Atmosphere as a function of Zenith angle?

In summary, the problem is to find the distance from a location to space, represented by a zenith angle and the height at 0 degrees, using either the "flat Earth" approximation or the "spherical Earth" approach. The latter may be more tedious but is still possible.
  • #1
Ai52487963
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Homework Statement


Find x, the distance from your location to space, as a function of the zenith angle. The height at 0 degrees, H, is ~100km.

A picture helps more: http://img23.imageshack.us/img23/3630/picture1orr.jpg



Homework Equations


?



The Attempt at a Solution


I've tried using the law of cosines to express the distance in terms of the Earth's radius and other known constants, but it seems like I'm over complicating the situation.
 
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  • #2
You can probably assume a plane - 100km is small compared to the radius of the earth.
 
  • #3
mgb_phys said:
You can probably assume a plane - 100km is small compared to the radius of the earth.

One http://www.astro.ufl.edu/~oliver/ast3722/lectures/EffectOfAtmosphere/EffectAtmos.pdf" I founddoes a taylor expansion, but why would I want to do that?
 
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  • #4
There are 2 approaches to this problem that I can think of.

1. Using the "flat Earth" approximation, as mgb_phys suggested. In this case it's a straightforward trig problem.

2. Consider a spherical Earth. In this case you need to find the intersection of a line and a circle (the upper atmosphere's edge). More tedious than #1, but I think it's possible.

Note, for angles approaching horizontal, the flat-Earth approximation answer approaches infinity rather than a finite value.
 

1. What is the atmosphere?

The atmosphere is a layer of gases that surround a planet or other celestial body. It is primarily composed of nitrogen, oxygen, and other trace gases. It plays a crucial role in regulating the planet's temperature and protecting it from harmful radiation.

2. How does the atmosphere change with different zenith angles?

The atmosphere's composition, density, and temperature change with increasing zenith angles. As the zenith angle increases, the path length of sunlight through the atmosphere also increases, leading to greater absorption and scattering of light by particles in the atmosphere.

3. What is the impact of zenith angle on atmospheric pressure?

As the zenith angle increases, the vertical component of the atmospheric pressure decreases, resulting in lower atmospheric pressure. This is because the weight of the overlying air decreases with increasing zenith angle.

4. How does the atmosphere affect the color of the sky at different zenith angles?

The atmosphere's scattering of sunlight is responsible for the blue color of the sky. At smaller zenith angles, more blue light is scattered, resulting in a darker blue color. As the zenith angle increases, less blue light is scattered, and the sky appears lighter or even white.

5. What role do clouds play in the atmosphere's response to zenith angle?

Clouds can significantly impact the atmosphere's response to zenith angle. They can block or reflect sunlight, affecting the amount of solar radiation that reaches the Earth's surface. Additionally, they can also influence the amount of scattering and absorption of light in the atmosphere, altering the colors of the sky and the overall atmospheric response to zenith angle.

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