane. For this lab, there is a grid with eight divisions in the reticle.
Measure the actual field of view seen in the eyepiece. In other word, focus on the meter stick and count how many centimeters are seen across the field of view. How many cm you can see will depend on exactly how far away the meter stick is. If it is farther, you will see more.
Number of cm seen across 8 divisions (full width of the eyepiece) is:
Width _______________________________ (cm).
The angle seen in the eyepiece as measured in radians is simply given by dividing the width by the distance. Angle (rad) = width/distance.
Angle _________________________________ (radians).
Just so you know what it is, convert your angle to degrees (multiply by 180/p).
Angle _________________________________ (deg).
What is the angle (in radians) from one tick mark to the next? (To calculate that, divide your previous answer in radians by 8.)
Angle _________________________________ (radians).
Part 2: Measure Parallax Inside
This first test will be to verify the distance between the telescope and the meter stick that you measured in the first step.
Move the telescope to the left side of the table and mark this location. While keeping your meter stick the same distance away from the telescope, stand it up vertically and turn it edge on, so you can't see the scale markings through the telescope. Carefully rotate the telescope to center the image of the meter stick in the eyepiece.
Next, slide the telescope to the right 5 cm and observe the new location of the meter stick in your eyepiece. You will probably want to repeat this sliding motion several times. The table will wobble a little, and the telescope board may shift a little as you slide it. See if you can come up with a consistent image shift as you slide the board.
Measure how far the scope shifted on the table. This is your baseline. Baseline ________________________________ (cm).
How many tick marks has the image shifted when you move the telescope? ____________________________
Use your previous value for the angle between tick marks to calculate the parallax angle (in radians) of your observed shift. _______________________________ (rad)
Now calculate the distance to the meter stick using the formula:
distance = (baseline/parallax shift in radians)
Distance = _________________________________ (cm).
Comment on how different this measurement is compared to your direct measurement? (If it is very different, you should check your work. If it is identical, one might suspect that you fudged your baseline measurement to make the distances agree.)
Part 3: Measure Parallax Outside
On more distant objects, you may want to make your first observation with the image to the far right or left of the field of view in the reticle eyepiece and then move the telescope and observe the image shifting across the tick marks on the reticle.
Pick out an object that is about 25-30 m away. This could be a tree or a sign or a certain brick on a building. If the weather is bad, you can observe down the hall, but people going to classes might get in your way. Perform your distance calculations for your chosen object. Mark the table at both the left end and the right end of your "slide" and observe how much the image appears to shift in the eyepiece.
What parallax angle (in radians) has the image shifted? _______________________________ (rad) Note that the angle that the image shifts is still related to the angle between tick marks that you measured earlier in this experiment.
Measure your baseline (how far the telescope slides across the table). Baseline ________________________________(cm).
Calculate the distance to the object using the formula you used in part 2.
Distance = _________________________________ (cm).
Now to check your work, measure the distance to this object using one of the tape measures. How much different is this than your direct measurement? (If it is very different, you should check your work.)
Part 4: Measure Parallax to Distant Objects
Assume that you can repeatably slide the telescope table and measure a parallax shift of one tick mark on the reticle eyepiece.
What is that angle? _________________________ (radians)
What is that angle? _________________________ (degrees)
What is the maximum baseline you can use with the current apparatus? ________________________________ (cm)
What, then, is the maximum practical distance you can measure with the current apparatus? (Convert your answer from centimeters to meters.) _________________________ (m)
Assume the radio towers on top of smelter mountain are 3 kilometers away. What baseline would you want to have available to measure its distance, assuming that your observed angular shift is the same? ____________________________________ (cm)
Now assume you are using a large observatory and can accurately measure angles as small as 0.1 arc second. How many radians in 0.1"?_______________________________
The nearest star, Proxima Centauri, is at a distance of 1.3 pc? (You should first convert this distance to km.) What baseline (in km) would you need to measure the distance to Proxima Centauri? _________________________________ (km)
Could you use the diameter of the Earth for your baseline?
How does this calculated baseline compare to the diameter of the Earth's orbit around the sun?