Atmospheric scale height

The atmospheric scale height, H, characterizes the extent of the atmosphere. It is defined as

\[H = \frac{k_B T}{\mu m_u g}\]

where \(k_B\) is the Boltzmann constant, T is the atmospheric temperature, \(\mu\) is the mean molecular weight, \(m_u\) is the unified atomic mass unit and g is the gravitational acceleration. PyAstronomy provides a function accepting SI units (atmosphericScaleHeight()) and an alternative accepting Earth or Jovian units atmosphericScaleHeight_MR()). Required conversion constants are adopted from PyA’s constants package.

Example:

from PyAstronomy import pyasl

T, mu, g = 290, 28.97, 9.8
she = pyasl.atmosphericScaleHeight(T, mu, g)

print("Earth")
print(f"T, mu, g = {T} K, {mu}, {g} m/s**2")
print(f"Scale height = {she:4.1f} [km]")


T, mu, mp, rp = 165, 2.2, 1, 1
shj = pyasl.atmosphericScaleHeight_MR(T, mu, mp, rp, "J")

print("Jupiter")
print(f"T, mu, mp, rp = {T} K, {mu}, {mp} [MJ], {rp} [RJ]")
print(f"Scale height = {shj:4.1f} [km]")

API documentation

PyAstronomy.pyasl.atmosphericScaleHeight(T, mu, g)

Atmospheric scale height

Parameters

Tfloat

Temperature in K

mufloat

Mean olecular weight

gfloat

Gravitational acceleration [m/s**2]

Returns

Scale heightfloat

Atmospheric scale height in km

PyAstronomy.pyasl.atmosphericScaleHeight_MR(T, mu, Mp, Rp, ref)

Atmospheric scale height

Parameters

Tfloat

Temperature in K

mufloat

Mean olecular weight

Mpfloat

Mass of planet [wrt Jupiter or Earth (see ref)]

Rpfloat

Radius of planet [wrt Jupiter or Earth (see ref)]

refstring, {J, E}

Determines whether Mp and Rp are considered in units of the Earth (E) or Jupiter (J)

Returns

Scale heightfloat

Atmospheric scale height in km