Methods for orbit optimization for the LISA gravitational wave observatory
ABSTRACT The Laser Interferometer Space Antenna (LISA) mission is a joint ESA-NASA mission for detecting low-frequency gravitational waves in the frequency range from 0.1 mHz to 1 Hz, by using accurate distance measurements with laser interferometry between three spacecraft, which will be launched around 2015 and one year later reach their orbits around the Sun. In order to operate successfully, it is crucial for the constellation of the three spacecraft to have extremely high stability. In this paper, several problems of the orbit optimization of the LISA constellation are discussed by using numerical and analytical methods for satisfying the requirements of accuracy. On the basis of the coorbital restricted problem, analytical expressions of the heliocentric distance and the trailing angle to the Earth of the constellation's barycenter are deduced, with the result that the approximate analytical solution of first order will meet the accuracy requirement of the spacecraft orbit design. It is proved that there is a value of the inclination of the constellation plane that will make the variation of the arm-length a minimum. The principle for selecting the optimum starting elements of orbits at any epoch is proposed. The method and programming principles of finding the optimized orbits are also presented together with examples of the optimization design.
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ABSTRACT: We analytically work out the long-term orbital perturbations induced by a homogeneous circular ring of radius R r and mass m r on the motion of a test particle in the cases (I): r > R r and (II): r < R r. In order to extend the validity of our analysis to the orbital configurations of, e.g., some proposed spacecraft-based mission for fundamental physics like LISA and ASTROD, of possible annuli around the supermassive black hole in Sgr A* coming from tidal disruptions of incoming gas clouds, and to the effect of artificial space debris belts around the Earth, we do not restrict ourselves to the case in which the ring and the orbit of the perturbed particle lie just in the same plane. From the corrections to the standard secular perihelion precessions, recently determined by a team of astronomers for some planets of the Solar System, we infer upper bounds on m r for various putative and known annular matter distributions of natural origin (close circumsolar ring with R r = 0.02 − 0.13 au, dust ring with R r = 1 au, minor asteroids, Trans-Neptunian Objects). We find mr1410−4m (circumsolar ring with R r = 0.02 au), mr2610−6m (circumsolar ring with R r = 0.13 au), mr8810−7m (ring with R r = 1 au), mr7310−12M (asteroidal ring with R r = 2.80 au), mr1110−11M (asteroidal ring with R r = 3.14 au), mr2010−8M (TNOs ring with R r = 43 au). In principle, our analysis is valid both for baryonic and non-baryonic Dark Matter distributions.Earth Moon and Planets 06/2012; 108(3-4):189-217. · 0.83 Impact Factor
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ABSTRACT: The Laser Interferometer Space Antenna (LISA) is a joint ESA-NASA mission for detecting low-frequency gravitational waves in the frequency range from 0.1 mHz to 1 Hz, by using accurate laser interferometry between three spacecrafts, which will be launched around 2018 and one year later reach their operational orbits around the Sun. In order to operate successfully, it is crucial for the constellation of the three spacecrafts to have extremely high stability. Based on the study of operational orbits for a 2015 launch, we design the operational orbits of beginning epoch on 2019-03-01, and introduce the method of orbit design and optimization. We design the orbits of the transfer from Earth to the operational orbits, including launch phase and separation phase; furthermore, the relationship between energy requirement and flight time of these two orbit phases is investigated. Finally, an example of the whole orbit design is presented.Science China: Physics, Mechanics and Astronomy 01/2010; 53(1):179-186. · 1.17 Impact Factor
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ABSTRACT: Based on large quantities of co-orbital phenomena in the motion of natural bodies and spacecraft, a model of the co-orbital restricted three-body problem is put forward. The fundamental results for the planar co-orbital circular restricted three-body problem are given, which include the selection of variables and equations of motion, a set of approximation formulas, and an approximate semi-analytical solution. They are applied to the motion of the barycenter of the planned gravitational observatory LISA constellation, which agrees very well with the solution of precise numerical integration.Science China: Physics, Mechanics and Astronomy 01/2010; 53(1):171-178. · 1.17 Impact Factor