Flyby Trajectories Research Articles

Broad-search algorithms for the spacecraft trajectory design of Callisto–Ganymede–Io triple flyby sequences from 2024 to 2040, Part I: Heuristic pruning of the search space

Triple flybys of the Galilean moons of Jupiter can capture a spacecraft into orbit about Jupiter or quickly adjust the Jupiter-centered orbit of an already captured spacecraft. Because Callisto does not participate in the Laplace resonance among Ganymede, Europa, and Io, triple flyby sequences involving gravity-assists of Callisto, Ganymede, and Io occur only aperiodically for limited time windows. An exhaustive search of triple-flyby trajectories over a 16-year period from 2024 to 2040 using “blind” searching would require 8,415,358 Lambert function calls to find only 127,289 possible triple flyby trajectories. Because most of these Lambert function calls would not converge to feasible solutions, it is much more efficient to prune the solution space using a heuristic algorithm and then direct a much smaller number of Lambert function calls to find feasible triple flyby solutions. The novel “Phase Angle Pruning Heuristic” is derived and used to reduce the search space by 99%.

Near-Earth asteroid flyby trajectories from the Sun-Earth L2 for Chang’e-2’s extended flight

Driven by curiosity about possible flight options for the Chang’e-2 spacecraft after it remains at the Sun-Earth L2 point, effective approaches were developed for designing preliminary fuel-optimal near-Earth asteroid flyby trajectories. The approaches include the use of modified unstable manifolds, grid search of the manifolds’ parameters, and a two-impulse maneuver for orbital phase matching and z-axis bias change, and are demonstrated to be effective in asteroid target screening and trajectory optimization. Asteroid flybys are expected to be within a distance of 2 × 107 km from the Earth owing to the constrained Earth-spacecraft communication range. In this case, the spacecraft’s orbital motion is significantly affected by the gravities of both the Sun and the Earth, and therefore, the concept of the “heliocentric oscillating-Kepler orbit” is proposed, because the classical orbital elements of the flyby trajectories referenced in the heliocentric inertial frame oscillate significantly with respect to time. The analysis and results presented in this study show that, among the asteroids whose orbits are the most accurately predicted, “Toutatis”, “2005 NZ6”, or “2010 CL19” might be encountered by Chang’e-2 in late 2012 or 2013 with total impulses less than 100m/s.

Trajectory Analysis and Design for A Jupiter Exploration Mission

The trajectory design for a Jupiter exploration mission is investigated in this paper. The differences between the Jupiter exploration trajectory and the Mars or Venus exploration trajectory are mainly concerned about. Firstly, the selection of the Jupiter-centered orbit is analyzed based on the Galileo Jupiter mission. As for the Earth-Jupiter transfer orbit, the fuel consumption of the direct transfer is too large. So the energy-saving technologies such as the planetary gravity assist should be used for the trajectory to the Jupiter. The different sequences of planetary gravity assists are examined by applying the Particle Swarm Optimization (PSO). According to the searched result, the Venus-Earth-Earth sequence (VEEGA) is the most effective one for the Jupiter mission. During the Jupiter mission, the spacecraft will pass though the main asteroid belt between the orbits of Mars and Jupiter, and may encounter multiple asteroids. Therefore the Jupiter mission is able to combine with the main-belt asteroid flyby mission. The design method of the intermediate asteroid flyby trajectory is also considered. At last, an entire trajectory for the Jupiter mission launched in 2023 is presented.

Design of Earth—Moon Free-Return Trajectories

A new algorithm for designing free-return lunar flyby trajectories between the Earth and the moon is developed. The pseudostate theory is adopted to get the initial solution of the free-return trajectory. Using this initial solution, an improved differential-correction method is employed to find the final solution with a more complicated dynamic model. Compared with the original differential-correction method, the improved one can extend the convergence domain and have a fast convergence speed. A large number of numerical examples are carried out to test the reliability and efficiency of the algorithm, and also study the global features of free-return lunar flyby trajectories. The features are mainly affected by the geometric relationship between the Earth and the moon, the altitude of perilune, and the transfer time from perigee to perilune.

