BSTAR

BSTAR is a way of modeling aerodynamic drag on a satellite in the simplified general perturbation model 4 satellite orbit propagation model.{{cite web|title=BSTAR Drag Term|url=http://www.castor2.ca/03_Mechanics/03_TLE/B_Star.html|access-date=November 8, 2022}}

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

:$F\_\backslash text\{D\}\; =\; \backslash frac\{1\}\{2\}\; \backslash rho\; C\_\backslash text\{d\}\; A\; v^2$

where

$\backslash rho$ is the air density,

$C\_\backslash text\{d\}$ is the drag coefficient,

$A$ is the frontal area, and

$v$ is the velocity.

The acceleration due to drag is then

:$a\_\backslash text\{D\}\; =\; \backslash frac\{F\_\backslash text\{D\}\}\{m\}\; =\; \backslash frac\{\backslash rho\; C\_\backslash text\{d\}\; A\; v^2\}\{2m\}$

In aerodynamic theory, the factor

:$B\; =\; \backslash frac\{C\_\backslash text\{d\}\; A\}\{m\}$

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:

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

thus reducing the expression for the acceleration due to drag to

:$a\_\backslash text\{D\}\; =\; \backslash frac\{\backslash rho\}\{\backslash rho\_0\}\; B^*\; v^2$

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.{{cite web|title=Frequently Asked Questions: Two-Line Element Set Format|first=T.S. |last=Kelso|url=http://celestrak.com/columns/v04n03/ |access-date=November 8, 2022}} The corresponding reference air density is given as $0.15696615\backslash text\{\; kg\}/(\backslash mathrm\{m\}^2\; \backslash cdot\; R\_\backslash text\{Earth\})$.{{cite report|title=SPACETRACK Report No. 3 Models for Propagation of NORAD Element Sets|first1=Felix R. |last1=Hoots |first2=Ronald L. |last2=Roehrich|date=December 1980|url=https://celestrak.com/NORAD/documentation/spacetrk.pdf|access-date=November 8, 2022}} 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.Vallado, David A., and Paul J. Cefola. "Two-line element sets-Practice and use." 63rd International Astronautical Congress, Naples, Italy. 2012.