BSTAR

BSTAR is a way of modeling aerodynamic drag on a satellite in the simplified general perturbation model 4 satellite orbit propagation model.^[1]

Traditionally, aerodynamic resistance ("drag") is given by

${\displaystyle F_{\text{D}}={\frac {1}{2}}\rho C_{\text{d}}Av^{2}}$

where ${\displaystyle \rho }$ is the air density, ${\displaystyle C_{\text{d}}}$ is the drag coefficient, ${\displaystyle A}$ is the frontal area, and ${\displaystyle v}$ is the velocity.

The acceleration due to drag is then

${\displaystyle a_{\text{D}}={\frac {F_{\text{D}}}{m}}={\frac {\rho C_{\text{d}}Av^{2}}{2m}}}$

In aerodynamic theory, the factor

${\displaystyle B={\frac {C_{\text{d}}A}{m}}}$

is the inverse of the ballistic coefficient, and its unit is area per mass. Further incorporating a reference air density and the factor of two in the denominator, we get the starred ballistic coefficient:

${\displaystyle B^{*}={\frac {\rho _{0}B}{2}}={\frac {\rho _{0}C_{\text{d}}A}{2m}}}$

thus reducing the expression for the acceleration due to drag to

${\displaystyle a_{\text{D}}={\frac {\rho }{\rho _{0}}}B^{*}v^{2}}$

As it can be seen, ${\displaystyle B^{*}}$ has a unit of inverse length. For orbit propagation purposes, there is a field for BSTAR drag in two-line element set (TLE) files, where it is to be given in units of inverse Earth radii.^[2] The corresponding reference air density is given as ${\displaystyle 0.15696615{\text{ kg}}/(\mathrm {m} ^{2}\cdot R_{\text{Earth}})}$.^[3] One must be very careful when using the value of ${\displaystyle B^{*}}$ released in the TLEs, as it is fitted to work on the SGP4 orbit propagation framework and, as a consequence, may even be negative as an effect of unmodelled forces on the orbital determination process.^[4]