The role of true anomaly in ballistic capture
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The role of true anomaly in ballistic capture Nicola Hyeraci · Francesco Topputo
Received: 4 January 2013 / Revised: 11 March 2013 / Accepted: 23 March 2013 / Published online: 20 April 2013 © Springer Science+Business Media Dordrecht 2013
Abstract A massless particle may perform a ballistic capture about a primary when two or more gravitational attractions are considered. The dynamics governing the ballistic capture depend on the mutual position of the primaries, if these are let to revolve in eccentric orbits. This paper studies the effect of the primaries true anomaly on the ballistic capture about the smaller primary in the planar elliptic restricted three-body problem. The dynamics of the Hill curves are studied, and the conditions for a favorable capture are derived. It is shown that these lead to regular, quasi-stable post-capture orbits. This is confirmed by numerical simulations implementing the concept of capture set: a set of initial conditions that generates ballistic capture orbits with a prescribed stability number. Keywords Ballistic capture · Low energy transfer · Elliptic restricted three-body problem · Sun-Mercury model
1 Introduction The ballistic capture is a process through which a massless particle with initial positive Kepler energy can approach and orbit a primary in a totally natural way. By definition, this mechanism can take place when n-body dynamics are considered, with n ≥ 3 (Egorov 1961; Bailey 1972; Heppenheimer and Porco 1977). Most of times the capture lasts only for a limited period of time; this is called weak or temporary capture. For the capture to be permanent, a dissipation must occur. Ballistic capture may be achieved by spacecraft, asteroids, and comets about moons, planets, and stars (Belbruno 2004; Belbruno et al. 2012).
N. Hyeraci SERCO Services GmbH, 64283 Darmstadt, Germany e-mail: [email protected] F. Topputo (B) Politecnico di Milano, 20156 Milano, Via La Masa, 34, Italy e-mail: [email protected]
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In spacecraft trajectory design, the ballistic capture reduces the relative hyperbolic excess velocity upon arrival, which in turn makes it possible to save propellant mass in the arrival maneuver. This can be achieved through a wise exploitation of the inherent dynamics characterizing the Solar System, rather than from its classical Keplerian decomposition. A number of missions have made use of ballistic capture (Belbruno and Miller 1993; Schoenmaekers et al. 2001; Jehn et al. 2004; Chung et al. 2010). The ballistic capture can be viewed under the perspective of Lagrange point dynamics (Conley 1968). As the invariant manifolds of the collinear libration point orbits separate different states of motions, orbits inside the stable manifolds lead to ballistic capture (Koon et al. 2000; Gómez et al. 2001). Thus, ballistic capture can be designed by a global representation and manipulation of the invariant manifolds (Koon et al. 2001; Topputo et al. 2005). Although this approach allows us to unveil the free transport mechanis
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