Abstract
We now shift attention from gravity to other aspects of physics that are relevant for astronomical systems. We begin with gas physics, which has two facets. Thermodynamics describes the bulk properties of a gas (such as temperature, density, and pressure), while statistical mechanics describes the microscopic motions of gas particles. In this chapter we use both to study Earth’s atmosphere in the context of a basic theory of planetary atmospheres.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Had we tried to evaluate \(\left \langle v\right \rangle\), we would not have been able to separate the integral into three distinct terms as we have done here.
- 2.
Note that velocity and momentum enter this analysis in different ways. While the two quantities are related, keeping them separate lets the framework describe either classical or relativistic motion.
- 3.
We could equivalently write the integral in terms of velocity using N(v x ) dv x .
- 4.
Internal modes play a more significant role in the specific heat of a gas, which quantifies the amount of energy required to raise the temperature by a certain amount (see Sect. 16.1.2).
- 5.
While atoms and molecules do not have sharp edges and need not be spheres, the simple assumption is adequate for rough estimates.
- 6.
This is appropriate if we think of particles as billiard balls that literally hit one another, but the concept of cross section can be generalized to other interactions (see Sect. 15.2.3).
- 7.
We could divide space in different ways and still obtain the same result.
- 8.
The net horizontal force vanishes by symmetry: the pressure on the “left” side of the volume element is balanced by the pressure on the “right” side, and likewise for the “front” and “back.”
- 9.
You may be more familiar with the derivative written in terms of \([P(r + \Delta r) - P(r)]/\Delta r\), but in the limit \(\Delta r \rightarrow 0\) it is equivalent to use \([P(r + \Delta r/2) - P(r - \Delta r/2)]/\Delta r\). By introducing a derivative, we are assuming that P is a continuous function. While gas is made of discrete particles on a microscopic scale, the sheer number of particles allows us to treat pressure as effectively continuous on a macroscopic scale.
- 10.
This analysis draws from the book by Carroll and Ostlie [1].
- 11.
Recall from calculus: \(\int u\,\mathrm{d}v = uv -\int v\,\mathrm{d}u\).
- 12.
Whether or not a particular molecule is abundant depends on whether any was present in the first place; that, in turn, depends on how planets formed (see Chap. 19) and how life subsequently modified Earth’s atmospheric composition. What this analysis tells us is that if a certain gas is present, it will stick around.
Reference
B.W. Carroll, D.A. Ostlie, An Introduction to Modern Astrophysics, 2nd edn. (Addison-Wesley, San Francisco, 2007)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Keeton, C. (2014). Planetary Atmospheres. In: Principles of Astrophysics. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9236-8_12
Download citation
DOI: https://doi.org/10.1007/978-1-4614-9236-8_12
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-9235-1
Online ISBN: 978-1-4614-9236-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)