Stefano Campagnola

Endgame Problem Part 2: Multibody Technique and the Tisserand-Poincare Graph

This two-part series studies the anatomy of the endgame problem, the last part of the spacecraft trajectory before the orbit-insertion maneuver into the science orbit. The endgame provides large savings in the capture A v, and therefore it is an important element in the design of ESA and NASA missions to the moons of Jupiter and Saturn. The endgame problem has been approached in different ways with different results: the ν ∞ -leveraging-maneuver approach leads to high-Δ ν, short-time-of-flight transfers, and the multibody technique leads to low-Δν, long-time-of-flight transfers. This paper series investigates the link between the two approaches, giving a new insight to the complex dynamics of the multibody gravity-assist problem. In this paper we focus on the multibody approach using a new graphical tool, the Tisserand-Poincare graph. The Tisserand-Poincare graph shows that ballistic endgames are energetically possible and it explains why they require resonant orbits patched with high-altitude flybys, whereas in the ν ∞ -leveraging-maneuver approach, flybys alone are not effective without impulsive maneuvers in between them. We then use the Tisserand-Poincare graph to design quasi-ballistic transfers. Unlike previous methods, the Tisserand-Poincare graph provides a valuable energy-based target point for the design of the endgame and begin-game and a simple way to patch them. Finally, we present two transfers. The first transfer is between low-altitude orbits at Europa and Ganymede using almost half the Δν of the Hohmann transfer; the second transfer is a 300-day quasi-ballistic transfer between halo orbits of the Jupiter-Ganymede and Jupiter-Europa. With approximately 50 m/s the transfer can be reduced by two months.

Endgame Problem Part 1: V-Infinity-Leveraging Technique and the Leveraging Graph

Renewed interest by ESA and NASA in missions to Europa, Ganymede, Enceladus, and Titan poses the question of how to best solve the endgame problem. Endgames typically aim at an inexpensive insertion maneuver into the science orbit and can be designed using either V ∞ -leveraging maneuvers or the multibody dynamics. Although historically linked to insertion maneuvers, the endgame problem is symmetric and equally applies to departure. In this two-part series, we analyze and draw connections between the two apparently separate approaches, providing insight into the dynamics of the multibody gravity-assist problem. In this paper we derive new formulas for the V ∞ -leveraging maneuver and build the leveraging graph to be used as a reference guide for designing endgame tours. We prove that the cost of a V ∞ -leveraging-maneuver sequence decreases when using high-altitude flybys (as done in the multibody technique). Finally, we find a simple quadrature formula to compute the minimum ΔV transfer between moons using V ∞ -leveraging maneuvers, which is the main result of the paper, and a method to estimate transfer times. The leveraging graphs and associated formulas are derived in canonical units and therefore apply to any celestial system with a smaller body in a circular orbit around a primary. Specifically, we demonstrate the new method to provide rapid calculations of the theoretical boundary values for ΔV requirements and estimated transfer times for moon tours in the Saturn and Jupiter systems using the V ∞ -leveraging-maneuver model.

Solar Electric Propulsion Gravity-Assist Tours For Jupiter Missions

Several Hall thrusters (e.g. BPT-4000, BHT-600, SPT-100, etc.) are able that operate with useful thrust at the sub-kilowatt power levels that would be available from solar arrays at Jupiter distance. We have found that a combination of a multi-kilowatt thruster (e.g. the BPT-4000) for the interplanetary trajectory with a sub-kilowatt thruster (e.g. the BHT-600) is sufficient for a Europa flyby mission. A roughly 1200 kg spacecraft using this propulsion approach would be able to launch on a Falcon 9 and reach Jupiter in 4.9 years. We demonstrate the feasibility of a Solar Electric Propulsion (SEP) Jovian tour with an example tour that reaches Europa 1.6 years after Jupiter arrival with a remaining capability of 400 m/s of ΔV for additional flybys.

Tisserand-Leveraging Transfers

Tisserand-leveraging transfers (TILTs) are introduced as a new method for computing low-Δv orbit transfers with the help of third-body perturbations. The TILTs can mitigate the costs and risk of planetary missions by reducing the orbit insertion maneuver requirements while maintaining short flight times. TILTs connect two flybys at the minor body with an impulsive maneuver at an apse. Using the circular, restricted three-body problem, TILTs extend the concept of v-infinity leveraging beyond the patched-conics domain. In this paper, a new method is presented to compute TILTs and to patch them together to design low-energy transfers. The presented solutions have transfer times similar to the high-energy solutions, yet the Δv cost is significantly reduced. For this reason, TILTs are used in the reference endgame of ESA’s new mission option to Ganymede, JUICE, which is also presented here. JUICE’s low-energy endgame halves the cost of similar high-energy endgames, which makes TILTs a mission-enabling technolo...

