Abstract
In Chap. 12 we saw how a planet’s temperature and gravity combine to determine whether the planet has an atmosphere. In this chapter we study the physical processes that determine the temperature in the first place. Intuitively, we expect a planet close to the Sun to be warmer than a planet farther away, but we seek to quantify that effect. We also consider ways in which a planet’s atmosphere can act as a blanket to trap heat. The physical phenomena that play a role here are blackbody radiation and the interaction of light with matter.
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- 1.
Solid angle is like an angular area, dΩ = sinθ dθ dϕ, and it is measured in steradians. There are 4π steradians on a sphere.
- 2.
In principle, this could be reduced to \(\,\mathrm{kg}\,{\mathrm{m}}^{-1}\,{\mathrm{s}}^{-3}\,{\mathrm{sr}}^{-1}\), but that would make the physical meaning much less clear.
- 3.
We now use “quantum” as a general term, and “photon” when speaking specifically of light.
- 4.
Here P denotes power, not pressure.
- 5.
This analysis is inspired by Problems 19.13 and 20.7 in the book by Carroll and Ostlie [1].
- 6.
To get true energy flux we need a factor of σ multiplying each T 4, but those all factor out.
- 7.
This is why we wear more layers of clothing in the winter.
- 8.
We can picture a cloud for two reasons: according to quantum mechanics the electron wavefunctions are shells; even in classical mechanics, if we took a long-exposure photograph the electrons would look smeared out due to their motion.
- 9.
In analogy with gravity, the portion of the cloud outside the hydrogen ion’s position produces no net force.
- 10.
Incidentally, microwave ovens operate using molecular rotation. Microwave radiation induces water molecules in food to rotate; friction then disperses the rotational energy as heat.
- 11.
Venus’s cloud cover creates a high albedo, so the predicted temperature is actually lower than Earth’s even though Venus is closer to the Sun.
- 12.
On Earth, most of the carbon is locked up in the crust.
References
B.W. Carroll, D.A. Ostlie, An Introduction to Modern Astrophysics, 2nd edn. (Addison-Wesley, San Francisco, 2007)
J.T. Kiehl, K.E. Trenberth, Bull. Am. Meteorol. Soc. 78, 197 (1997)
T.M. Donahue, J.H. Hoffman, R.R. Hodges, A.J. Watson, Science 216, 630 (1982)
C. de Bergh, B. Bezard, T. Owen, D. Crisp, J.P. Maillard, B.L. Lutz, Science 251, 547 (1991)
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Keeton, C. (2014). Planetary Temperatures. In: Principles of Astrophysics. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9236-8_13
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DOI: https://doi.org/10.1007/978-1-4614-9236-8_13
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