Formation around planetary displaced orbit

The paper investigates the relative motion around the planetary displaced orbit. Several kinds of displaced orbits for geocentric and martian cases were discussed. First, the relative motion was linearized around the displaced orbits. Then, two seminatural control laws were investigated for each kind of orbit and the stable regions were obtained for each case. One of the two control laws is the passive control law that is very attractive for engineering practice. However, the two control laws are not very suitable for the Martian mission. Another special semi-natural control law is designed based on the requirement of the Martian mission. The results show that large stable regions exist for the control law.

Displaced orbits generated by solar sails for the hyperbolic and degenerated cases

Displaced non-Keplerian orbits above planetary bodies can be achieved by orientating the solar sail normal to the sun line. The dynamical systems techniques are employed to analyze the nonlinear dynamics of a displaced orbit and different topologies of equilibria are yielded from the basic configurations of Hill＇s region, which have a saddlenode bifurcation point at the degenerated case. The solar sail near hyperbolic or degenerated equilibrium is quite unstable. Therefore, a controller preserving Hamiltonian structure is presented to stabilize the solar sail near hyperbolic or degenerated equilibrium, and to generate the stable Lissajous orbits that stay stable inside the stabilizing region of the controller. The main contribution of this paper is that the controller preserving Hamiltonian structure not only changes the instability of the equilibrium, but also makes the modified elliptic equilibrium become unique for the controlled system. The allocation law of the controller on the sail＇s attitude and lightness number is obtained, which verifies that the controller is realizable.

Coupled trajectory and attitude stability of displaced orbits

Coupled trajectory and attitude stability of displaced solar orbits is studied by using sailcraft with a kind of two-folding construction with two unequal rectangular plates forming a right angle. Three-dimensional coupled trajectory and attitude equations are developed for the coupled dynamical system, and the results show that all three types of displaced solar orbits widely referenced can be achieved through selecting an appropriate size of the two-folding sail. An anal- ysis of the corresponding linear stability of the trajectory and attitude coupled system is carried out, and both trajectory and attitude linearly stable orbits are found to exist in a small range of parameters, whose non-linear stability is then examined via numerical simulations. Finally, passively stable orbits are found to have weak stability, and such passive means of station-keeping are attractive and useful in practice because of its simplicity.

Optimal solar sail transfers to circular Earth-synchronous displaced orbits

The aim of this paper is to evaluate the minimum flight time of a solar sail-based spacecraft towards Earth-synchronous(heliocentric)circular displaced orbits.These are special displaced non-Keplerian orbits characterized by a period of one year,which makes them suitable for the observation of Earth’s polar regions.The solar sail is modeled as a flat and purely reflective film with medium-low performance,that is,with a characteristic acceleration less than one millimeter per second squared.Starting from a circular parking orbit of radius equal to one astronomical unit,the optimal steering law is sought by considering the characteristic acceleration that is required for the maintenance of the target Earth-synchronous displaced orbit.The indirect approach used for the calculation of the optimal transfer trajectory allows the minimum flight time to be correlated with several Earth-synchronous displaced orbits,each one being characterized by given values of Earth-spacecraft distance and displacement over the ecliptic.The proposed mathematical model is validated by comparison with results available in the literature,in which a piecewise-constant steering law is used to find the optimal flight time for a transfer towards a one-year Type I non-Keplerian orbit.