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BSTAR

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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 D = 1 2 ρ C d A v 2 {\displaystyle F_{\text{D}}={\frac {1}{2}}\rho C_{\text{d}}Av^{2}}

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

The acceleration due to drag is then

a D = F D m = ρ C d A v 2 2 m {\displaystyle a_{\text{D}}={\frac {F_{\text{D}}}{m}}={\frac {\rho C_{\text{d}}Av^{2}}{2m}}}

In aerodynamic theory, the factor

B = C d A m {\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:

B ∗ = ρ 0 B 2 = ρ 0 C d A 2 m {\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

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

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

References

  1. "BSTAR Drag Term". Retrieved November 8, 2022.
  2. Kelso, T.S. "Frequently Asked Questions: Two-Line Element Set Format". Retrieved November 8, 2022.
  3. Hoots, Felix R.; Roehrich, Ronald L. (December 1980). SPACETRACK Report No. 3 Models for Propagation of NORAD Element Sets (PDF) (Report). Retrieved November 8, 2022.
  4. Vallado, David A., and Paul J. Cefola. "Two-line element sets-Practice and use." 63rd International Astronautical Congress, Naples, Italy. 2012.
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