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{\bf 29:61 General Astronomy\\
     Fall 2004\\
     Lecture 1 \ldots August 23,2004\\
     The Earth's Atmosphere and the Boundary of Space}\\

{\em Just the facts, Ma'am}
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$\bullet$ Atmospheric pressure at sea level: $1.013 \times 10^5$ Newtons/m$^2$

\noindent 
$\bullet$ Change in atmospheric pressure associated with increase in altitude $\Delta z$
\begin{equation}
\Delta p = -\rho g \Delta z
\end{equation}
where $\rho$ is the gas density (kilograms/m$^3$), $g$ acceleration due to gravity at Earth's surface (9.8 m/sec$^2$).

\noindent
$\bullet$ Perfect gas law
\begin{eqnarray}
p V = N k_B T\\
p = n k_B T
\end{eqnarray}
$V=$ volume of gas, $N$ total number of particles (atoms and/or molecules) in the gas, $n$ number density of atoms and/or molecules (units are particles/m$^3$), $T$ is the temperature (degrees Kelvin), $k_B =1.3807 \times 10^{-23}$ J/K.  

\noindent
$\bullet$ Differential form of change in atmospheric pressure with altitude
\begin{equation}
\frac{dp}{dz} = -\left( \frac{mg}{k_B T}\right) p
\end{equation} 
where $m$ mass of atom or molecule composing the atmosphere.  

\noindent
$\bullet$ Pressure as function of height in an isothermal atmosphere
\begin{equation}
p(z) = p_0 \exp(-z/Z_0)
\end{equation}

\noindent
$\bullet$ Isothermal pressure scale height
\begin{equation}
Z_0 = \frac{k_B T}{m g}
\end{equation}

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