Research on the transfers to Halo orbits from the view of invariant manifolds

This paper discusses the evolutions of invariant manifolds of Halo orbits by low-thrust and lunar gravity. The possibility of applying all these manifolds in designing low-thrust transfer, and the presence of single-impulse trajectories under lunar gravity are also explained. The relationship between invariant manifolds and the altitude of the perigee is investigated using a Poincare map. Six types of single-impulse transfer trajectories are then attained from the geometry of the invariant manifolds. The evolutions of controlled manifolds are surveyed by the gradient law of Jacobi energy, and the following conclusions are drawn. First, the low thrust (acceleration or deceleration) near the libration point is very inefficient that the spacecraft free-flies along the invariant manifolds. The purpose is to increase its velocity and avoid stagnation near the libration point. Second, all controlled manifolds are captured because they lie inside the boundary of Earth’s gravity trap in the configuration space. The evolutions of invariant manifolds under lunar gravity are indicated from the relationship between the lunar phasic angle and the altitude of the perigee. Third and last, most of the manifolds have preserved their topologies in the circular restricted three-body problem. However, the altitudes of the perigee of few manifolds are quite non-continuous, which can be used to generate single- impulse flyby trajectories.

Small-Body Postrendezvous Characterization via Slow Hyperbolic Flybys

DOI: 10.2514/1.53722 The most crucial task for a spacecraft upon arriving at a small body is to determine the strength of the body's gravity field. This research proposes and models this initial characterization via a series of slow flybys and analyzes how rapidly the gravity field can be estimated and the precision to which it can be determined. Two analytical issues areaddressedinthispaperthatarepertinenttothedesignofthischaracterizationprocessandcanbeusedtoevaluate whether thereis aneed for lidarmeasurements. A new operational procedure calledV rangingis proposed, which can eliminate the need for lidar during the initial characterization phase. Following this, the characterization of the gravity field is addressed by performing a covariance analysis around three asteroids: Itokawa, Didymos, and Eros, representing a two-order-of-magnitude difference in size. I. Introduction T HEREisanincreasinginterestinstudyingsmall-bodysystems, such as asteroids and comets, with spacecraft rendezvous missions. On arrival to a small body, one of the most important tasks is for the spacecraft to characterize the body's environment to determine the gravitational parameterand the gravity field of the body. This is the major source of spacecraft perturbation when in proximity to the body, and lack of knowledge of thegravity field can delay the start of the main scientific mission. Thus, it is of interest to carry out this initial characterization of the body in as rapid amanner as is feasible and with minimum risk to the spacecraft. Estimation of thegravitationalparameterandgravitational fieldofabodygenerally uses a least-squares filter, most commonly a batch square-root infor- mation filter (SRIF) due to its numerical stability (1-3), assuming that the deviation from the true dynamics can be approximated within the linear range of the modeled nonlinear dynamics of the spacecraft (4). In addition to the gravity terms, other commonly estimated parameters in the filter are the spacecraft state, body's spin state, and navigationV maneuvers. The estimated parameters can be time-dependent as in spacecraft position and velocity, or time- independent (i.e., global) as in the higher-degree and higher-order gravity field. As will be shown later, a method for carrying out this initial estimation task throughaseriesof relativelyslow flybys ofthe body is proposed. We probe the level of characterization that can occur using this approach, and whether such an approach could eliminate the need for a dedicated orbital phase for some mission types. This topic is studied using both analytic and numerical methods. For definiteness, we assume that the target body is a near- Earth asteroid, with additional details on its size, shape, spin state, and heliocentric orbit given later. This paper consists of an analytical section and a numerical section, bothof whichwill discussthe estimation ofthesmall body's gravitational environment. The results presented here combine two previous conference papers (5,6). The first (analytical) part of the paperanalyzestheeffectivenessofperformingaprecisemaneuverto break the scale invariance in a hyperbolic flyby with optical-only observations. The goal of this analysis is to characterize the need for carrying a laser or radar ranging instrument to sense distance to the asteroid, and replaces this with a concept calledV ranging. A similar concept using optical-based navigation is also discussed by Alonso et al. (7) to estimate the relative position and attitude in the contextofformation flyingandValaseketal.(8)fortheapplicationof autonomous air refueling. Following this, we provideV ranging, which is a derivation of a new method to analytically estimate the precision of the gravitational parameter determination based on the geometry and time of the spacecraft trajectory around an asteroid. Specifically, wederiveanalytical expressionsfor the uncertainty of a small-body gravity field and spacecraft relative trajectory using Doppler tracking and optical navigation. The conventional method derivesby leveraging the property that the inbound and outbound hyperbolicvelocitiesV1 areequalinmagnitudeandseparatedbythe hyperbolic turn angle� . This method rendersas a function ofb1 (impact radius),V1, and change in hyperbolic velocityVflyby. Our new analytical estimate is based on the measured time of flight of a flyby trajectory to derive an expression for� . These two analytical expressionsforarecomparedwiththefullleast-squarescovariance discussedinthesecondpartofthispaperinordertodeterminewhich effect actually controls the full estimation.

