 Name: Partner(s): Day/Time: Version: intro

# Parallax Worksheet

Note part 2 steps 1 - 4 is data collection and can be completed before doing any other parts of the activity. Your GSI may have half the class start with that.

## Part 1: Some basics of Parallax

Figure 3 shows two objects, O and P, and two observing positions X and Y. 1. Use a ruler and sketch in the lines to make the triangle needed to measure the distance to object O.
2. Use a protractor to measure the parallax angle αO at observing position Y. Record the value on figure 3.
3. Use a ruler and a different color writing utensil to sketch the lines to make the triangle needed to measure the distance to object P.
4. Use a protractor to measure the parallax angle αP at observing position Y. Record the value on figure 3.
5. Which object has the bigger parallax angle? Does that make sense? Explain.

Figure 4 shows an object O at some distance R from two observing positions X and Y with reference object V. 1. Use a protractor to measure the angles βx and βy. Record the values on figure 4.
2. Use a ruler to measure the baseline B in cm and record that value on figure 4.
3. Calculate the parallax angle α. show your work.

4. Calculate the distance R. Show your work.

5. Use a ruler to measure the distance R. Rmeasuresd=___________

## Part Two: Parallax Across Town

Proceed to the roof, where you will use parallax on a slightly larger scale to determine the distance to a structure in downtown Ann Arbor. The target object will be pointed out by your lab instructor, but is usually a parking structure on the west side of the building.

For the purposes of our lab, the reference object can be any of the tall radio/TV antennas on the horizon as long as it's in the same direction as your object and it stays on the same side of the object as you move from viewpoint X to Y (i.e. if it appears on the right of the object at one end of the roof it should appear on the right side of the object at the other end of the roof, Y).The more distant your reference object is, the more accurate your results will be.

1. Using one of the sighting telescopes, sight on the distant antenna as accurately as possible. Line up the top of the antenna with the center of the cross hairs, then have your partner read the angle indicated by the pointer on the base of the telescope. Estimate the angle to the nearest quarter of a degree (half the smallest division on the base). Enter this as the angle to V for the position X in table 1.
2. Turn the telescope (not the base!) to align the target object with the cross hairs. It may help to leave both eyes open and move the telescope until you see the same thing with both eyes. Have your lab partner read the angle again. Enter this as the angle to O for the position X in table 1.
3. To increase your precision, measure both angles 3 times, preferrably by 3 different people. Make sure each person measures from the same antenna to the same position on the target.
4. If the other viewing station for your object is open, go to it and repeat the above steps at that station, entering the data under the Y position in table 1. Be sure to put the cross hairs on the same part of the building as before.
5. Before leaving the roof, be sure to measure the baseline B in meters between the two viewing stations. Enter the value in table 2.
6. The angle βx is the absolute value of the difference between your two measurements at position X: | angle to V - angle to O|. For each trial, calculate βx and record this number in the table.  note it is the absolute value because the positve or negative depends on whether your distant object is to the right or the left of object V. As long as it stays on the same side for both positions, it doesn't matter which side it's on.
7. Average your readings to get your final value for βx and record the result in table 1.
8. Repeat the two previous steps for βy.
9. Calculate the parallax angle α by subtracting the averages of βx from βy. Record this value in table 2.
10. Calculate the distance to V. Show your work here.

11. To get the true distance, use the attached map of Ann Arbor or Google Earth on the lab computers. Make sure you know what structure V is! Be sure to measure on the map between the center of your baseline (not X or Y itself) and the part of the building that you sighted.
Table 1: Data from the rooftop measurements
Trial Position X Position Y
angle to V angle to O βx angle to V angle to O βy
1
2
3
AVE xx xx   xx xx

Table 2: Rooftop Parallax and Distance
α (degrees) B (m) R (m)(parallax) R (m) (map)

## Concluding Questions

1. What do you think was the leading source of error in your measurements of the distances using parallax?

2. Fig 5 shows how astronomers measure the parallax to a star. The parsec was defined based on parallax. An object 1 parsec away has a parallax angle of 1 arc second for a baseline of 1 AU. 1. How long is the baseline in fig. 5 in AUs?

2. If O is 1 parsec away, what is the parallax angle in degrees?

3. Calculate the length of a parsec in AUs. Show your work.

4. If the parallax angle of the star in figure 5 is 1 arc second, how many parsecs away is it?

3. Why does a parallax measurement become less accurate as the target object gets to be very distant?

4. We can use parallax to measure objects out to about 300 parsecs. If we wanted to use parallax for objects farther away, we could build a satellite and put it in orbit around the Sun. Would it be better to place the satellite in an orbit near Mercury, or Mars? Explain.

Last updated: 11/10/11 by SAM