The dynamical architecture and habitable zones of the quintuplet planetary system 55 Cancri

We perform numerical simulations to study the secular orbital evolution and dynamical structure of the quintuplet planetary system 55 Cancri with the self-consistent orbital solutions by Fischer and coworkers. In the simulations, we show that this system can be stable for at least 108 yr. In addition, we extensively investigate the planetary configuration of four outer companions with one terrestrial planet in the wide region of 0.790AU 〈 a 〈 5.900AU to examine the existence of potential asteroid structure and Habitable Zones （HZs）. We show that there are unstable regions for orbits about 4：1, 3：1 and 5：2 mean motion resonances （MMRs） of the outermost planet in the system, and several stable orbits can remain at 3：2 and 1：1 MMRs, which resembles the asteroid belt in the solar system. From a dynamical viewpoint, proper HZ candidates for the existence of more potential terrestrial planets reside in the wide area between 1.0 AU and 2.3 AU with relatively low eccentricities.

Image Smearing Modeling and Verification for Strapdown Star Sensor

To further extend study on celestial attitude determination with strapdown star sensor from static into dynamic field, one prerequisite is to generate precise dynamic simulating star maps. First a neat analytical solution of the smearing trajectory caused by spacecraft attitude maneuver is deduced successfully, whose parameters cover the geometric size of optics, three-axis angular velocities and CCD integral time. Then for the first time the mathematical law and method are discovered about how to synthesize the two formulae of smearing trajectory and the static Gaussian distribution function （GDF） model, the key of which is a line integral with regard to the static GDF attenuated by a factor 1/Ls （Ls is the arc length of the smearing trajectory） along the smearing trajectory. The dynamic smearing model is then obtained, also in an analytical form. After that, three sets of typical simulating maps and data are simulated from this dynamic model manifesting the expected smearing effects, also compatible with the linear model as its special case of no boresight rotation. Finally, model validity tests on a rate turntable are carried out, which results in a mean correlation coefficient 0.920 0 between the camera images and the corresponding model simulated ones with the same parameters. The sufficient similarity verifies the validity of the dynamic smearing model. This model, after pa- rameter calibration, can serve as a front-end loop of the ground semi-physical simulation system for celestial attitude determination with strapdown star sensor.

Systematic centroid error compensation for the simple Gaussian PSF in an electronic star map simulator

Simulated star maps serve as convenient inputs for the test of a star sensor, whose standardability mostly depends on the centroid precision of the simulated star image, so it is necessary to accomplish systematic error compensation for the simple Gaussian PSF（or SPSF, in which PSF denotes point spread function）. Firstly, the error mechanism of the SPSF is described, the reason of centroid deviations of the simulated star images based on SPSF lies in the unreasonable sampling positions（the centers of the covered pixels） of the Gaussian probability density function. Then in reference to the IPSF simulated star image spots regarded as ideal ones, and by means of normalization and numerical fitting, the pixel center offset function expressions are got, so the systematic centroid error compensation can be executed simply by substituting the pixel central position with the offset position in the SPSF. Finally, the centroid precision tests are conducted for the three big error cases of Gaussian radius r = 0.5, 0.6, 0.671 pixel, and the centroid accuracy with the compensated SPSF（when r = 0.5） is improved to 2.83 times that of the primitive SPSF, reaching a 0.008 pixel error, an equivalent level of the IPSF. Besides its simplicity, the compensated SPSF further increases both the shape similarity and the centroid precision of simulated star images, which helps to improve the image quality and the standardability of the outputs of an electronic star map simulator（ESS）.