29:61 General Astronomy
Fall 2004
Lecture 1 ...August 23,2004
The Earth's Atmosphere and the Boundary of Space

Just the facts, Ma'am

$\bullet$ Atmospheric pressure at sea level: $1.013 \times 10^5$ Newtons/m$^2$

$\bullet$ Change in atmospheric pressure associated with increase in altitude $\Delta z$

$$\Delta p = -\rho g \Delta z$$ (1)

where $\rho$ is the gas density (kilograms/m$^3$), $g$ acceleration due to gravity at Earth's surface (9.8 m/sec$^2$).

$\bullet$ Perfect gas law

$$p V = N k_B T$$ (2)

$$p = n k_B T$$ (3)

$V=$ 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.

$\bullet$ Differential form of change in atmospheric pressure with altitude

$$\frac{dp}{dz} = -\left( \frac{mg}{k_B T}\right) p$$ (4)

where $m$ mass of atom or molecule composing the atmosphere.

$\bullet$ Pressure as function of height in an isothermal atmosphere

$$p(z) = p_0 \exp(-z/Z_0)$$ (5)

$\bullet$ Isothermal pressure scale height

$$Z_0 = \frac{k_B T}{m g}$$ (6)