Asteroid 21 Lutetia: Low Mass, High Density

Asteroid 21 Lutetia was approached by the Rosetta spacecraft on 10 July 2010. The additional Doppler shift of the spacecraft radio signals imposed by 21 Lutetia's gravitational perturbation on the flyby trajectory were used to determine the mass of the asteroid. Calibrating and correcting for all Doppler contributions not associated with Lutetia, a least-squares fit to the residual frequency observations from 4 hours before to 6 hours after closest approach yields a mass of (1.700 ± 0.017) × 10(18) kilograms. Using the volume model of Lutetia determined by the Rosetta Optical, Spectroscopic, and Infrared Remote Imaging System (OSIRIS) camera, the bulk density, an important parameter for clues to its composition and interior, is (3.4 ± 0.3) × 10(3) kilograms per cubic meter.

Magnetic signatures of a tenuous atmosphere at Dione

We present Cassini magnetic field observations from the only two close flybys (16DI and 129DI) of Saturn's icy satellite Dione which have been carried out so far. Data from 16DI show a weak field perturbation in the upstream region, indicative of a tenuous atmosphere around the satellite. By applying an analytical model of the perturbations caused by subalfvénic atmosphere‐magnetosphere interactions, we demonstrate that an atmospheric column density of approximately 1 · 1017 m−2 would be able to sustain the observed field signature. Magnetic field data from 16DI also contain hints that Dione's gas envelope might possess a slight asymmetry between the Saturn‐facing and the Saturn‐averted hemisphere. The detection of a thin atmosphere at Dione might be correlated to the occurrence of a transient radiation belt near the moon's L‐shell at the time of the 16DI flyby, as reported by Roussos et al. (2008b). On the other hand, magnetic field observations from the subsequent downstream encounter 129DI show no clear evidence of an atmosphere, probably due to the flyby trajectory being unsuitable for the detection of the associated perturbations.

A Dynamical Systems Analysis of Resonant Flybys: Ballistic Case

In this analysis, resonant flybys were explored within the context of the circular restricted three-body problem using dynamical systems theory. The first step in this process involved the construction of a flyby trajectory continuously transiting between 3:4 and 5:6 resonances in the Jupiter-Europa circular restricted three-body problem. An examination of this trajectory revealed that it followed the invariant manifolds of resonant orbits during these transitions. It was discovered that these transitions occurred for specific energies where the invariant manifolds of the 3:4 and 5:6 resonant orbits were closely related. The potential of the information obtained from this analysis for use in mission design was demonstrated by developing resonance transition trajectories using resonant orbit homoclinic and heteroclinic connections.

