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Date
Apr 3, 2024
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Uploaded by ChiefNightingaleMaster694
The Parallax Experiment
11/13/2022
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Taking Parallax Measurements
1. Estimate the distance to the horizon, or to a distant landmark in line with your measuring device and your object at Position 1, by eye. I estimate the distance is 400 feet by eye Table 5.2: Direct Measurements of Distance
Distances from observer to object, in inches, to the nearest half-inch.
Position 1
Position 2
Position 3
120
240
360
(Distance from observer and apparatus to three foreground objects.)
2. Estimate the uncertainty
in your measurement of the object's apparent
shift. For example, do you think your recorded measurements could be off by ten degrees? One degree? One tenth of a degree? There is some uncertainty, so I would guess that the measurements could be off by about 4 degrees.
Table 5.3: Parallax Measurements
Record angles to the nearest tenth-degree, distances to the nearest half-inch.
Angle 1
(
°
)
1
Angle 2
(
°
)
2
2α (
°
)
3
α (
°
)
r/d
4
d (in)
5
Trial 1
Posn. 1
87
80
7
3
.061
196.1
Posn. 2
86
85
2
5
.017
658.7
Posn. 3
87
86
1
.5
.008
1379.3
Trial 2
Posn. 1
90
80
10
5
.087
137.1
Posn. 2
90
85
5
2
.004
2745
Posn. 3
90
87
3
1
.026
457
Trial 3
Posn. 1
85
76
9
4.5
.078
152.5
Posn. 2
85
80
3
1.5
.026
457
Posn. 3
85
83
2
1
.017
685
Dependence of Parallax on Vantage Point Separation
3. What would happen if the vantage points were farther apart? We separated our vantage points by two feet, to simulate the two astronomical
units by which the Earth shifts position over a six month period. What if we had used a separation of ten feet instead? How would you expect the angular shift of the object (the difference between Angle 1 and Angle 2) to change? The difference between the angle of something in the fixed background and the object would be greater than it is now.
4. By how many degrees did the object move using the more widely 1Landmark angle.
2Foreground object angle.
32
α
= Angle 1 - Angle 2.
4r/d values can be looked up in Table 5.4.
5d = r / (r/d), where 2r is the vantage point separation (24 inches).
separated vantage points?
I would guess that it moved 8 degrees.
5. For an object at a fixed distance, how does the apparent shift change as you observe from more widely separated vantage points?
The shift changes because it increases in distance Measuring Distances using Parallax
6. The apparent shift of the object is caused by looking at the object from two different vantage points. Qualitatively, what do you see changing from
viewpoint to viewpoint? As a foreground object moves farther away from you, does its apparent shift increase or decrease?
the viewpoint changes with different objects but the foreground move further away with the shift change 7
. Based on your estimate of the uncertainty in the angular
measurements of 2α, estimate the uncertainty in your measurements of the object distances.
I would estitmate the uncertainty to be about 4 inches 8
. Now look at the spread in the three values for each position in the last
column of Table 5.3. Is this spread consistent with your estimated uncertainty?
The spread is consistant but it does leave some room for error, give or take
9
. Now 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 (in Table 5.2). How well did the parallax technique work? Are the differences between the direct measurements and your parallax-derived measurements within your errors (within 2
σ
)? I think the parallax measurements worked because theyre within the 2 deviations
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