EUROPA multiple-flyby trajectory design

As reinforced by the 2011 NRC Decadal Survey, Europa remains one of the most scientifically intriguing targets in planetary science due to its potential suitability for life. However, based on JEO cost estimates and current budgetary constraints, the Decadal Survey recommended-and later directed by NASA Headquarters-a more affordable pathway to Europa exploration be derived. In response, a flyby-only proof-of-concept trajectory has been developed to investigate Europa. The trajectory, enabled by employing a novel combination of new mission design techniques, successfully fulfills a set of Science Definition Team derived scientific objectives carried out by a notional payload including ice penetrating radar, topographic imaging, and short wavelength infrared observations, and ion neutral mass spectrometry in-situ measurements. The current baseline trajectory, referred to as 11-F5, consists of 34 Europa and 9 Ganymede flybys executed over the course of 2.4 years, reached a maximum inclination of 15 degrees, has a deterministic delta v of 157 m/s (post-PJR), and has a total ionizing dose of 2.06 Mrad (Si behind 100 mil Al, spherical shell). The 11-F5 trajectory and more generally speaking, flyby-only trajectories-exhibit a number of potential advantages over an Europa orbiter mission.

Three-Dimensional Resonant Hopping Strategies and and the Jupiter Magnetospheric Orbiter

S INCE Mariner 10’s first swingby at Venus in 1974, gravity assists have been used successfully in many missions. The missionsGalileo andCassini, and the planned Jupiter EuropaOrbiter (NASA) and Jupiter Ganymede Orbiter (ESA), implement several gravity assists connecting resonant orbits to reduce the spacecraft energy. The missions Ulysses and Cassini, and the planned Solar Orbiter (SOLO) (ESA) and Solar-C [Japan Aerospace Exploration Agency (JAXA)], use gravity assists to increase the inclination. JAXA’s planned Jupiter Magnetospheric Orbiter (JMO) is an example of amission exploring amoon system at high latitudes. JMO requires 10s of gravity assists to both reduce the apocenter and increase the inclination. Each gravity assist connects two resonant orbits, so that the entire sequence is an example of resonant hopping. The solution space of such problems is very large, andmethods are needed to explore it quickly during preliminary design. This Note studies the three-dimensional (3-D)-resonant hopping strategy in general, and it presents an automated trajectory design method. The first part of this work shows that the Tisserand constant is the main problem parameter, and it introduces the 3-D-Tisserand graph, which gives insight to the problem. Somenewanalytical formulas are used to compute fixed-altitude gravity assists connecting resonant orbits. The graph and the formulas are the first main results of the Note. The second part of this work implements the formulas in a branchand-bound algorithm. The algorithm is applied to the JMO mission design, providing almost 10,000 solutions in just a fewminutes. The algorithm and the solution space are the second main results of this work. Details are given for one particular solution that reaches 48 inclination on the Jovian equator in less than 1.5 years.

Stochastic Differential Dynamic Programming with Unscented Transform for Low-Thrust Trajectory Design

Low-thrust propulsion is a key technology for space exploration, and much work in astrodynamics has focused on the mathematical modeling and the optimization of low-thrust trajectories. Typically, ...

V-Infinity Leveraging Boundary-Value Problem and Application in Spacecraft Trajectory Design

Interplanetary and intermoon tour missions have benefited from the implementation of leveraging maneuvers that efficiently change spacecraft energy relative to a flyby body. In the current work, these v∞ leveraging maneuvers are generalized and reformulated into a boundary-value problem suitable for broad trajectory searches using only one additional continuous degree of freedom. The presented method naturally incorporates noncircular orbits and arbitrary ephemeris locations for bodies as well as leveraging maneuvers between different bodies. These advantages come from using the same boundary conditions as the Lambert problem, which also maintains the Lambert-based outer-loop search architecture used in many trajectory design tools. The general maneuver formulation of the presented method allows it to be used for interplanetary or intermoon trajectories and allows the incorporation of nontangent leveraging transfers. Some examples of the new formulation’s utility are also explored using representative tra...

Mission design for the exploration of Neptune and Triton

In early 2013, the European Space Agency (ESA) invited the scientific community to propose themes for the next decades of fag-ship missions (specifically for the next L-class missions, L2 and L3). Researchers from European, American, and Japanese institutions submitted a white paper on the scientific case for a mission to Neptune and Triton. The document included an example mission concept and aimed to demonstrate that the proposed science theme can be addressed with technology that is expected to become available within the L2 and L3 time frames (2028 and 2034). We present here the trajectory design for the mission concept and a high-level discussion on its feasibility, which was included in the white paper. We also present details on the example Triton tour, a new search for interplanetary transfers, and a preliminary analysis of the gravity losses at Neptune orbit insertion (NOI), which suggests the use of a large chemical propulsion system.