The 2D Necklace Flower Constellation theory is a new design framework based on the 2D Lattice Flower Constellations that allows to expand the possibilities of design while maintaining the number of satellites in the configuration. The methodology presented is a generalization of the 2D Lattice design, where the concept of necklace is introduced in the formulation. This allows to assess the problem of building a constellation in orbit, or the study of the reconfiguration possibilities in a constellation. Moreover, this work includes three counting theorems that allow to know beforehand the number of possible configurations that the theory can provide. This new formulation is especially suited for design and optimization techniques.
Analytical theories based on Lie-Deprit transforms are used to obtain families of periodic orbits for the problem of an orbiter around the Moon. Low and moderately high orbit models are analyzed. Equilibria of the normalized equations of motion provides the representation of a global portrait of families of frozen orbits depending on values of the inclination, eccentricity and semimajor axis. By means of the inverse transformation it is possible to refine the initial conditions for frozen orbits of a simplified model; these initial conditions may be used as starter of numerical continuation methods when more complex models are considered.
The aim of the time distribution methodology presented in this paper is to generate constellations whose satellites share a set of relative trajectories in a given time, and maintain that property over time without orbit corrections. The model takes into account a series of orbital perturbations such as the gravitational potential of the Earth, the atmospheric drag, the Sun and the Moon as disturbing third bodies and the solar radiation pressure. These perturbations are included in the design process of the constellation. Moreover, the whole methodology allows to design constellations with multiple relative trajectories that can be distributed in a minimum number of inertial orbits.
This article provides a method for finding initial conditions of frozen orbits for a probe around Mercury. Frozen orbits are those whose orbital elements remain constant on average. Thus, at a given latitude, the satellite always passes at the same altitude. This is very interesting for scientific missions that require close inspection of any celestial body. The orbital dynamics of an artificial satellite about Mercury is governed by the potential attraction of the main body. Besides the Keplerian attraction, we consider the inhomogeneities of the potential of the central body. We include secondary terms of Mercury gravity field from J2 up to J6, and the tesseral harmonics C22 that is of the same magnitude than zonal J2. In the case of science missions about Mercury, it is also important to consider third-body perturbation (Sun). Circular restricted three body problem can not be applied to Mercury-Sun system due to its non-negligible orbital eccentricity. Besides the harmonics coefficients of Mercury's gravitational potential, and the Sun gravitational perturbation, our average model also includes solar acceleration pressure. This simplified model captures the majority of the dynamics of low and high orbits about Mercury. In order to capture the dominant characteristics of the dynamics, short-period terms of the system are removed applying a double averaging technique. This algorithm is a two-fold process which firstly averages over the period of the satellite, and secondly averages with respect to the period of the third body. This simplified Hamiltonian model is introduced in the Lagrange Planetary equations. Thus, frozen orbits are characterized by a surface depending on three variables: the orbital semimajor axis, eccentricity and inclination. We find frozen orbits for an average altitude of 400 km and 1000 km, which are the predicted values for the BepiColombo mission. Finally, the paper delves into the orbital
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