Spacecraft Relative Motion

An online implementation of different algorithms to solve the spacecraft relative motion problem is presented. It focuses on the theory of asynchronous relative motion, that provides simple mechanisms for introducing nonlinear terms in the solution. The relative state vector is projected onto the Euler-Hill rotating reference frame. The relative velocity is referred to the rotating frame as well.

The program computes the error with respect to a reference solution. The error is measured as the offset in position and velocity. The reference solution is computed by solving the unperturbed two-body problem for the leader and follower, and then subtracting the absolute state-vectors. The error in position is given col. 15 and the error in velocity in col. 16. At the end of the file the mean values of the error in position and velocity are provided. The exact solution is written in cols. 9-11 and cols. 12-14 (relative position and velocity vectors, respectively).


Reference Orbit

Relative position

Propagation Parameters


For further details and citing, please refer to:

  1. Roa, J. and Pelaez, J.: 'The theory of asynchronous relative motion', Celestial Mechanics and Dynamical Astronomy (2015). Submitted
  2. Roa, J. and Pelaez, J.: 'Unified solutions to linear relative motion about any type of reference orbit', Celestial Mechanics and Dynamical Astronomy (2015). Submitted
  3. Roa, J. and Pelaez, J: 'Frozen-anomaly transformation in the elliptic rendezvous problem', Celestial Mechanics and Dynamical Astronomy (2014). DOI 10.1007/s10569-014-9585-0
  4. Clohessy, W.H. and Wiltshire, R.S.: 'Terminal guidance system for satellite rendezvous', Journal of the Aerospace Sciences (1960) DOI: 10.2514/8.8704
  5. Yamanaka, K. and Ankersen, F.: 'New state transition matrix for relative motion on an arbitrary elliptical orbit', Journal of Guidance, Control and Dynamics (2002) DOI: 10.2514/2.4875

Javier Roa
Fall, 2014
Space Dynamics Group. Technical University of Madrid (SDG-UPM)


These routines have been implemented for academic and research purposes only. We are not responsible for its use in other applications.