Methods for orbit optimization for the LISA gravitational wave observatory

International Journal of Modern Physics D (Impact Factor: 1.74). 07/2008; 17(7). DOI: 10.1142/S021827180801267X
Source: OAI


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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Available from: Guangyu Li, Jan 09, 2014
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    • "The distance of any two of three spacecraft must be maintained as close as possible during geodetic flight. LISA orbit configuration has been studied analytically and numerically in various previous works (Vincent and Bender, 1987; Folkner et al, 1997; Cutler, 1998; Hughes, 2002; Hechler and Folkner, 2003; Dhurandhar et al, 2005; Yi et al, 2008; Li et al, 2008). In the mission orbit optimization for eLISA/NGO, we follow the analytical procedure of Dhurandhar et al (2005) to make our initial choice of initial conditions and then use the CGC ephemeris to numerically optimize the orbit configuration as we have done in ASTROD-GW orbit design (Men et al, 2009, 2010; Wang and Ni, 2011, 2012 , 2013). "
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    ABSTRACT: In this paper, we present an overview of ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) and ASTROD I mission concepts and studies. The missions employ deep-space laser ranging using drag-free spacecraft to map the gravitational field in the solar-system. The solar-system gravitational field is determined by three factors: the dynamic distribution of matter in the solar system; the dynamic distribution of matter outside the solar system (galactic, cosmological, etc.) and gravitational waves propagating through the solar system. Different relativistic theories of gravity make different predictions of the solar-system gravitational field. Hence, precise measurements of the solar-system gravitational field test all these. The tests and observations include: (i) a precise determination of the relativistic parameters beta and gamma with 3-5 orders of magnitude improvement over previous measurements; (ii) a 1-2 order of magnitude improvement in the measurement of G-dot; (iii) a precise determination of any anomalous, constant acceleration Aa directed towards the Sun; (iv) a measurement of solar angular momentum via the Lense-Thirring effect; (v) the detection of solar g-mode oscillations via their changing gravity field, thus, providing a new eye to see inside the Sun; (vi) precise determination of the planetary orbit elements and masses; (viii) better determination of the orbits and masses of major asteroids; (ix) detection and observation of gravitational waves from massive black holes and galactic binary stars in the frequency range 0.05 mHz to 5 mHz; and (x) exploring background gravitational-waves.
    Full-text · Article · Jan 2008 · International Journal of Modern Physics D
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    ABSTRACT: On the basis of many coorbital phenomena in astronomy and spacecraft motion, a dynamics model is proposed in this paper — treating the coorbital restricted prob-lem together with method for obtaining a general approximate solution. The design of the LISA spacecraft orbits is a special 2+3 coorbital restricted problem. The problem is analyzed in two steps. First, the motion of the barycenter of the three spacecraft is ana-lyzed, which is a planar coorbital restricted three-body problem. And an approximate analytical solution of the radius and the argument of the center is obtained consequently. Secondly, the configuration of the three spacecraft with minimum arm-length variation is analyzed. The motion of a single spacecraft is a near-planar coorbital restricted three-body problem, allowing approximate analytical solutions for the orbit radius and the argument of a spacecraft. Thus approximative expressions for the arm-length are given.
    Full-text · Article · Jul 2008 · International Journal of Modern Physics D
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