Environment: Thermosphere Exponential

Description

The exponential atmosphere module is able to evaluate an analytical approximation of an atmosphere that can be added to any celestial body. It is able to determine the density and temperature of any location in the atmosphere of a planet. The density decays under an exponential law and the temperature is a constant that is set by the user. This model is able to approximate the atmosphere of any celestial body, provided the base density and scale heights can be entered into the system.

Example Use Cases

Use a computationally efficient model for quickly assessing the effect of atmospheric drag on the decay of a spacecraft's orbit.
Find the amount of propellant needed to compensate for drag over a mission sequence.
Determine the temperature of the atmosphere at particular locations around a body.

Module Implementation

The model is symmetric about all spherical angles. Assuming spherical coordinates \(\{r, \theta, \phi\}\), this atmosphere is constant about \(\phi\) and \(\theta\), but tapers exponentially about \(h\), where \(h\) is the altitude of the body above the surface of the planet (\(h = r - R_{p}\)).

\[ \rho = \rho_0e^{-h \over h_0} \]

Here, \(\rho\) defines the density at some location \(h\), \(\rho_0\) is the density at the surface and \(h_0\) defines the scale height at which \(\rho_0\) is defined.

Assumptions / Limitations

The temperature of the atmosphere is agnostic of any rotation or location within the atmosphere, provided it is within the bounds defined.
The atmosphere is defined everywhere and all spacecraft will read an atmosphere value if they are within the atmosphere defined.
Unless a component is added, the dynamic effects of the atmospheric drag will not contribute to the dynamic orbit of the spacecraft by default.
Two exponential atmospheres cannot be added to the same body at the same time.

References