Port-Hamiltonian Based Control of the Sun-Earth 3D Circular Restricted Three-Body Problem: Stabilization of the <i>L</i>₁Lagrange Point

In this paper, we use Port-Hamiltonian framework to stabilize the Lagrange points in the Sun-Earth three-dimensional Circular Restricted Three-Body Problem (CRTBP). Through rewriting the CRTBP into Port-Hamiltonian framework, we are allowed to design the feedback controller through energy-shaping and dissipation injection. The closed-loop Hamiltonian is a candidate of the Lyapunov function to establish nonlinear stability of the designed equilibrium, which enlarges the application region of feedback controller compared with that based on linearized dynamics. Results show that the Port-Hamiltonian approach allows us to successfully stabilize the Lagrange points, where the Linear Quadratic Regulator (LQR) may fail. The feedback system based on Port-Hamiltonian approach is also robust against white noise in the inputs.

The Criteria for Reducing Centrally Restricted Three-Body Problem to Two-Body Problem

Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubation of much heavier planets such as Jupiter and Saturn if the natural satellite lies deep inside the respective host Planet Hill sphere. Each planet has a Hill radius aH and planet mean radius RP and the ratio R1=RP/aH. Under very low R1 (less than 0.006) the approximation of CRTBP (centrally restricted three-body problem) to two-body problem is valid and planet has spacious Hill lobe to capture a satellite and retain it. This ensures a high probability of capture of natural satellite by the given planet and Sun’s perturbation on Planet-Satellite binary can be neglected. This is the case with Earth, Mars, Jupiter, Saturn, Neptune and Uranus. But Mercury and Venus has R1=RP/aH =0.01 and 5.9862 × 10-3 respectively hence they have no satellites. There is a limit to the dimension of the captured body. It must be a much smaller body both dimensionally as well masswise. The qantitative limit is a subject of an independent study.

First-round design of the flight scenario for Chang’e-2’s extended mission:take off from lunar orbit

Chang＇e-2, Chinese second lunar probe, was inserted into a 100 km altitude low lunar orbit on October 9th, 2010, its purpose is to continuously photograph the lunar surface and possibly chosen landing sites for future lunar missions. The probe will still carry considerable amount of propellant after completing all prescribed tasks in about six months. After the successful launch of Chang＇e-2, we began designing the probe＇s subsequent flight scenario, considering a total impulse of 1 100 m/s for takeoff from low lunar orbit and a maximum 3× 10^6 km distance for Earth-probe telecom- munication. Our first-round effort proposed a preliminary flight scenario that involves consecutive arrivals at the halo orbits around the Earth-Moon L1/L2 and Sun-Earth L1/L2 points, near-Earth asteroid flyby, Earth return, and lunar impact. The designed solution of Chang＇e-2＇s subsequent flight scenario is a multi-segment flight trajectory that serves as a reference for making the final decision on Chang＇e-2＇s extended mission, which is a flight to the Sun-Earth L2 point, and a possible scheme of lunar impact via Earth flyby after remaining at the Sun-Earth L2 point was also presented. The proposed flight trajectory, which possesses acceptable solution accuracy for mission analysis, is a novel design that effectively exploits the invariant manifolds in the circular restricted three-body problem and the patched-manifold-conic method.

Lunar landing trajectory design based on invariant manifold

The low-energy lunar landing trajectory design using the invariant manifolds of restricted three-body problem is studied. Considering angle between the ecliptic plane and lunar orbit plane, the four-body problem of sun-earth-moon-spacecraft is divided into two three-body problems, the sun-earth-spacecraft in the ecliptic plane and the earth-moon-spacecraft in the lunar orbit plane. Using the orbit maneuver at the place where the two planes and the invariant manifolds intersect, a general method to design low energy lunar landing trajectory is given. It is found that this method can save the energy about 20% compared to the traditional Hohmann transfer trajectory. The mechanism that the method can save energy is investigated in the point of view of energy and the expression of the amount of energy saved is given. In addition, some rules of selecting parameters with respect to orbit design are provided. The method of energy analysis in the paper can be extended to energy analysis in deep space orbit design.

Feasibility study of autonomous orbit determination using only the crosslink range measurement for a combined navigation constellation

In order to expand the coverage area of satellite navigation systems, a combined navigation constellation which is formed by a global navigation constellation and a Lagrangian navigation constellation was studied. Only the crosslink range measurement was used to achieve long-term precise autonomous orbit determination for the combined navigation constellation, and the measurement model was derived. Simulations of 180 days based on the international global navigation satellite system（GNSS） service（IGS） ephemeris showed that the mentioned autonomous orbit determination method worked well in the Earth–Moon system. Statistical results were used to analyze the accuracy of autonomous orbit determination under the influences of different Lagrangian satellite constellations.