The equatorial shape and gravity field of Mercury from MESSENGER flybys 1 and 2

On 14 January and 6 October 2008 the MESSENGER spacecraft passed within 200 km of the surface of Mercury. These flybys by MESSENGER provided the first observations of Mercury from a spacecraft since the Mariner 10 flybys in 1974 and 1975. Data from the Mercury Laser Altimeter (MLA) provided new information on the equatorial shape of Mercury, and Doppler tracking of the spacecraft through the flybys provided new data on the planet’s gravity field. The MLA passes were on opposite hemispheres of the planet and span collectively ∼40% of the equatorial circumference. The mean elevation of topography observed during flyby 1, in the longitude range 0–90°E, is greater than that seen during flyby 2 in the longitude range 180–270°E, indicating an offset between centers of mass and figure having a magnitude and phase in general agreement with topography determined by Earth-based radar. Both MLA profiles are characterized by slopes of ∼0.015° downward to the east, which is consistent with a long-wavelength equatorial shape defined by a best-fitting ellipse. The Doppler tracking data show sensitivity to the gravitational structure of Mercury. The equatorial ellipticity of the gravitational field , C 2,2, is well determined and correlates with the equatorial shape. The S 2,2 coefficient is ∼0, as would be expected if Mercury’s coordinate system, defined by its rotational state, is aligned along its principal axes of inertia. The recovered value of the polar flattening of the gravitational potential, J 2, is considerably lower in magnitude than the value obtained from Mariner 10 tracking, a result that is problematic for internal structure models. This parameter is not as well constrained as the equatorial ellipticity because the flyby trajectories were nearly in the planet’s equatorial plane. The residuals from the Doppler tracking data suggest the possibility of mascons on Mercury, but flyby observations are of insufficient resolution for confident recovery. For a range of assumptions on degree of compensation and crustal and mantle densities, the allowable crustal thickness is consistent with the upper limit of about 100 km estimated from the inferred depth of faulting beneath a prominent lobate scarp, an assumed ductile flow law for crustal material, and the condition that temperature at the base of the crust does not exceed the solidus temperature. The MESSENGER value of C 2,2 has allowed an improved estimate of the ratio of the polar moment of inertia of the mantle and crust to the full polar moment ( C m/C ), a refinement that strengthens the conclusion that Mercury has at present a fluid outer core.

Aurora and magnetic field of Uranus

Resolution of the details of a planetary magnetic field from magnetometer measurements made during a single flyby can be severely limited because of the incomplete geometrical sampling of the planetary neighborhood by the flyby trajectory. This problem was especially severe for the only spacecraft encounter with Uranus, that of Voyager 2 in 1986. Fortunately, auroras at the magnetic field line footprints serve as additional constraints that may be used to determine the higher multipole moments of planetary fields (Connerney et al.'s (1998) VIP‐4 model of for Jupiter). In the present work, this approach is applied to improving the resolution of the magnetic field of Uranus. The auroral emission distribution at Uranus is determined from scans by the Voyager 2 Ultraviolet Spectrometer (UVS), enhancing an earlier analysis by Herbert and Sandel (1994) by incorporating more observations and by using more powerful analysis techniques. The resulting new determination of the auroral ovals is well correlated with the field lines associated with the strongest plasma wave and radio emissions but differs from model ovals computed by Connerney et al. (1987) from the Q3 magnetic field model for Uranus. Consequently, a search has been initiated for model coefficients of the planetary magnetic field that agree both with the magnetic field observations and also with the reasonable assumption that the newly determined auroral emissions lie at the magnetic footprints of an equidistant circum‐Uranian region of the magnetosphere. The dipole and quadrupole terms of the new field model, termed AH5, are similar to those of the dipole + quadrupole Q3 model, but the AH5 higher multipole terms diverge from the dipole + quadrupole + octupole I3E1 model of Connerney et al. (1987), from which the Q3 model was derived. Inasmuch as the I3E1 octupole terms were not resolved, the AH5 model derived here comprises a first estimate of the higher multipole moments of Uranus's magnetic field.

Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

In this paper an optimisation algorithm based on Differential dynamic programming is applied to the design of rendezvous and fly-by trajectories to near Earth objects. Differential dynamic programming is a successive approximation technique that computes a feedback control law in correspondence of a fixed number of decision times. In this way the high dimensional problem characteristic of low-thrust optimisation is reduced into a series of small dimensional problems. The proposed method exploits the stage-wise approach to incorporate an adaptive refinement of the discretisation mesh within the optimisation process. A particular interpolation technique was used to preserve the feedback nature of the control law, thus improving robustness against some approximation errors introduced during the adaptation process. The algorithm implements global variations of the control law, which ensure a further increase in robustness. The results presented show how the proposed approach is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution.

