## Parallax Measuring Device

Name:
Lab Instructor: Lab Section:
Parallax Measurement
Student Worksheet
1. [40 pts] Taking Your Parallax Measurements Refer to Figure 3 and Section 3 of the lab
PDF For instructions on how to take your parallax measurements using the UTK Parallax
Measuring Device (PMD). On the PMD, the two posts are separated by 20 inches, which
serves as the baseline for the parallax measurement. Use the leftpost to align a distant
object and a background reference. Then using the rightpost measure the angle of the
apparent displacement due to parallax.
As you move your object to the three distance positions, directly measure the distances
using the provided measuring tape. When you move the object to a new position, extend
the tape measure from the point directly below your PMD under the table to the point
directly below the distant object. You are aiming for roughly Position 1 = 10 ft, Position 2
= 20 ft, and Position 3 = 30 ft. Record your direct measurements in Table 1.
Table 1. Direct Measurements of Distance
Measure distances in inches, to the nearest halfinch.
Position 1 (in) Position 2 (in) Position 3 (in)
As you measure the angles you will use to determine the observed parallax, record in
Table 2 found on the next page.

Table 2. Your Parallax Measurements & Calculated Distances
Record angles to the nearest tenthdegree,
distances to the nearest halfinch.
Angle 1 ( ) Angle 2
( ) 2???? ( ) ???? ( ) D (in)
Position 1 (Approximately 10 ft)
Trial 1
Trial 2
Trial 3
Position 2 (Approximately 20 ft)
Trial 1
Trial 2
Trial 3
Position 3 (Approximately 30 ft)
Trial 1
Trial 2
Trial 3

2. [4 pts] In our experiment, we used a baseline of 20 inches. What would happen if the
vantage points were farther apart? For example, how would our measured parallaxes
change if we used a baseline of 100 inches instead?
(Note that there is no wrong answer to this question. The point is to take a guess, and then
to verify or to disprove it.)
3. [5 pts] Repeat the experiment with the object at Position 3, but this time use a baseline
distance of 40 inches by shifting your PMD 20 inches to the right after selecting your
landmark on the left upright post. Record the data for the increased baseline below
Angle 1 ( ) Angle 2 ( ) 2???? ( ) ???? ( )
Baseline of 40 in. at
Position 3
4. [3 pts] For an object at a fixed distance, how does observed parallax change as the
baseline increases?
5. [3 pts] Calculate the distance of the object at Position 3 using the equation below.
???? = 20 in
tan (????)
How does the distance compare to the distance you calculated for your three trials at
position 3?

6. [2 pts] Which remote distance calculations do you trust more the ones made with the
smaller or larger baseline distance? Why?
7. [10 pts total] In this question, you are going to analyze your distance and measured
parallax data to confirm the relationship between distance and parallax.
a. [1 pts] Calculate the average parallax your group measured for each of the three
object positions (~10 ft, 20 ft, and 30 ft)
Position 1 Average:
Position 2 Average:
Position 3 Average:
b. [4 pts] In a Google Spreadsheet, make a plot of Parallax vs. Distance using your
direct measurements of distance (Table 1) for the xaxis (the independent variable)
and your average measured parallax for the three positions on the yaxis.
c. [1 pt] Fit a powerseries to your data and display the equation. Since you put your
average parallax values on the uaxis, use p for your variable name instead of y.
Since you put the directly measured distances on the xaxis, use D instead of x.
d. [4 pts] In your own works, describe the relationship between distance and parallax.
That is, how does the parallax change as the distance changes.

8. [3 pts] Estimate the uncertainty in your measurement of the object’s apparent shift (your
measured values for 2????). For example, do you think your recorded measurements could be
off by ten degrees? One degree? One tenth of a degree?
9. [3 pts] Based on your estimate of the uncertainty in the angular measurements of 2????,
estimate the uncertainty in your measurements of the object distances. For example, do
you think the distances are different from the directly measured distances by 1 inch, 1 foot,
several feet, etc.?
(Note that there is no wrong answer to this question. The point is to take a guess, and then
to verify or to disprove it.)
10. [3 pts] Calculate the average distances determined using parallax using your three trials
for Position 1, Position 2, and Position 3
Position 1 Average:
Position 2 Average:
Position 3 Average:

11. [5 pts] Calculate the absolute error of your distances determined using parallax compared
to the directly measured distance. Use your average distances from your parallax
measurements for the “Parallax Distance.” The vertical bars in the equation indicate
absolute value. That means ignore the negative sign if you get a negative number.
???????????????????????????????? ???????????????????? (%) = 100 :???????????????????????????????? ???????????????????????????????? ???????????????????????????????? ????????????????????????????????
???????????????????????????????? ???????????????????????????????? :
Absolute Error for Position 1:
Absolute Error for Position 2:
Absolute Error for Position 3:
12. [3 pts] For which measurement was your error the greatest? Do you think there is a reason
why this measurement had the greatest error?
13. [6 pts] Compare the distances that you calculated for each position using the parallax
method to the distances that you measured directly at the beginning of the experiment.
calculated in Question 11.

14. [5 pts] Now that we have some understanding of the accuracy and precision of
determining distances using parallax, let’s see how this works for real parallax data for a
star.
Here you will use Equation 3, ???? = !
, where the distance D is in parsec and parallax p is in
arcsec.
The star Canopus has a measured parallax of ???? = 0.01055 ± 0.00056 arcsec. The
0.01055 arcsec is the best estimate for the parallax measurement. The ± 0.00056 arcsec
(plus and minus 0.00056 arcsec) is the 1sigma (1 standard deviation) uncertainty in the
parallax measurement. Recall that in science, we can never measure something exactly.
We always list our best estimate and the wiggle room.
a. [2 pts] What is our best estimate for the distance, in parsec, to Canopus?
b. [1 pt] Using the minus part of the uncertainty (i.e., 0.01055 0.00056 arcsec),
what is the distance to Canopus?
c. [1 pt] Using the plus part of the uncertainty (i.e., 0.01055 + 0.00056 arcsec),
what is the distance to Canopus?
d. [ 1 pt] Estimate the uncertainty in the distance to Canopus.
15. [5 pts] Relate the parallax experiment you did in today’s lab to the way that parallax is
used by astronomers to measure the distances to nearby stars. Your answer should include
what your two vantage points represented and how you measured the parallax angle
corresponds to what astronomers observe to determine the parallax of a star.