Broad-search algorithms for the spacecraft trajectory design of Callisto–Ganymede–Io triple flyby sequences from 2024 to 2040, Part II: Lambert pathfinding and trajectory solutions

Triple-satellite-aided capture employs gravity-assist flybys of three of the Galilean moons of Jupiter in order to decrease the amount of ΔV$\mathrm{\Delta }V$ required to capture a spacecraft into Jupiter orbit. Similarly, triple flybys can be used within a Jupiter satellite tour to rapidly modify the orbital parameters of a Jovicentric orbit, or to increase the number of science flybys. In order to provide a nearly comprehensive search of the solution space of Callisto–Ganymede–Io triple flybys from 2024 to 2040, a third-order, Chebyshev's method variant of the p-iteration solution to Lambert's problem is paired with a second-order, Newton–Raphson method, time of flight iteration solution to the _V∞$V_{\infty }$-matching problem. The iterative solutions of these problems provide the orbital parameters of the Callisto–Ganymede transfer, the Ganymede flyby, and the Ganymede–Io transfer, but the characteristics of the Callisto and Io flybys are unconstrained, so they are permitted to vary in order to produce an even larger number of trajectory solutions. The vast amount of solution data is searched to find the best triple-satellite-aided capture window between 2024 and 2040.     

Design of transfer trajectories between resonant orbits in the Earth–Moon restricted problem

The application of dynamical systems techniques to mission design has demonstrated that employing invariant manifolds and resonant flybys enables previously unknown trajectory options and potentially reduces the ΔV$\mathrm{\Delta }V$ requirements. In this investigation, planar and three-dimensional resonant orbits are analyzed and cataloged in the Earth–Moon system and the associated invariant manifold structures are computed and visualized with the aid of higher-dimensional Poincaré maps. The relationship between the manifold trajectories associated with multiple resonant orbits is explored through the maps with the objective of constructing resonant transfer arcs. As a result, planar and three-dimensional homoclinic- and heteroclinic-type trajectories between unstable periodic resonant orbits are identified in the Earth–Moon system. To further illustrate the applicability of 2D and 3D resonant orbits in preliminary trajectory design, planar transfers to the vicinity of L₅ and an out-of-plane transfer to a 3D periodic orbit, one that tours the entire Earth–Moon system, are constructed. The design process exploits the invariant manifolds associated with orbits in resonance with the Moon as transfer mechanisms.     

Polyhedron tracking and gravity tractor asteroid deflection

In the wake of the Chelyabinsk airburst, the defense against hazardous asteroids is becoming a topic of high interest. This work improves the gravity tractor asteroid deflection approach by tracking realistic small body shapes with tilted ion engines. An algorithm for polyhedron tracking was evaluated in a fictitious impact scenario. The simulations suggest a capability increase up to 38.2% with such improved tilting strategies. The long- and short-term effects within polyhedron tracking are illustrated. In particular, the orbital reorientation effect is influential when realistic asteroid shapes and rotations are accounted for. Also analyzed is the subject of altitude profiles, a way to tailor the gravity tractor performance, and to achieve a steering ability within the B-plane. A novel analytical solution for the classic gravity tractor is derived. It removes the simulation need for classic tractor designs to obtain comparable two body model Δv$\mathrm{\Delta }v$ figures. This paper corroborates that the asteroid shape can be exploited for maximum performance. Even a single engine tilt adjustment at the beginning of deflection operations yields more deflection than a fixed preset tilt.     

Navigation Solution to Maneuver a Spacecraft Relative to a Sphere Centered on a Cooperative Satellite

A differential correction algorithm is presented to deliver an impulsive maneuver to a satellite to place it within a sphere, with a user defined radius, centered around a non-maneuvering satellite within a constrained time. The differential correction algorithm develops and utilizes the State Transition Matrix along with the Equations of Motion and multiple satellite?s state information to determine the optimum trajectory to achieve the desired results. The results from the differential correction algorithm are very accurate for prograde orbits, as presented. The results allow for orbit design trade-offs, including satellites? initial inclinations, semi-major axes, as well as the ballistic coefficients. The results also provide an empirical method to determine the optimum ΔV$\mathrm{\Delta }V$ solution for the provided problem. Understanding that the minimum fuel solution lies with a semi-major axis ratio of 1, a very accurate empirical approximation is presented for semi-major axis ratio values less than and greater than 1. This work ultimately provides the generalized framework for applying the algorithm to a unique user defined maneuvering spacecraft scenario.     

Effects of stand-off bursts on rubble-pile targets: Evaluation of a hazardous asteroid mitigation strategy

We explore the aftereffects of stand-off burst mitigation on kilometer-scale rubble pile asteroids. We use a simple model of X-ray energy deposition to calculate the impulse transferred to the target, in particular to burst-facing blocks on the target surface. The impulse allows us to estimate an initial velocity field for the blocks on the outer side of the target facing the burst. We model the dynamics using an N-body polyhedron program built on the Open Dynamics Engine, a “physics engine” that integrates the dynamical equations for objects of general shapes and includes collision detection, friction, and dissipation.We tested several different models for target objects: rubble piles with different mass distributions, a “brick-pile” made of closely fitting blocks and zero void space, and a non-spherical “contact binary” rubble pile. Objects were bound together by self-gravity and friction/inelastic restitution with no other cohesive forces. Our fiducial cases involved objects of m=3.5×10¹² kg (corresponding to a radius of 0.7 km for the bulk object), an X-ray yield of 1 megaton, and stand-off burst distances of R=0.8–2.5 km from the target center of mass.Kilometer-scale rubble piles are robust to stand-off bursts of a yield ($Y\sim 1$ megaton) that would be sufficient to provide an effective velocity change ($\mathrm{\Delta }v\sim 0.05\mathrm{m}{\mathrm{s}}^{-1}$). Disaggregation involving some tens of percent of the target mass happens immediately after the impulse; the bulk of the object re-accretes on a few gravitational timescales, and the final deflected target contains over 95% (typically, 98–99%) of the original mass. Off-center components of the mitigation impulse and the target mass distribution cause a small amount of induced spin and off-axis components of velocity change. The off-axis velocity component amounts to an angular deviation of $\sim$ 0.05–0.1 radians from the nominal impulse vector, which may be important for mitigation planning.