Modified double-averaged Hamiltonian in hierarchical triple systems

In this work, we introduce a modified double-averaging approach by considering the shortterm effects and formulate a more accurate double-averaged Hamiltonian (in comparison to the classical octupole-level Hamiltonian) for hierarchial triple systems. The Hamiltonian is expressed as a power series in the ratio of the semi-major axes of the inner and outer binaries. Both the Delaunay's elements and the classical orbit elements are adopted to describe the motion. To derive the secular Hamiltonian, the short-term oscillations in the Hamiltonian are averaged out by means of a double-averaging approach. In particular, during the average over the orbital period of the outer binary, the periodic corrections to the secular motion are taken into account. Based on the double-averaged Hamiltonian, we provide two versions of equations of secular motion, given in the form of canonic relations and Lagrange planetary equations. The resulting secular evolution equations can be utilized to reproduce the long-term behaviours for those physical systems where the perturbations coming from the disturbing bodies are relatively strong. To test the approach, we use the averaged Hamiltonian to predict the longterm motions of a planet in a stellar binary system and natural satellites in Sun-planet systems. Simulation results show that the modified Hamiltonian can reproduce secular behaviours with high accuracy. Additionally, the comparison of dynamical models truncated at different orders indicates that the secular Hamiltonian with inclusion of higher order terms has better accuracy in predicting long-term evolution

Optimization of Interplanetary Trajectories Using the Colliding Bodies Optimization Algorithm

In this paper, a recent physics-based metaheuristic algorithm, the Colliding Bodies Optimization (CBO), already employed to solve problems in civil and mechanical engineering, is proposed for the optimization of interplanetary trajectories by using both indirect and direct approaches. The CBO has an extremely simple formulation and does not depend on any initial conditions. To test the performances of the algorithm, missions with remarkably different orbital transfer energies are considered: from the simple planar case, as the Earth-Mars orbital transfer, to more energetic ones, like a rendezvous with the asteroid Pallas

Interplanetary CubeSats system for space weather evaluations and technology demonstration

The paper deals with the mission analysis and conceptual design of an interplanetary 6U CubeSats system to be implemented in the L1 Earth-Sun Lagrangian Point mission for solar observation and in-situ space weather measurements. Interplanetary CubeSats could be an interesting alternative to big missions, to fulfill both scientific and technological tasks in deep space, as proved by the growing interest in this kind of application in the scientific community and most of all at NASA. Such systems allow less costly missions, due to their reduced sizes and volumes, and consequently less demanding launches requirements. The CubeSats mission presented in this paper is aimed at supporting measurements of space weather. The mission envisages the deployment of a 6U CubeSats system in the L1 Earth-Sun Lagrangian Point, where solar observations for in situ measurements of space weather to provide additional warning time to Earth can be carried out. The proposed mission is also intended as a technology validation mission, giving the chance to test advanced technologies, such as telecommunications and solar sails, envisaged as propulsion system. Furthermore, traveling outside the Van Allen belts, the 6U CubeSats system gives the opportunity to further investigate the space radiation environment: radiation dosimeters and advanced materials are envisaged to be imple- mented, in order to test their response to the harsh space environment, even in view of future implementation on other spacecrafts (e.g. manned spacecrafts). The main issue related to CubeSats is how to fit big science within a small package - namely power, mass, volume, and data limitations. One of the objectives of the work is therefore to identify and size the required subsystems and equipment, needed to accomplish specific mission objectives, and to investigate the most suitable configuration, in order to be compatible with the typical CubeSats (multi units) standards