Astronomy related angle question (more of a Trig Q)

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SUMMARY

This discussion focuses on the application of trigonometry in measuring the height of lunar craters using pixel distances and shadow lengths. The user seeks clarification on whether the angle of altitude (theta) should be expressed in radians when applying the tangent function to calculate height from shadow length. The relationship between theta, the distance to the terminator (D), and the radius of the Moon is established, with the user questioning the necessity of converting D/radius into radians. The conclusion is that theta, being a dimensionless ratio, does not require conversion to radians for the tangent function.

PREREQUISITES
  • Understanding of basic trigonometry, specifically the tangent function.
  • Familiarity with lunar measurements, including crater dimensions.
  • Knowledge of angular measurements in both degrees and radians.
  • Experience with astronomical calculations involving distances and ratios.
NEXT STEPS
  • Research the application of trigonometric functions in astronomical measurements.
  • Learn about the conversion between degrees and radians in mathematical contexts.
  • Explore methods for measuring celestial bodies using pixel data from images.
  • Investigate the significance of the terminator in lunar observations and its impact on measurements.
USEFUL FOR

Astronomy students, educators in physics and mathematics, and anyone involved in lunar research or astronomical imaging will benefit from this discussion.

conquertheworld5
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For an astronomy lab I am looking at pictures of the moon, measuring pixel distances and converting to km. Easy enough for the diameter of a crater, but the depth gets more complicated. To find the wall height of the crater, you measure the shadow length and the angle of altitude (theta in diagram). I was told that theta is equal to the distance to the terminator(D in diagram) divided by the radius of the moon, which is also easy to calculate. But to use the trig tangent(theta)=height/shadow, doesn't theta have to be in radians? the dist. to terminator over the radius is a dimensionless number (km/km after conversions)... should I multiply by a factor of 2pi to get theta, or is it okay for theta to be dimensionless?
 

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well... looks like I'm handing in my lab report as is whether it's right or wrong... just printed it.

Still would like to get an answer though!
 

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