Astrometric solar-system anomalies

AbstractThere are at least four unexplained anomalies connected with astrometric data. Perhaps the most disturbing is the fact that when a spacecraft on a flyby trajectory approaches the Earth within 2000 km or less, it often experiences a change in total orbital energy per unit mass. Next, a secular change in the astronomical unit AU is definitely a concern. It is reportedly increasing by about 15 cm yr−1. The other two anomalies are perhaps less disturbing because of known sources of nongravitational acceleration. The first is an apparent slowing of the two Pioneer spacecraft as they exit the solar system in opposite directions. Some astronomers and physicists, including us, are convinced this effect is of concern, but many others are convinced it is produced by a nearly identical thermal emission from both spacecraft, in a direction away from the Sun, thereby producing acceleration toward the Sun. The fourth anomaly is a measured increase in the eccentricity of the Moon's orbit. Here again, an increase is expected from tidal friction in both the Earth and Moon. However, there is a reported unexplained increase that is significant at the three-sigma level. It is prudent to suspect that all four anomalies have mundane explanations, or that one or more anomalies are a result of systematic error. Yet they might eventually be explained by new physics. For example, a slightly modified theory of gravitation is not ruled out, perhaps analogous to Einstein's 1916 explanation for the excess precession of Mercury's perihelion.

Can the flyby anomaly be attributed to earth-bound dark matter?

We make preliminary estimates to assess whether the recently reported flyby anomaly can be attributed to dark matter interactions. We consider both elastic and exothermic inelastic scattering from dark matter constituents; for isotropic dark matter velocity distributions, the former decrease, while the latter increase, the final flyby velocity. The fact that the observed flyby velocity anomaly shows examples with both positive and negative signs, requires the dominance of different dark matter scattering processes along different flyby trajectories. The magnitude of the observed anomalies requires dark matter densities many orders of magnitude greater than the galactic halo density. Such a large density could result from an accumulation cascade, in which the solar system-bound dark matter density is much higher than the galactic halo density, and the earth-bound density is much higher than the solar system-bound density. We discuss a number of strong constraints on the hypothesis of a dark matter explanation for the flyby anomaly. These require dark matter to be non-self-annihilating, with the dark matter scattering cross section on nucleons much larger, and the dark matter mass much lighter, than usually assumed.

New Horizons Mission Design

In the first mission to Pluto, the New Horizons spacecraft was launched on January 19, 2006, and flew by Jupiter on February 28, 2007, gaining a significant speed boost from Jupiter’s gravity assist. After a 9.5-year journey, the spacecraft will encounter Pluto on July 14, 2015, followed by an extended mission to the Kuiper Belt objects for the first time. The mission design for New Horizons went through more than five years of numerous revisions and updates, as various mission scenarios regarding routes to Pluto and launch opportunities were investigated in order to meet the New Horizons mission’s objectives, requirements, and goals. Great efforts have been made to optimize the mission design under various constraints in each of the key aspects, including launch window, interplanetary trajectory, Jupiter gravity-assist flyby, Pluto–Charon encounter with science measurement requirements, and extended mission to the Kuiper Belt and beyond. Favorable encounter geometry, flyby trajectory, and arrival time for the Pluto–Charon encounter were found in the baseline design to enable all of the desired science measurements for the mission. The New Horizons mission trajectory was designed as a ballistic flight from Earth to Pluto, and all energy and the associated orbit state required for arriving at Pluto at the desired time and encounter geometry were computed and specified in the launch targets. The spacecraft’s flight thus far has been extremely efficient, with the actual trajectory error correction ΔV being much less than the budgeted amount.

Guidance Strategy for Hyperbolic Rendezvous

In cycler and semi-cycler Mars mission architectures a crew “taxi” docks with the interplanetary transfer vehicle on a hyperbolic flyby trajectory, hence the term “hyperbolic rendezvous.” An algorithm that guides the taxi to intercept the transfer vehicle is presented with a control law for final approach. When navigation and thrust uncertainties are included, the vehicles dock at a closing rate of a few cm/s with a misalignment of a few cm. Because this maneuver is critical to crew survival, we advocate redundant systems and propellant margin for 3-σ (~99.7%) reliability. These safety measures lead to marginal increases in taxi mass.

