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Observational Measurements Using Angles Ap parent vs. Actual Size and Distance

Observational Measurements Using Angles Ap parent vs. Actual Size and Distance. Terms. Arc angle – angle – the opening between 2 lines that meet at a point (measured in degrees) Angular diameter – angle size – the arc angle across an object Degree – a unit of angular measure

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Observational Measurements Using Angles Ap parent vs. Actual Size and Distance

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  1. Observational Measurements Using Angles Apparent vs. Actual Size and Distance

  2. Terms • Arc angle – angle – the opening between 2 lines that meet at a point (measured in degrees) • Angular diameter – angle size – the arc angle across an object • Degree – a unit of angular measure • 1° = 60 arc minutes, 60 arcmin, or 60’ • 1 arcmin = 60 arc seconds, 60 arcsec, or 60” • 1° = 3600 arc seconds, 3600 arcsec, or 3600”

  3. Estimating Angles by Hand • Parts of hand extended to arm’s length can be used to estimate angular distances and sizes in the sky.

  4. Example • The angular diameter of the moon is ½°, so it subtends, extends across, an angle of ½°. • Convert ½° into arcmin… ~30’

  5. Example • The Big Dipper: The angular distance between the two “pointer stars” at the front of the Big Dipper is about 5°.

  6. Example • Neptune: The angular diameter of Neptune when visible from the Earth is ~2”… That’s the same as looking at a dime head on from 1 mile away!!! Dang, that’s small!!!

  7. What does this tell us about actual physical size?? • NOTHING!! • But… • If you know the distance to the object, you can calculate physical diameter! • You will need the formula!!! physical diameter = distance X tan(ang. dia.)

  8. Consider the Dime… • We’re looking for the dime’s diameter • The distance to the dime is 1 mile or 1.6km • The ang. dia. is 2” (convert to degrees 2/3600) p.d. = 1.6km X tan(5.6x10^-4) p.d. = 1.6X10^-5 km (convert to mm) p.d.= ~16mm • Actual diameter of a dime…17mm!

  9. Let’s try the Moon now… • Moon’s distance from Earth – 384,000km • Angular diameter – ½° • What is the diameter of the Moon? p.d. = 384,000km X tan(.5) p.d. = 3,355km • Actual diameter = 3,476km

  10. Now the Sun… • Sun’s distance from Earth – 149,600,000km • Sun’s diameter – 1,391,000km • What is the arc angle? 1.4X10^6 = 1.5X10^8 X tan(x) Calculator – (1.4X10^6)/(1.5X10^8) = 0.0093 then, tan^-1(0.0093) = 0.53° So the arc angle is ~.53°

  11. What if the Moon were twice as far? • Distance to the Moon – 768,800km • Diameter of the Moon – 3,476km (actual) • What is the arc angle? 3,476 = 768,000 X tan(x) Arc angel ~.26°

  12. What if the Moon were half as far? • Distance to the Moon – 192,200km • Diameter of the Moon – 3,476km (actual) • What is the arc angle? 3,476 = 192,200 X tan(x) Arc angle ~ 1°

  13. Confused???

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