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A globally valid analytically averaged Hamiltonian model for the coorbital motion is hard to construct because the analytical expansions of the disturbing function usually diverge in the quasi-satellite domain that is close to collision singularity. In this paper, an analytically averaged model for the coorbital motion is proposed in case of the circular restricted three-body problem, which can describe properly the transitions that occur at small eccentricities and inclinations, such as the transition between the horseshoe orbit and the quasi-satellite orbit. With the help of the numerical averaging method, numerical experiments are carried out to show the validity and accuracy of the analytically averaged model. The averaged model proposed here can be easily extended to more complicated cases such as the elliptic three-body problem or the planetary three-body problem.

With more and more missions around the Moon, a communication/navigation constellation around the Moon is necessary. Halo orbits, due to their unique geometry, are extensively studied by researchers for this purpose. A dedicated survey is carried out in this work to analyse the coverage ability of halo orbits. It is found that a two-satellite constellation is enough for continuous one-fold coverage of the north or the south polar regions but never both. A three-satellite constellation is enough for continuous one-fold coverage of both north and south polar regions. A four-satellite constellation can cover nearly 100% of the whole lunar surface. In addition, the coverage ability of another special orbit – distant retrograde orbit (DRO) – is analysed for the first time in this study. It is found that three satellites on DROs can cover 99·8% of the lunar surface, with coverage gaps at polar caps. A four-satellite constellation moving on spatial DROs can cover nearly the whole lunar surface. By combining halo orbits and DROs, we design a five-satellite constellation composed of three halo orbit satellites and two DRO satellites. This constellation can provide 100% continuous one-fold coverage of the whole lunar surface.

The motion around the collinear libration points in the restricted three body problem is unstable. But there exist conditionally stable periodic orbits around these points. Special-purpose space probes located in the vicinity of these points (e.g., ISEE-3, SOHO) can benefit from this dynamical property, in regard to maintaining the orbit in position and the energy required of placing the probe in position. As an example, we study in this paper the launch and orbital control of a space probe around the L1 libration point in the system consisting of the Sun and the Earth-Moon. We present some theoretical and numerical simulations’ results, which may serve as a basis for the realization of such a space probe in future.

Nowadays, the orbit determination (OD) of GEO/IGSO satellites mainly depends on the observation data from the ground stations. While the ground stations are not available, the orbits of the GEO/IGSO satellites can not be precisely determined by themselves. One effective approach to increase the OD accuracy and to realize the autonomous orbit determination of the GEO/IGSO satellites is to add the highly accurate inter-satellite range data. But a serious problem of merely using this type of data is the uncertainty of the orbital plane of the GEO/IGSO satellites. So external references such as the ground stations or the special celestial bodies in space are needed. The research in this work is to replace the ground stations with some probes located on some special orbits. These special orbits are carefully chosen so that the uncertainty of the orbital plane of the GEO/IGSO satellites can be significantly eliminated in autonomous OD and thus make the combined autonomous OD of the GEO/IGSO satellites and the probes possible.

A new stray light analysis method and some suppression principles of panoramic annular lens (PAL) are introduced in this paper. The proposed method is to find stray light paths which are caused by ray splitting on two refractive surfaces of the PAL block and then cut them off. Following this principle, the stray light paths can be eliminated in the design progress by adding specific merit functions into the optical software. The methods to reduce scatter, diffraction and other stray light are also proposed. A new PAL with a field of view (FOV) of 30° ~ 100° × 360° is designed. The stray light is suppressed more than 80% compared with a similar conventional PAL. The stray light path analysis method also can be used in other catadioptric optics.

A new improved design method of the panoramic annular lens (PAL) with aspheric surfaces is introduced. The structure is not only helpful to enlarge the field of view (FOV) of the system, but also help to make a horizontal symmetric field of view. The field of view reaches （-30°—+30°）x 360 and was distortion controlled to reduce blind zone in the center. The field of view and distortion of PAL was investigated theoretically and method of aspheric surface design was also discussed. An aspheric PAL and its relay lens group were designed. The total length was 20.4mm, and the focal length was 0.3mm. To get bright and clear image, the aperture of the system was set to f/2.88, and the diameter was 16.6mm. The spectral range was from 0.486~0.656um. The relay lens group was consisted of 8 pieces of lenses, with a back focal length (BFL) of 2mm. MTF below 70 lp/mm of the system is above 0.5. The result shows that the aberrations are corrected well.

A novel panoramic stereo imaging system with double panoramic annular lenses (PAL) is introduced in this paper. The proposed system consists of two coaxial PAL units and images on one sensor. The imaging rings are concentric. The object position can be calculated by triangulation. The novelty of this system is that the central blind zone of one PAL unit is partly used by the other as an image zone. The stereo field of view is 60°~105° × 360°. The depth extracting resolution is about 500 mm at 1line/cm. The F# of the system is about 3, facilitating the system to be applied in low illumination environment. A design is presented and the depth extracting precision is analyzed.