Venus atmospheric circulation: Known and unknown

After a pause of more than two decades, Venus' atmosphere is being explored again. Since April 2006, European Space Agency's Venus Express has been acquiring data, exploiting the near‐infrared windows that allow us to peer into the deep night‐side atmosphere. In June 2007, NASA's MESSENGER mission will fly past Venus on its way to Mercury, collecting useful data for a few weeks. Instruments and experiments on Venus Express are expected to provide a more comprehensive set of atmospheric observations over three and perhaps more Venus days. Venus Express observations are already providing clues about the processes that maintain the rapid circulation of Venus' atmosphere. The early observations show not only that the global circulation is organized into two hemispheric vortices centered over respective poles, but also that the vortex organization extends deep into the atmosphere. The limited Galileo NIMS near‐infrared observations in 1989 had revealed the deep circulation in the equatorial regions, but because of the spacecraft, flyby trajectory could not observe the high latitudes to elucidate the polar circulation and its organization. The long hiatus in systematic Venus observations has provided an opportunity to perform some new analysis of the previous Pioneer Venus observations. This paper presents a synopsis of the circulation measurements at high latitudes and an analysis of the solar thermal tides seen in the cloud motions and suggests some limitations of previous estimates of transport of angular momentum by eddies.

Rosetta Asteroid Targets: 2867 Steins and 21 Lutetia

In preparation for the flyby of the Rosetta spacecraft, the state of the knowledge of 21 Lutetia and 2867 Steins obtained by ground based observations is reported. Preliminary determination of shape and/or size, rotational properties and taxonomic types are presented for both asteroids. The dusty environment of the targets has been studied in order to help in defining safe fly-by trajectories without the risk of damaging collisions. The expected science return from the asteroid fly-by is also discussed.

Radial diffusion of geomagnetically trapped protons observed by the Galileo Energetic Particle Detector

The Galileo spacecraft encountered the Earth once on 8 December 1990 (Earth‐I) and again on 8 December 1992 (Earth‐II). These flybys provided excellent opportunities to evaluate the performance of the Energetic Particle Detector (EPD) and establish analysis procedures in a relatively well‐known environment. Further, because Galileo's Earth flyby trajectories were very rapid and nearly radial, the radiation belt measurements provided an excellent “snapshot” of trapped radiation. Because of the rapid flyby and the 20‐s spin period of Galileo, great care had to be taken to remove time aliasing from the pitch angle distributions. Large anisotropies were also present due to intrinsic density gradients. Spherical harmonics were fitted to the pitch and phase distributions in order to obtain fluxes from which phase space densities could be computed. The phase space density (PSD) was calculated from the fitted count rate for the particles (protons) that conserve the first and second adiabatic invariants. The values of 10.0, 15.0, 20.0, 25.0 30.0, 35.0, 40.0, 45.0, and 50.0 MeV/G were used for the first adiabatic invariant, and the values of 0.10, 0.15, 0.20, 0.25, 0.30, and 0.50 G0.5 RE were used for the second adiabatic invariant to determine the PSD from Earth‐I and Earth‐II observations. The extracted PSDs were examined for radial diffusion. Results show there is no unique global dependency of the diffusion coefficient to L, except for a limited region of the first and second adiabatic invariants.

Analytical Control Laws for Planet-Centered Solar Sailing

With increased interest in solar sailing from both ESA and NASA for future science missions comes the requirement to assess potential planet-centered orbits and generate algorithms for effective orbit maneuvering and control. Previous planet-centered solar-sail trajectory work has been limited mostly to Earth-escape or lunar flyby trajectories as a result of the difficulties of fully optimizing multirevolution orbits. A new method of blending locally optimal control laws is introduced, where each control law is prioritized by consideration of how efficiently it will use the solar sail and how far each orbital element is from its target value. The blended, locally optimal sail thrust vector is thus defined to use the sail as efficiently as possible, allowing the rapid generation of near-optimal trajectories. The blending method introduced is demonstrated for a complex orbit transfer and for two stationkeeping applications. Furthermore, the algorithms developed are explicitly independent of time, and as such the control system is demonstrated suitable as a potential future onboard sail controller.