Averaging analyses for spacecraft orbital motions around asteroids

This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orbits between the spacecraft mean motion and the central body＇s rotation. Averaging conditions for these cases are given. As a major extension, a few classes of near resonant orbits are analyzed by the averaging method. Then some resulted conclusions of these averaging analyses are applied to understand the stabil- ity regions in a numerical experiment. Some stability conclu- sions are obtained. As a typical example, it is shown in detail that near circular 1 ： 2 resonant orbit is always unstable.

Particle Motion in Surface Gravity Waves

Fluid particles in translating surface gravity waves have an orbital motion which decreases in size with increasing mean depth. These wave characteristics came from observations and were not forecast theoretically. The classical potential flow model is incapable of explaining the particle movement due to the irrotational assumption and to a flaw in carrying out the method. When a wave passes by an observer from left to right, the particles move clockwise under a crest and a trough. This correct conclusion is consistent with what the incorrect standard theory implies but should not be considered to have been derived from it.

The Absolute Proper Motion of M3 and Its Galactic Orbit

We have obtained the absolute proper motion of globular cluster M3 from measurements of 14 plates taken with the 40cm refractor at Sheshan station of Shanghai observatory, spanning epoch is about 80 years. The positions and absolute proper motions of 24 stars in ACT catalogue are used as the reference frame. The reduction was made with the central overlapping principle. The absolute proper motions of 534 stars in the region of about 1° 5×1° 5 around the cluster M3 are determined. With the new data of proper motions, the membership probabilities of the stars are determined. The mean absolute proper motions for the cluster of -0 3±0 3 mas/yr in R.A. and -3 1±0 3 mas/yr in Dec. were obtained.Combining our results with the known distance and radial velocity of the cluster, we obtained its space motions and Galactic orbits in two different three component Galactic potentials.

Determination of the Proper Motions and Membership of the Globular Cluster M3 and of its Orbit in the Galaxy

We examine 14 plates of the globular cluster M3 (NGC 5272) taken with the 40 cm refractor at the Sheshan station of Shanghai Astronomical Observatory. The plates span over a period of about 77 years. The positions and absolute proper motions of eight stars in the Hipparcos Catalogue and of 49 stars in the Tycho-2 Catalogue are used as the reference frame. The astrometric reduction is made with the central overlapping principle. The absolute proper motions of 534 stars in a region of about 100' × 100' around the cluster are measured. With the new proper motion data the membership probabilities of the stars are determined. The average absolute proper motion obtained for the cluster is -0.06±0.30 mas yr-1 in R.A. and -2.6±0.30 mas yr-1 in Decl. By combining this result with the known distance and radial velocity of the cluster, we also obtained the Galactic orbit of M3 for a chosen three-component Galactic potential.

Distribution of Time-Averaged Suspended Sediment Concentration Due to Waves

According to the mechanism of sediment suspension under waves, namely, the main reason of sediment suspension changes from the turbulent mixing in the bottom boundary layer to the periodic motion of the water particle near the free water surface, a three-layer model of sediment concentration distribution due to waves is presented along the whole water depth based on the concept of the finite mixing length. 1he determination of the parameters in the model is discussed and an empirical formula is suggested. Comparisons between the calculated results and the measurements indicate that the resuits of the model agree well with the data from both the large and small scale flume experiments.

Effects of storm waves on rapid deposition of sediment in the Yangtze Estuary channel

Recent research on short-term topographic change in the Yangtze Estuary channel under storm surge conditions is briefly summarized. The mild-slope, Boussinesq and action balance equations are compared and analyzed. The action balance equation, SWAN, was used as a wave numerical model to forecast strong storm waves in the Yangtze Estuary. The spherical coordinate system and source terms used in the equation are described in this paper. The significant wave height and the wave orbital motion velocity near the bottom of the channel during 20 m/s winds in the EES direction were simulated, and the model was calibrated with observation data of winds and waves generated by Tropical Cyclone 9912. The distribution of critical velocity for incipient motion along the bottom was computed according to the threshold velocity formula for bottom sediment. The mechanism of rapid deposition is analyzed based on the difference between the root-mean-square value of the near-bottom wave orbital motion velocity and the bottom critical tractive velocity. The results show that a large amount of bottom sediments from Hengsha Shoal and Jiuduan Shoal are lifted into the water body when 20 m/s wind is blowing in the EES direction. Some of the sediments may enter the channel with the cross-channel current, causing serious rapid deposition. Finally, the tendency of the storm to induce rapid deposition in the Yangtze Estuary channel zone is analyzed.

Design and control of multiple spacecraft formation flying in elliptical orbits

Spacecraft formation flying is an attractive new concept in international aeronautic fields because of its powerful functions and low cost. In this paper, the formation design and PD closed-loop control of spacecraft formation flying in elliptical orbits are discussed. Based on two-body relative dynamics, the true anomaly is applied as independent variable instead of the variable of time. Since the apogee is considered as the starting point, the six integrating constants are calculated. Therefore, the algebraic solution is obtained for the relative motion in elliptical orbits. Moreover, the formation design is presented and both circular formation and line formation are provided in terms of an algebraic solution. This paper also discusses the PD-closed loop control for precise formation control in elliptical orbits. In this part, the error-type state equation is put forward and the linear quadratic regulator （LQR） method is used to calculate PD parameters. Though the gain matrix calculated from LQR is time-variable because the error-type state equation is time variable, the PD parameters are also considered as constants because of their small changes in simulation. Finally, taking circular formation as an example, the initial orbital elements are achieved for three secondary spacecraft. And the numerical simulation is analyzed under PD formation control with initial errors and J2 perturbation. The simulation results demonstrate the validity of PD closed-loop control scheme.

Evolutionary Algorithms in Astrodynamics

This paper presents the method of solving the equations of motions by evolutionary algorithms. Starting from random trajectory, the solution is obtained by accepting the mutation if it leads to a better approximations of Newton’s second law. The general method is illustrated by finding trajectory to the Moon.

The Gravitational Potential and the Gravitational Force According to the Correct Schwarzschild Metric

In a recent article, we have corrected the traditional derivation of the Schwarzschild metric, thus obtaining the formulation of the correct Schwarzschild metric, which is different from the traditional Schwarzschild metric. In this article, by starting from this correct Schwarzschild metric, we obtain the formulas of the correct gravitational potential and of the correct gravitational force in the case described by this metric. Moreover, we analyse these correct results and their consequences. Finally, we propose some possible crucial experiments between the commonly accepted theory and the same theory corrected according to this article.