\documentstyle [12pt] {article}
\textwidth= 16.0cm
\textheight=22.0cm
\oddsidemargin 0pt
\evensidemargin 0pt
\topmargin 0pt
\begin{document}
\begin{center}
{\bf 29:61 General Astronomy\\
     Fall 2004\\
     Lecture 11 \ldots November 8, 2004\\
     Planetary Magnetism}\\

{\em Just the facts, Ma'am}
\end{center}

\begin{center}
{\bf The Urey Cycle}
\end{center}
\noindent
$\bullet$ The mineralogical chemical cycle responsible for controlling the level of 
carbon dioxide in the Earth's atmosphere. 
\begin{equation}
MgSiO_3 + CO_2 \rightarrow MgCO_3 + SiO_2
\end{equation}
The arrow can point to the right or the left, depending on the temperature.  

\begin{center}
{\bf Photoionization}
\end{center}
\noindent
$\bullet$ The ionization of molecules by ultraviolet light in the upper atmosphere of the Earth (and elsewhere). 
\begin{equation}
O_2 + h \nu \rightarrow O_2^{+} + e
\end{equation}
where $h \nu$ represents the energy present in a photon of light.  

\begin{center}
{\bf The Lorentz Force}
\end{center}
\noindent
$\bullet$ The force acting on a charged particle moving in electric $\vec{E}$ and magnetic $\vec{B}$ fields is given by . 
\begin{equation}
\vec{F} = q \vec{E} + q \vec{v} \times \vec{B}
\end{equation}
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 {\em Tesla}, those of the electric field are {\em Volts/meter}.  

\begin{center}
{\bf Electromagnetic Radiation}
\end{center}
\noindent
$\bullet$ Light corresponds to electromagnetic waves with wavelengths in the range 
$4.0 \times 10^{-7} \leq \lambda \leq 7.0 \times 10^{-7}$ meters.  

\begin{center}
{\bf The Solar Constant}
\end{center}
\noindent
$\bullet$ The solar constant = 1370 W/m$^2$.  For other planets,  it is inversely proportional to the square of the distance from the Sun. 

\begin{center}
{\bf The Stefan Boltzmann Law}
\end{center}
\noindent
$\bullet$ 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.  
\begin{equation}
S = \sigma T^4 \mbox{  Watts/m}^2
\end{equation}
where $\sigma = 5.67 \times 10^{-8}$ Watts/m$^2$/K$^4$, and $T$ is the temperature in degrees Kelvin.  

\begin{center} 
{\bf The Equilibrium Temperature of a Planet}
\end{center}
$\bullet$ The equilibrium temperature of a planet, ignoring the greenhouse effect of its atmosphere (which often is a major correction) is
\begin{equation}
T_{eq} = \left[ \frac{(1-A)S_0}{\sigma}\right]^{\frac{1}{4}}
\end{equation}
where $S_0$ is the solar constant for that planet, and $A$ is the albedo.  

\begin{center} 
{\bf Wien's Law}
\end{center}
$\bullet$ The wavelength at which a blackbody radiator is brightest, $\lambda_{max}$ is given by
\begin{equation}
\lambda_{max} =\frac{hc}{5 k_B T}
\end{equation}
where $h = 6.626 \times 10^{-34}$ is Planck's constant, $c$ is the speed of light, and $T$ is the temperature.  












\end{document}
