Angulardistance - Lab reports from ast 131 PDF

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Estimating Distance Using Angles Ellexis Hoerl November 14, 2019 Aim ● To introduce students to the ability to estimate angles using their thumbs. ● Showing students how the angle subtended from their thumb can measure far away distances. ● To reinforce the effectiveness of the angular formula by estimating distance rather than angular measurement. Apparatus Thumb, meterstick, measuring tape, picture of a map, picture of globe, whiteboard, lab manual, pen. Diagram

Object One Globe

Object Two Map

Measuring Tape

Estimating Angular Size

Meterstick

1

Formulae Athumb = 57.3( DS ) Aobject = X (Athumb ) S object

D = 57.3( A

When X is the number of thumbs wide

)

object

distance−measured distance | % difference = | estimated measured × 100 distance Procedure 1. We began by becoming acquainted with the ways one can use their hands to measure angles. 2. Then, to find the angular size of our thumb when held outstretch in front of us, we measured the actual size of our thumb the distance between our eyes and our thumbs in this position using the meterstick. 3. After calculating the angular size of our individual thumbs we selected two objects to estimate the angular size and distance of. 4. Standing directly in front of each object, at eye level, with the one eye closed we extended our thumbs and counted the number of thumb-widths wide each of the objects were. Before leaving the locations from which we estimated the angular size to be we measured our actual distance from the objects using the tape measure. 5. With this information, we were able to go to the angular formula and estimate what our distance was from the object. 6. Checking our accuracy, we calculated the percent difference between our measured distance and the actual distance of the objects, rechecking our work until it showed a less than 10% difference. 7. We finish the experiment by recording our findings. Theory The theory of which this experiment was modeled after follows the idea of using the angular formula to determine the size and distance of a distant object. It states that one may use the angle subtended from their thumb to estimate the measurements for any other object. By having the students practice this method themselves it reinforces the significance of the angular formula.

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Observation Object

Number of Thumbs Wide

Total Angular Size Aobject

Globe

1

2.2°

Map

2

4.4°

Object

Total Angular Size Aobject

Actual Size S object

Estimated Distance

Globe

2.2°

24.5 cm

638.1 cm

Map

4.4°

60 cm

781.4 cm

Object

Estimated Distance

Distance Measured

% Difference

Globe

638.1 cm

24.5 cm

5%

Map

781.4 cm

60 cm

8%

Calculations Estimating the angular size of thumb: Athumb = 57.3( DS ) 2 Athumb = 57.3( 51 ) Athumb = 2.2°

Estimating the angular size of object #1: Aobject = X (Athumb ) When X is the number of thumbs wide Aobject = 1(2.2) Aobject = 2.2° Estimating the distance to object #1: S

D = 57.3( Aobject ) object

D = 57.3( 24.5 ) 2.2 D = 638.1 cm

3

Finding % difference: distance−measured distance | % difference = | estimated measured × 100 distance 638.1−675 % difference = | 675 | × 100 % difference = .05 × 100 % difference = 5% Results We found the angular formula to work as predicted. There was a % difference in both objects under 10% likely due to human error. Conclusions Upon concluding this lab I have a better understanding of the way the angular formula is calculated. I also learned how to estimate size and distance with only my hands. We found when conducting the experiment that it was very important to be directly eye level with the selected object in order to avoid a higher percent error. References ● Astronomy 131 Laboratory Manual by Tim Welling, Tony Zito, and Ian Freedman ● Google ● Lab partner Matt Scott

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