The 1:1 resonance in Extrasolar Systems: Migration from planetary to satellite orbits

We present families of symmetric and asymmetric periodic orbits at the 1/1 resonance, for a planetary system consisting of a star and two small bodies, in comparison to the star, moving in the same plane under their mutual gravitational attraction. The stable 1/1 resonant periodic orbits belong to a family which has a planetary branch, with the two planets moving in nearly Keplerian orbits with non zero eccentricities and a satellite branch, where the gravitational interaction between the two planets dominates the attraction from the star and the two planets form a close binary which revolves around the star. The stability regions around periodic orbits along the family are studied. Next, we study the dynamical evolution in time of a planetary system with two planets which is initially trapped in a stable 1/1 resonant periodic motion, when a drag force is included in the system. We prove that if we start with a 1/1 resonant planetary system with large eccentricities, the system migrates, due to the drag force, {\it along the family of periodic orbits} and is finally trapped in a satellite orbit. This, in principle, provides a mechanism for the generation of a satellite system: we start with a planetary system and the final stage is a system where the two small bodies form a close binary whose center of mass revolves around the star.Comment: to appear in Cel.Mech.Dyn.Ast

Easily retrievable objects among the NEO population

Asteroids and comets are of strategic importance for science in an effort to understand the formation, evolution and composition of the Solar System. Near-Earth Objects (NEOs) are of particular interest because of their accessibility from Earth, but also because of their speculated wealth of material resources. The exploitation of these resources has long been discussed as a means to lower the cost of future space endeavours. In this paper, we consider the currently known NEO population and define a family of so-called Easily Retrievable Objects (EROs), objects that can be transported from accessible heliocentric orbits into the Earth’s neighbourhood at affordable costs. The asteroid retrieval transfers are sought from the continuum of low energy transfers enabled by the dynamics of invariant manifolds; specifically, the retrieval transfers target planar, vertical Lyapunov and halo orbit families associated with the collinear equilibrium points of the Sun-Earth Circular Restricted Three Body problem. The judicious use of these dynamical features provides the best opportunity to find extremely low energy Earth transfers for asteroid material. A catalogue of asteroid retrieval candidates is then presented. Despite the highly incomplete census of very small asteroids, the ERO catalogue can already be populated with 12 different objects retrievable with less than 500 m/s of Δv. Moreover, the approach proposed represents a robust search and ranking methodology for future retrieval candidates that can be automatically applied to the growing survey of NEOs

Natural and sail-displaced doubly-symmetric Lagrange point orbits for polar coverage

This paper proposes the use of doubly-symmetric, eight-shaped orbits in the circular restricted three-body problem for continuous coverage of the high-latitude regions of the Earth. These orbits, for a range of amplitudes, spend a large fraction of their period above either pole of the Earth. It is shown that they complement Sun-synchronous polar and highly eccentric Molniya orbits, and present a possible alternative to low thrust pole-sitter orbits. Both natural and solar-sail displaced orbits are considered. Continuation methods are described and used to generate families of these orbits. Starting from ballistic orbits, other families are created either by increasing the sail lightness number, varying the period or changing the sail attitude. Some representative orbits are then chosen to demonstrate the visibility of high-latitude regions throughout the year. A stability analysis is also performed, revealing that the orbits are unstable: it is found that for particular orbits, a solar sail can reduce their instability. A preliminary design of a linear quadratic regulator is presented as a solution to stabilize the system by using the solar sail only. Finally, invariant manifolds are exploited to identify orbits that present the opportunity of a ballistic transfer directly from low Earth orbit

The Notch pathway in ovarian carcinomas and adenomas

Elements of the Notch pathway regulate differentiation; we investigated the expression of such elements in epithelial ovarian tumours. A total of 32 ovarian tumour samples (17 adenocarcinomas, three borderline tumours, 12 adenomas), two human ovarian cancer (A2780, OVCAR3), and one ovarian surface (IOSE 144) cell lines were analysed. The expression of Notch pathway elements was assessed by RT–PCR, real-time PCR (Notch 1), and by immunoblots (Notch 1 extracellular domain (EC), HES1). The proliferation and colony formation of A2780 cells were measured after stable transfection with activated Notch 1 (intracellular domain). Jagged 2, Delta-like-1, Manic Fringe, and TSL1 were expressed more frequently in adenocarcinomas whereas Deltex, Mastermind, and Radical Fringe were more frequent in adenomas. Quantitative PCR revealed decreased Notch 1 mRNA in ovarian adenocarcinomas compared with adenomas. The expression of Notch 1-EC protein was similar in benign and malignant tumours. HES1 protein was strongly expressed in 18/19 ovarian cancers and borderline tumours but not in adenomas. Transfecting A2780 cells with active Notch 1-IC resulted in a proliferative and colony formation advantage compared to mock transfected cells. Thus, Notch pathway elements are expressed in ovarian epithelial tumours and some of them are differentially expressed between adenomas and carcinomas. The Notch pathway could be a target for the development of therapies for ovarian cancer

Optimal solar sail interplanetary heteroclinic transfers for novel space applications

This paper investigates the design and optimization of solar sail interplanetary trajectories connecting both Libration Point Orbits (LPOs) and Distant Periodic Orbits (DPOs) belonging to different restricted three-body problems: namely the Sun-Earth model and the Sun-Venus one. Assuming the Sun always as first primary, the Earth and Venus are the second primary, and their relative models are coupled together with the view of defining heteroclinic connections. On suitable Poincare sections, solar sail sets are constructed to obtain transit conditions from LPOs of the departure dynamical system to either LPOs or DPOs of the arrival one. Starting from initial guesses that assume a constant attitude of the solar sail, an optimal control problem is formulated, encompassing a trade-off between minimum transfer time and minimum solar sail steering effort, and it is solved with a direct pseudospectral method. At the optimization stage, variable attitude solar sails are investigated, assuming spacecraft with different control capabilities