Physics and Astronomy Labs/Angular size/Preliminary Investigation

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Initial investigation[edit]

Approximate angles of 10°, 20°, 5°, and 1° for outstretched hand. Note the "fingers down" in the 20° case.
This "fingers up" method seems to measure 20° just as well as the "fingers-down" method shown above, provided the thumb and pinky are stretched as far as possible.

Students at Wright State University are have been estimating the angular size using the hand, as shown in the figure. These estimates can be compared with the measured value, which is obtained by measuring the length of an object, s, and the distance to that object, r. Measured in radians, θ ≈ s/r. The results shown below are based on this approximate relationship between angular size and distance. The "nominal" angle refers to the estimate shown in the figure.

Date course nominal
(degrees)
mean
(degrees)
stdev
(degrees)
Error
(degrees)
Number
students
1/20/15 phy1060 1 1.24 0.07 0.24 7
1/21/15 phy1060 10 8.54 0.12 -1.46 3
1/21/15 phy2400 20 19.8 1.1 -0.2 7
  • Nominal refers to the angular size (in degrees) as deduced using one's hand, as shown in the figure.
  • Mean and stdev refer to the average value and standard deviation, respectively, obtained by N students.
  • Error is the difference between the mean amd the nominal values.

The 20 degree measurement used the hand outstretched with all fingers held upward, not down as shown in the figure. This choice of hand position was chosen after a preliminary investigation by the Phy1120 class that suggested that the fingers-down position position was unreliable. These preliminary were not reported because we were just messing around. Moreover, subsequent investigation has suggested that both the "fingers-up" and "fingers-down" hand positions are nearly equivalent in both consistency as well as accuracy.