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(Optimal Computation of Collision Avoidance Maneuver)

Miss distance maximization

Consider two objects whose nominal orbits will intersect. The body 1 performs a collision avoidance maneuver some time before this conjunction, with an allotted $\Delta V$. In this page, the maneuver is designed to maximize the miss distance between the two objects. The time of the maneuver is a free parameter, which can range from the collision to $n_{orbits}$ before.
This approach is based on the works:

  • Collision Avoidance Maneuver Optimization. Claudio Bombardelli, Javier Hernando Ayuso and Ricardo García Pelayo. In Advances in the Astronautical Sciences (AAS 14-335). 2014. URL
  • Analytical formulation of impulsive collision avoidance dynamics. Claudio Bombardelli. In Celestial Mechanics and Dynamical Astronomy February 2014, Volume 118, Issue 2, pp 99-114. URL
  • Optimal Impulsive Collision Avoidance in Low Earth Orbit. Claudio Bombardelli and Javier Hernando Ayuso. In Journal of Guidance, Control, and Dynamics volume 38, issue 2 pp 217-225.
  • Series for Collision Probability in Short-Encounter Model. Ricardo García-Pelayo and Javier Hernando-Ayuso. In Journal of Guidance, Control, and Dynamics volume 39, issue 8, pp 1904-1912, 2016. doi: 10.2514/1.G001754

Warning: for miss distance exceeding $6000 \, \text{km}$, the results may be inaccurate.

Have fun!

Maneuver Parameters

$\Delta V$ = $\text{m} \, \text{s}^{-1}$
$n_{orbits}$ =

Body Sizes

$r_{1}$ = $\text{m}$
$r_{2}$ = $\text{m}$

Body 1 orbit parameters

$a_0$ = $\text{m}$
$e_0$ =
$\theta_c$ = $\text{deg}$

Collision geometry

$\phi$ = $\text{deg}$
$\psi$ = $\text{deg}$
$\chi$ =

Body 1 covariance matrix

$\sigma_{1T}$ = $\text{m}$
$\sigma_{1N}$ = $\text{m}$
$\sigma_{1H}$ = $\text{m}$

Body 2 covariance matrix

$\sigma_{2T}$ = $\text{m}$
$\sigma_{2N}$ = $\text{m}$
$\sigma_{2H}$ = $\text{m}$

Collision Probability calculation method

Garcia-Pelayo & Hernando-Ayuso
Foster (VERY SLOW, limited time resolution)

Calculation progress