ABSTRACTOrbital resonances play an important role in the dynamics of planetary systems. Classical theoretical analyses found in textbooks report that libration widths of first-order mean motion resonances diverge for nearly circular orbits. Here, we examine the nature of this divergence with a non-perturbative analysis of a few first-order resonances interior to a Jupiter-mass planet. We show that a first-order resonance has two branches, the pericentric and the apocentric resonance zone. As the eccentricity approaches zero, the centres of these zones diverge away from the nominal resonance location but their widths shrink. We also report a novel finding of ‘bridges’ between adjacent first-order resonances: at low eccentricities, the apocentric libration zone of a first-order resonance smoothly connects with the pericentric libration zone of the neighbouring first-order resonance. These bridges may facilitate resonant migration across large radial distances in planetary systems, entirely in the low-eccentricity regime.
In recent years, small satellites, which are more and more popular and affordable, have been already widely applied in observation and monitoring missions. However, it is a tough problem to meet the different mission requirements with such limits as space, energy, and devices. In this paper, we propose a practical target searching scheme for a small satellite which suffers from the device limits during the first 7.5 seconds after the launch separation. Due to the device limits at the beginning of the separation, the initial attitude of the satellite and the position of the target that the following observation task is based on are both unknown. In order to solve this problem, a backward integral strategy used to estimate the initial attitude and a target searching method intended to ensure the satellite acquires the target rapidly are included in the scheme. Simulation results proved that this scheme enabled the satellite, regardless of the initial conditions, to acquire the target within the limited observation time.
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