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

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In summary, the sun's elevation changes about 7-8 times faster at sunrise/sunset than it does at solar noon.
  • #1
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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  • #2
You are measuring elevation from the horizon - you are not at the centre of the Earth.
Draw the picture - it will help ;-)
 
  • #3
The sun moves across the sky at a constant rate, but in two dimensions, not just one.
 
  • #4
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?
 
  • #5
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.
 
  • #6
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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  • #8
You got it!
 

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

1. Why does the sun's elevation change throughout the day?

The sun's elevation changes throughout the day due to the Earth's rotation on its axis and its orbit around the sun. As the Earth rotates, different parts of the planet are exposed to the sun's rays, causing the sun's position in the sky to change.

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

The sun's rate-of-change in elevation is not constant because of the Earth's tilted axis and its elliptical orbit around the sun. These factors cause the sun's apparent path in the sky to vary throughout the year, resulting in changes in its rate of change in elevation.

3. How does the Earth's tilt affect the sun's elevation?

The Earth's tilt of approximately 23.5 degrees plays a significant role in the sun's elevation. As the Earth orbits the sun, its tilted axis causes different amounts of sunlight to reach different parts of the planet. This results in changes in the sun's elevation throughout the day and throughout the year.

4. Does the sun's elevation change at the same rate every day?

No, the sun's elevation does not change at the same rate every day. The rate of change is affected by various factors such as the Earth's rotation, its orbit around the sun, and the Earth's tilt. These factors cause the sun's elevation to change at different rates throughout the day and throughout the year.

5. How does the sun's elevation affect the length of daylight?

The sun's elevation affects the length of daylight by determining the amount of sunlight that reaches different parts of the Earth. When the sun is higher in the sky, more sunlight reaches the surface, resulting in longer days. When the sun is lower in the sky, less sunlight reaches the surface, resulting in shorter days.

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