BSTAR

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

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

$F_{\text{D}}=\frac{1}{2}\rho C_{\text{d}}A{v}^2$

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

The acceleration due to drag is then

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

In aerodynamic theory, the factor

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

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:

$B^{*}=\frac{{\rho }_{0}B}{2}=\frac{{\rho }_0{C}_{\text{d}}A}{2m}$

thus reducing the expression for the acceleration due to drag to

$a_{\text{D}}=\frac{\rho }{{\rho }_0}{B}^{*}{v}^2$

As it can be seen, $B^{*}$ 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. The corresponding reference air density is given as $0.15696615\text{ kg}/({\mathrm{m}}^2\cdot R_{\text{Earth}})$. One must be very careful when using the value of $B^{*}$ 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.