Clohessy-Wiltshire equations

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The Clohessy-Wiltshire equations describe a simplified model of orbital relative motion, in which the target is in a circular orbit, and the chaser spacecraft is in an elliptical or circular orbit. This model gives a first-order approximation of the chaser's motion in a target-centered coordinate system. It is very useful in planning rendezvous of the chaser with the target.[1]

\ddot{x} = 3n^2x+2n\dot{y}

\ddot{y} = -2n\dot{x}

\ddot{z} = -n^2z

n = \sqrt{\frac{\mu}{a^3}}

For intuition, in low earth orbit,  \mu = 3.986E14 \frac{m^3}{s^2} and a = 6378137m + 415000m = 6793137m, so n=0.0011 s^{-1}.


  1. ^ "Clohessy-Wiltshire equations" (PDF). University of Texas at Austin. Retrieved 12 September 2013.