This paper studies the relative motion of satellite formation flying in arbitrary elliptical orbits with no perturbation.
The trajectories of the leader and follower satellites are projected onto the celestial sphere. These two projections and
celestial equator intersect each other to form a spherical triangle, in which the vertex angles and arc-distances are used
to describe the relative motion equations. This method is entitled the reference orbital element approach. Here the dimensionless
distance is defined as the ratio of the maximal distance between the leader and follower satellites to the semi-major axis
of the leader satellite. In close formations, this dimensionless distance, as well as some vertex angles and arc-distances
of this spherical triangle, and the orbital element differences are small quantities. A series of order-of-magnitude analyses
about these quantities are conducted. Consequently, the relative motion equations are approximated by expansions truncated
to the second order, i.e. square of the dimensionless distance. In order to study the problem of periodicity of relative motion,
the semi-major axis of the follower is expanded as Taylor series around that of the leader, by regarding relative position
and velocity as small quantities. Using this expansion, it is proved that the periodicity condition derived from Lawden’s
equations is equivalent to the condition that the Taylor series of order one is zero. The first-order relative motion equations,
simplified from the second-order ones, possess the same forms as the periodic solutions of Lawden’s equations. It is presented
that the latter are further first-order approximations to the former; and moreover, compared with the latter more suitable
to research spacecraft rendezvous and docking, the former are more suitable to research relative orbit configurations. The
first-order relative motion equations are expanded as trigonometric series with eccentric anomaly as the angle variable. Except
the terms of order one, the trigonometric series’ amplitudes are geometric series, and corresponding phases are constant both
in the radial and in-track directions. When the trajectory of the in-plane relative motion is similar to an ellipse, a method
to seek this ellipse is presented. The advantage of this method is shown by an example. 相似文献
Urban agglomeration is caused by the continuous acceleration of the urbanization process in China. Studying the expansion of construction land can not only know the changes and development of urban agglomeration in time, but also obtain the great significance of the future management. In this study, taking Changsha-Zhuzhou-Xiangtan (Chang-Zhu-Tan) urban agglomeration in Hunan province as a study area, Landsat images from 1995 to 2014 and Autologistic-CLUE-S model simulation data were used. Moreover, several factors including gravity center, direction, distance and landscape index were considered in the analysis of the expansion. The results revealed that the construction area increased by 132.18%, from 372.28 km2 in 1995 to 864.37 km2 in 2014. And it might even reach 1327.23 km2 in 2023. Before 2014, three cities had their own respective and discrete development directions. However, because of the integration policy implementation in 2008, the Chang-Zhu-Tan began to gather, the gravity center moved southward after 2014, and the distance between cities decreased, which was in line with the development plan of urban expansion. The research methods and results were relatively reliable, and these results could provide some reference for the future land use planning and spatial allocation in the urbanization process of Chang-Zhu-Tan urban agglomeration.
Understanding the spatial scale sensitivity of cellular automata is crucial for improving the accuracy of land use change simulation. We propose a framework based on a response surface method to comprehensively explore spatial scale sensitivity of the cellular automata Markov chain (CA-Markov) model, and present a hybrid evaluation model for expressing simulation accuracy that merges the strengths of the Kappa coefficient and of Contagion index. Three Landsat-Thematic Mapper remote sensing images of Wuhan in 1987, 1996, and 2005 were used to extract land use information. The results demonstrate that the spatial scale sensitivity of the CA-Markov model resulting from individual components and their combinations are both worthy of attention. The utility of our proposed hybrid evaluation model and response surface method to investigate the sensitivity has proven to be more accurate than the single Kappa coefficient method and more efficient than traditional methods. The findings also show that the CA-Markov model is more sensitive to neighborhood size than to cell size or neighborhood type considering individual component effects. Particularly, the bilateral and trilateral interactions between neighborhood and cell size result in a more remarkable scale effect than that of a single cell size. 相似文献
Journal of Geographical Sciences - As the Rural Revitalization Strategy is gradually implemented, China’s rural areas are set to have more diverse function requirements. This paper selects... 相似文献