Periodic Orbits and Transfer Trajectories to Collinear Libration Points in the Circular

Periodic Orbits and Transfer Trajectories to Collinear Libration Points in the Circular

Periodic orbits and transfer trajectories to collinear Libration Points in the Circular Restricted Three - Body Problem

Alessio Di Salvo

Summer School “Advanced Topics in Astrodynamics”

Barcelona, Spain, July 5 – 10, 2004

ABSTRACT

Space missions to libration points are an interesting opportunity to perform deep space observations reducing costs and risks and to obtain better results by taking advantages of various benefits that these regions offer. Recent advances in dynamical systems theory and astrodynamics together with software and hardware improvements permitted to international space agencies and universities to perform more refined studies, planning new missions to libration points that will be launched in the next years. The Circular Restricted Three Body Problem (CRTBP) is the most common mathematical model used to describe the motion of a spacecraft in the gravitational field of two massive bodies, as the Sun and the Earth. Periodic orbits can be determined by using different analytical and numerical techniques. MATLAB simulations have been used to compute periodic and quasi periodic orbits (planar Lyapunov, three-dimensional Axial, Vertical, Halo and Lissajous orbits) around the collinear libration point L2, by integrating numerically the non linearized equations of motion. The same strategy has been used to study transfer trajectories to periodic and quasi periodic orbits near L2 in the Sun – Earth system. MATLAB simulations have also been used to compute transfers along stable manifolds of Halo and Lissajous orbits around the same collinear libration point. Finally a “free” transfer from the ARIANE 5 Geostationary Transfer Orbit (GTO) to a Lissajous orbit around L2 has been deeply analyzed and results compared with the preliminary analysis of the forthcoming Hershel ESA mission.

Main interests

  • Space missions around Libration Points
  • Applications, advantages and … disadvantages!
  • The Circular Restricted Three – Body Problem;
  • Methods to determine periodic orbits near collinear Libration Points:
  • Linear analysis, semi – analytical, numerical methods and other approaches;
  • Periodic and quasi periodic orbits near collinear Libration points:
  • Lyapunov, Axial, Vertical, Halo and Lissajous orbits and their applications in space mission design;
  • Transfer trajectories to collinear Libration Points:
  • Direct transfers and transfers along stable manifolds of Halo and Lissajous orbits around L2 in the Sun – Earth system;

Case study: a “free” transfer to L2

•Transfer from the ARIANE 5 geostationary transfer orbit (GTO)…

perigee height 620 km, apogee height 35780 km, inclination 7° (launch from Kourou), argument of perigee about 180°, velocity at perigee 9.89 km/s, orbital period 10.652 h, eccentricity 0.715

•…to a Lissajous orbit around L2 in the Sun – Earth system

with no amplitude reduction manoeuvre;

as for Herschel ESA mission (launched in 2007); the stable manifold of the final orbit touches perigee conditions, guaranteeing a “free” transfer (no supplementary manoeuvres, except orbit corrections) from the initial ARIANE 5 GTO parking orbit;

• for the injection in the final orbit around L2:

with ,(free transfer!)

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