Astronomy

Two spacecraft on a tether

Deploy a tether between two spacecraft. Watch gravity-gradient libration and see how reeling changes the angular motion and tension.

By Mykhailo Makarov

Actual application image

The model and its limits

Relative Hill dynamics of two equal masses and a unilateral massless cable. The powered reel changes length; slack endpoints move freely. Time is accelerated 60×. Display scale is uniform; slack cable curvature is illustrative. Cable bending waves and electrodynamics are omitted.

Equations used in the module

Equations
x_ddot = 2 n y_dot + 3 n² x - T x/(mu r); y_ddot = -2 n x_dot - T y/(mu r); mu = m/2; T >= 0; r <= L

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