Calculate Sun Angle: Length of Object by Shadow

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Discussion Overview

The discussion revolves around calculating the sun's angle in the sky at a specific time of day, particularly in relation to determining the length of an object based on its shadow. The scope includes theoretical aspects of celestial mechanics and practical measurement techniques.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asks for an explanation on calculating the sun's angle to determine the length of an object's shadow.
  • Another participant suggests using the law of cosines from spherical trigonometry and references a specific website for further information.
  • A different viewpoint proposes a practical method involving a short stick to measure the angle, emphasizing the need for quick measurements due to the changing angle of the sun.
  • Some participants mention the use of planetarium programs as an alternative to manual calculations, while others express a preference for hands-on methods.
  • One participant shares an anecdote about celestial navigation, highlighting the complexity and satisfaction of manual measurements and calculations.
  • A later post elaborates on the two components affecting the sun's angle: a daily variation due to Earth's rotation and a seasonal variation influenced by the observer's latitude, while also noting the effects of Earth's axial tilt.

Areas of Agreement / Disagreement

Participants express various methods and perspectives on calculating the sun's angle, with no consensus on a single approach. Some prefer practical measurement techniques, while others suggest theoretical methods or software solutions.

Contextual Notes

Participants mention the importance of local noon for accurate measurements and the influence of Earth's axial tilt, but there are unresolved details regarding the specific calculations and assumptions involved.

Ba
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Can somebody explain how to calculate the sun's angle in the sky at a certain time of day? It is wanted to calculate the length of an object by it's shadow.
 
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It's based on the law of cosines from spherical trigonometry. The site http://www.krysstal.com/sphertrig.html has what you want about the shadow, but you have to scroll past a lot of stuff about great circle distances and the direction of Mecca.
 
The easiest way to get the angle it set up a short stick you can measure, then compute the angle. You can then apply that to an object you wish to find the height of. You need to work fast, the angle is always changing.
 
A planetarium program will tell you if you don't feel like calculating it...
 
russ_watters said:
A planetarium program will tell you if you don't feel like calculating it...

Aww, that's no fun! See Asimov's story "The Feeling of Power".
 
Well, I will say you haven't lived until you've done celestial navigation... after a half an hour of measurements, calculations, and plotting, you'll know that half an hour ago, you were within 5 miles or so of where the GPS told you you were.
 
Thanks, we wanted to try and find the angle as exact as possible.
 
Ba said:
Can somebody explain how to calculate the sun's angle in the sky at a certain time of day? It is wanted to calculate the length of an object by it's shadow.

There are two components to the suns angle in the sky.

One of them varies with a 24 hour period, you can correct for this component by making your measurements at local noon. This component is due to the rotation of the earth.

The other component will vary with the season, it will have a 1 year period, and it will depend on the latitude of the observer.

If you ignore the axial tilt of the earth, you can probably see if you think aobut it a lot that the sun would be always on the horizon at the poles, and it would pass directly overhead on the equator.

Because of the axial tilt of the earth, this actually happens only on the equniox.
 

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