The Flower Constellations
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The Flower Constellations 1,2 Daniele Mortarf', Matthew P. Wilkins4, and Christian Bruccolerf Dedicated to the memory of Luigi Broglio
Abstract This paper introduces a methodology to design a set of satellite constellations, called the Flower Constellations, which is generally characterized by repeatable ground tracks and a suitable phasing mechanism. A Flower Constellation, which can be complete or restricted, is identified by a number of parameters. Three are integer parameters: the number of petals (Np ) , the number of sidereal days to repeat the ground track (Nd ) , and the number of satellites (Ns ) . The others include the phasing parameters and three orbit parameters equal for all satellites: the argument of perigee (ce), the orbit inclination (i), and the perigee altitude (hp ) . Flower Constellations present beautiful and interesting dynamical features that allow us to explore a wide range of potential applications that include: telecommunications, Earth and deep space observation, global positioning systems, distributed space systems, and new kind of formation flying schemes. A Flower Constellation can be reoriented arbitrarily; however, the repeating ground track property is lost. To demonstrate their potential, some specific Flower Constellations are briefly described and discussed.
Introduction In this paper, we consider constellations of satellites all having the same compatible orbits (repeating ground track). That is to say, no matter how many satellites are considered for the constellation, from an Earth Centered Fixed (ECF) reference frame (i.e. a frame rotating with the Earth), they all follow a single ECF relative trajectory. The concept of repeating ground track constellations has been around for a number of years. Thus, we start off with a brief survey of those constellations on the way to the generalization of the Flower Constellations.
'Dedicated to John L. Junkins on the occasion of his sixtieth birthday. 2Work previously presented in part as paper AAS 03-274 at the John L. Junkins Astrodynamics Symposium, College Station, TX, May 23-24,2003. Software disclosure filed with the Technology Licensing Office at Texas A&M University. 3Associate Professor, Department of Aerospace Engineering, 741A H.R. Bright Building, Texas A&M University, 3141 TAMU, College Station, Texas 77843-3141. Email [email protected], member AAS. "Graduate Research Assistant, Aerospace Engineering Department, 631B H.R. Bright Building, Texas A&M University, 3141 TAMU, College Station, Texas 77843-3141. Email [email protected], member AAS. 5Graduate Research Assistant, Department of Aerospace Engineering, 620C H.R. Bright Building, Texas A&M University, College Station, TX 77843-3141. Email bruccoleri @tamu.edu.
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Survey of the Satellite Constellations
Dating back to 1967, first reported in 1981 as part of the University of Rome/ NASA San Marco Project, Luigi Broglio conceptualized the Sistema Quadrifoglio (Four-Leaf Clover System) [1] as an equatorial constellation of
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