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name MEASURING ANGLES Fig 1: Islamic Astronomers of the Middle Ages in an Observatory in Istanbul. Fig 2: Tycho Brahe in Denmark. His observations...

please do only Part I and either A or B of Part II

Measuring Angles ± Lab 1 ± 1 name M EASURING A NGLES Fig 1: Islamic Astronomers of the Middle Ages in an Observatory in Istanbul. Image can be found in the book “History of the Modern World” by Palmer, Colton & Kramer at http://highered.mcgraw- or nomers-MS-1.jpg Fig 2: Tycho Brahe in Denmark. His observations were later used by Kepler. Image from or or or y.png Have you ever thought how we determine the positions of stars, or the sizes of anything? If you want to know the size of Jupiter (or even just the moon), you can hardly fly to it with your ruler in your hand and measure it. However, the moon has a definite size in the sky. And what’s the size of the entire sky? This seems a ridiculous question, however if we think in terms of angles it gets easier. One whole circle has 360 degrees. A huge cloud that occupies about one 10 th of the sky then has a diameter of 180 o /10, i.e., 18 o . Similarly, you can measure the diameter of the moon, which turns out to be about 0.5 o . So in Astronomy we always think in angles - i.e. , in “angular sizes.” Thousands of years ago we observed and measured angles in the sky, and today we still do the same - and ironically we still use pretty much the same methods. In this Lab you will learn the simplest and most basic method of how to measure angles.
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2 ± Lab 1 ± Measuring Angles P ART I There are several methods of measuring angles and rather sophisticated instruments have been designed. Yet it is surprising how few people actually know how to determine angles with their own body parts… Maybe it is not quite as accurate, but at least it provides rather good estimates. This is how you do it – stretch out your arm. Your fist will cover an angle of about 10 o , your index finder 1 o , and you whole hand about 20 o . Let’s check if this hypothesis. What is the angular size of your finger? a) Extend your arm in front of you. Measure the distance between your eye and the tip of your index finger. cm b) Measure the width of your index finger (across your finger nail). cm c) Calculate the angular size of your finger in degrees. Consult the TOOLKIT to figure out which trigonometric function to use. Write the trigonometric function into the box. S HOW your calculation; ZERO points otherwise! d) Rewrite your answer using the rules of significant figures degrees e) How could you determine the uncertainty in the angular size? Make a suggestion. Your estimated uncertainty (guess this) in the width of your finger is degrees f) Rewrite your answer using significant figures and error estimates ± degrees (Your answer should have the form of 13.4 ± 0.5 or so.) f) Does the One-Degree-per-Finger Rule apply to you? (In Astronomy we often use estimates. If your value falls within 30% of the expected value, your estimate is considered reasonable.) Distance from eye to finger width of finger Angle
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a) 75 cm
b) 1.7 cm
c) Tan(angle)=Width of finger/Distance from eye to finger
Tan^-1(0.02)=1.14576 deg
d) angle = 1.1 degrees to 2 significant figures
e) To...

1 comment
  • Thank you for your patience. Any questions or clarification is welcomed.
    • cplusplusexpert
    • Jul 20, 2016 at 2:29pm

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