The Flower Constellations - theory, design process, and applications

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Title: The Flower Constellations - theory, design process, and applications
Author: Wilkins, Matthew Paul
Abstract: In this research , constellations of satellites all having orbits compatible with rotating reference frames are considered . That is to say , no matter how many satellites are considered for the constellation , when viewed from an arbitrarily defined rotating reference frame of interest , they all follow a single , identical relative trajectory . In this regard , one could think of the relative trajectories as ?space trajectories on a rotating reference frame . ? In particular , this research concerns itself with reference frames constrained to rotate with the planet under consideration (e .g . the Earth Centered Earth Fixed (ECEF ) frame , a frame rotating with the Earth ) . When the axis of symmetry of these constellations is aligned with the spin axis of the planet , then the ground track as projected onto the planet surface will be repeating . Flower Constellations are identified by eight parameters . Five are integer parameters : the number of petals (Np ) , the number of sidereal days to repeat the ground track (Nd ) , the number of satellites (Ns ) , and two integers to govern the phasing (Fn and Fd ) . Three are orbit parameters that are generally equal for all satellites : the argument of perigee (w ) , the orbit inclination (i ) , and the perigee altitude (hp ) . Each of these parameters has a unique effect on the overall design of a Flower Constellation . Based upon specific choices of these parameters , some broad categories of constellation types are presented along with some unique cases . Often , a large number of satellites are used to completely visualize these constellations . While Flower Constellations lend themselves to micro - and nano -satellite constellations very easily , they are also readily scalable to any mission requirement . Also investigated are inverse design techniques where the governing equations are solved for the Flower Constellation parameters to achieve a desired final constellation or formation shape . 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 , and new kinds of formation flying schemes among others . To demonstrate their potential , some specific Flower Constellations are described and discussed . Finally , the effect of perturbations such as the Earth ?s oblateness are investigated and options for mitigating perturbations are discussed .
URI: http : / /hdl .handle .net /1969 .1 /3053
Date: 2006-04-12


The Flower Constellations - theory, design process, and applications. Available electronically from http : / /hdl .handle .net /1969 .1 /3053 .

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