29:61 General Astronomy
Fall 2004
Lecture 11 ...November 8, 2004
Planetary Magnetism

Just the facts, Ma'am

The Urey Cycle

$\bullet$ The mineralogical chemical cycle responsible for controlling the level of carbon dioxide in the Earth's atmosphere.

$$MgSiO_3 + CO_2 \rightarrow MgCO_3 + SiO_2$$ (1)

The arrow can point to the right or the left, depending on the temperature.

Photoionization

$\bullet$ The ionization of molecules by ultraviolet light in the upper atmosphere of the Earth (and elsewhere).

$$O_2 + h \nu \rightarrow O_2^{+} + e$$ (2)

where $h \nu$ represents the energy present in a photon of light.

The Lorentz Force

$\bullet$ The force acting on a charged particle moving in electric $\vec{E}$ and magnetic $\vec{B}$ fields is given by .

$$\vec{F} = q \vec{E} + q \vec{v} \times \vec{B}$$ (3)

where $q$ is the charge of the particle. For a proton, the charge is $1.6022 \times 10^{-19}$ Coulombs, and for an electron, $q = -1.6022 \times 10^{-19}$ Often the symbol $e$ is used for this fundamental charge of an electron or proton. The units of magnetic field are Tesla, those of the electric field are Volts/meter.

Electromagnetic Radiation

$\bullet$ Light corresponds to electromagnetic waves with wavelengths in the range $4.0 \times 10^{-7} \leq \lambda \leq 7.0 \times 10^{-7}$ meters.

The Solar Constant

$\bullet$ The solar constant = 1370 W/m$^2$. For other planets, it is inversely proportional to the square of the distance from the Sun.

The Stefan Boltzmann Law

$\bullet$ A perfect blackbody radiator radiates the following amount of power into space per unit of surface area. The power consists of energy carried out by waves with a range of wavelengths.

$$S = \sigma T^4 \mbox{ Watts/m}^2$$ (4)

where $\sigma = 5.67 \times 10^{-8}$ Watts/m$^2$/K$^4$, and $T$ is the temperature in degrees Kelvin.

The Equilibrium Temperature of a Planet

$\bullet$ The equilibrium temperature of a planet, ignoring the greenhouse effect of its atmosphere (which often is a major correction) is

$$T_{eq} = \left[ \frac{(1-A)S_0}{\sigma}\right]^{\frac{1}{4}}$$ (5)

where $S_0$ is the solar constant for that planet, and $A$ is the albedo.

Wien's Law

$\bullet$ The wavelength at which a blackbody radiator is brightest, $\lambda_{max}$ is given by

$$\lambda_{max} =\frac{hc}{5 k_B T}$$ (6)

where $h = 6.626 \times 10^{-34}$ is Planck's constant, $c$ is the speed of light, and $T$ is the temperature.