# Atmosphere as a function of Zenith angle?

1. Mar 7, 2009

### Ai52487963

1. The problem statement, all variables and given/known data
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 [Broken]

2. Relevant equations
???

3. 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.

Last edited by a moderator: May 4, 2017
2. Mar 7, 2009

### mgb_phys

You can probably assume a plane - 100km is small compared to the radius of the earth.

3. Mar 8, 2009

### Ai52487963

One http://www.astro.ufl.edu/~oliver/ast3722/lectures/EffectOfAtmosphere/EffectAtmos.pdf" [Broken] I founddoes a taylor expansion, but why would I want to do that?

Last edited by a moderator: May 4, 2017
4. Mar 9, 2009

### Redbelly98

Staff Emeritus
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.