Why isn't the sun's rate-of-change in elevation constant?

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Discussion Overview

The discussion revolves around the non-constant rate of change in the sun's elevation angle throughout the day, as observed by a participant using the 'solpos' library for solar position calculations. The inquiry seeks to understand the underlying reasons for this phenomenon, particularly in relation to trigonometric principles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant notes that the sun's elevation changes more rapidly at sunrise and sunset compared to solar noon, citing specific calculations for Toronto.
  • Another participant emphasizes that elevation is measured from the horizon and suggests that a diagram could clarify the situation.
  • A participant states that the sun moves across the sky at a constant rate in two dimensions, implying that this affects the perceived rate of elevation change.
  • There is a request for a simple diagram to illustrate the sun's motion, as the participant struggles to create an intuitive representation.
  • A suggestion is made that the sun's path can be depicted as a sinusoidal arc, with trigonometric relationships used to analyze its motion in both x and y directions.
  • A participant shares a diagram they created based on earlier suggestions and seeks feedback on it.

Areas of Agreement / Disagreement

Participants generally agree on the complexity of visualizing the sun's motion and the need for diagrams, but there is no consensus on a single clear representation or explanation of the observed phenomenon.

Contextual Notes

Some participants express uncertainty about how to effectively illustrate the sun's motion and its implications for elevation changes, indicating that existing diagrams may not adequately convey the concept.

Who May Find This Useful

This discussion may be useful for individuals interested in solar position calculations, trigonometry in astronomy, or those looking to understand the dynamics of solar elevation changes throughout the day.

irotas
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I have been experimenting with the 'solpos' library from NREL, which is a very nice library for computing solar position (and related) calculations given date/time and coordinates.

One thing that surprised me is that the sun's rate-of-change in elevation (angle from the horizon) is not constant throughout the day. In fact, the elevation changes about 7-8 times faster at sunrise/sunset than it does at solar noon.

Here's sample calculations for Toronto Canada for January 19, 2009:
07:52:00: azim=118.788 elev=0.109222
07:59:00: azim=120.007 elev=1.209
...
12:28:00: azim=179.905 elev=25.9437
13:18:00: azim=192.848 elev=24.9487

I'm sure there's some perfectly good trigonometric reason why this should be the case, but at the moment I haven't been able to come up with a good explanation.

Can anyone help unravel this mystery?

Thanks,
Adam
 
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You are measuring elevation from the horizon - you are not at the centre of the Earth.
Draw the picture - it will help ;-)
 
The sun moves across the sky at a constant rate, but in two dimensions, not just one.
 
Is there really a simple picture to clarify this observation? I've been scribbling diagrams all day and they all end up terribly complex and totally unenlightening. Any advice on how to draw this out?
 
russ_watters said:
The sun moves across the sky at a constant rate, but in two dimensions, not just one.

Yeah, I realized that a while ago, but I'd still like to be able to draw a simple picture to help illustrate the point. I might end up having to demonstrate this to higher-ups in my company so I want to make absolutely sure I've got a simple clear picture that they can intuitively understand.

I'll continue to work on this, but any guidance is certainly appreciated.
 
The diagram would be a sinusoidal arc, depicting the motion of the sun across the sky as viewed by a person standing on the earth, facing south. The sun travels along that arc at a constant rate and at any point in the arc, you can draw a triangle and do some trig to figure out how fast it is moving in the x and y directions.
 
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