Orbital mechanics is most often concerned with the trajectories of point particles. These trajectories are fixed given some initial position and velocity but are most often changed by firing a rocket. However, by stepping away from the point particle approximation and now considering an extended spacecraft, it will be shown that changes can be made to its orbit, without the use of a reaction mass. By strategically varying the spacecraft’s mass distribution, it can, over time, result in large changes to the spacecraft’s orbit in the 2 and 3-body problem. Doing this can allow for an extended spacecraft to perform fuel-free orbital manoeuvres such as transferring its orbit from one primary body to another or to escape the 3-body system.
In contrast to much of the current literature, here we do not adopt a model for the extended spacecraft and more importantly, show how some
general extended spacecraft can be torque-free by requiring that the radial vectors from the primary bodies are eigenvectors of the quadrupole moment of the spacecraft’s mass distribution. To the author’s knowledge, keeping the spin angular momentum constant by ensuring the radial vectors are eigenvectors of the quadrupole moment has not been demonstrated before.
We show that the change in energy and Jacobi constant is proportional to the difference in the minimum and maximum of the eigenvalue of the quadrupole moment. It is also shown that the sum of the minimum and maximum eigenvalue is proportional to the precession of the orbit as a result of the spacecraft being an extended body and this can be used to offset the precession induced in the 3-body problem.
Finally, it is shown that changing the sign of the eigenvalue either side of an unstable equilibrium can allow for an extended spacecraft to stabilise itself about otherwise unstable points. The saddle point of Lagrange point 1 was used as an example to also show numerically that strategically changing the sign of the eigenvalue either side of L1 stabilises the spacecraft in the region about the equilibrium point.