Multiple-satellite-aided capture trajectories at Jupiter using the Laplace resonance

Satellite-aided capture is a mission design concept used to reduce the delta-v required to capture into a planetary orbit. The technique employs close flybys of a massive moon to reduce the energy of the planet-centered orbit. A sequence of close flybys of two or more of the Galilean moons of Jupiter may further decrease the delta-v cost of Jupiter orbit insertion. A Ganymede-Io sequence can save 207 m/s of delta-v over a single Io flyby. A phase angle analysis based on the Laplace resonance is used to find triple-satellite-aided capture sequences involving Io, Europa, and Ganymede. Additionally, the near-resonance of Callisto and Ganymede is used to find triple-satellite-aided capture sequences involving Callisto, Ganymede, and another moon. A combination of these techniques is used to find quadruple-satellite-aided capture sequences that involve gravity-assists of all four Galilean moons. These sequences can save a significant amount of delta-v and have the potential to benefit both NASA’s Jupiter Europa orbiter mission and ESA’s Jupiter Ganymede orbiter mission.     

Using space manifold dynamics to deploy a small satellite constellation around the Moon

The possibility of communicating with the far side of the Moon is essential for keeping a continuous radio link with lunar orbiting spacecraft, as well as with manned or unmanned surface facilities in locations characterized by poor coverage from Earth. If the exploration and the exploitation of the Moon must be sustainable in the medium/long term, we need to develop the capability to realize and service such facilities at an affordable cost. Minimizing the spacecraft mass and the number of launches is a driving parameter to this end. The aim of this study is to show how Space Manifold Dynamics can be profitably applied in order to launch three small spacecraft onboard the same launch vehicle and send them to different orbits around the Moon with no significant difference in the Delta-V budgets. Internal manifold transfers are considered to minimize also the transfer time. The approach used is the following: we used the linearized solution of the equations of motion in the Circular Restricted Three Body Problem to determine a first–guess state vector associated with the Weak Stability Boundary regions, either around the collinear Lagrangian point L1 or around the Moon. The resulting vector is then used as initial state in a numerical backward-integration sequence that outputs a trajectory on a manifold. The dynamical model used in the numerical integration is four-body and non-circular, i.e. the perturbations of the Sun and the lunar orbital eccentricity are accounted for. The trajectory found in this way is used as the principal segment of the lunar transfer. After separation, with minor maneuvers each satellite is injected into different orbits that lead to ballistic capture around the Moon. Finally, one or more circularization maneuvers are needed in order to achieve the final circular orbits. The whole mission profile, from launch to insertion into the final lunar orbits, is modeled numerically with the commercial software STK.     

Ultra-low delta-v objects and the human exploration of asteroids

Missions to near-Earth objects (NEOs) are key destinations in NASA's new ‘Flexible Path’ approach. NEOs are also of interest for science, for the hazards they pose, and for their resources. We emphasize the importance of ultra-low delta-v from LEO to NEO rendezvous as a target selection criterion, as this choice can greatly increase the payload to the NEO. Few such ultra-low delta-v NEOs are currently known; only 65 of the 6699 known NEOs (March 2010) have delta-v <4.5 km/s, 2/3 of typical LEO-NEO delta-v. Even these are small and hard to recover. Other criteria – short transit times, long launch windows, a robust abort capability, and a safe environment for proximity operations – will further limit the list of accessible objects. Potentially there is at least an order of magnitude more ultra-low delta-v NEOs, but finding them all on a short enough timescale (before 2025) requires a dedicated survey in the optical or mid-IR, optimally from a Venus-like orbit because of the short synodic period for NEOs in that orbit, plus long arc determination of their orbits.     

Analysis of impulsive maneuvers to keep orbits around the asteroid 2001SN<Subscript>263</Subscript>

The strongly perturbed environment of a small body, such as an asteroid, can complicate the prediction of orbits used for close proximity operations. Inaccurate predictions may make the spacecraft collide with the asteroid or escape to the deep space. The main forces acting in the dynamics come from the solar radiation pressure and from the body’s weak gravity field. This paper investigates the feasibility of using bi-impulsive maneuvers to avoid the aforementioned non-desired phenomena (collisions and escapes) by connecting orbits around the triple system asteroid 2001SN₂₆₃, which is the target of a proposed Brazilian space mission. In terms of a mathematical formulation, a recently presented rotating dipole model is considered with oblateness in both primaries. In addition, a “two-point boundary value problem” is solved to find a proper transfer trajectory. The results presented here give support to identifying the best strategy to find orbits for close proximity operations, in terms of long orbital lifetimes and low delta-\(V\) consumptions. Numerical results have also demonstrated the significant influence of the spacecraft orbital elements (semi-major axis and eccentricity), angular position of the Sun and spacecraft area-to-mass ratio, in the performance of the bi-impulsive maneuver.     

Analytical design methods for transfer trajectories between the Earth and the Lunar Orbital Station

Lunar Orbital Station (LOS) is proposed as support of manned lunar exploration missions. A fast-converging iteration method for determining the initial conditions of two-impulse transfer trajectories between the Earth and the LOS is proposed based on the patched conic approach. In the Earth phase, near Earth state is connected with the state at the lunar sphere of influence (LSOI) based on the relationship between the initial and terminal orbital state. Then, an analytical algorithm is proposed to find the state vector at LSOI, such to satisfy the LOS orbital constraint. An iterative process is finally adopted to generate favorable initial solutions that satisfy the constraint near the Earth and at the perilune. The algorithm convergence is investigated, and two types of transfer trajectories are found for both Earth-LOS and LOS-Earth transfer. Based on the algorithm, orbital transfer windows, velocity impulse and time of flight are analyzed in the typical years 2025 and 2034. At last, the initial solution is corrected with a high fidelity model based on the active-set method, which shows the precision of this algorithm. The novel procedure for the transfer trajectories design and the analytic result can be used as a basis for rapid mission evaluation and design for future manned lunar missions based on the LOS.     

Delta-v requirements for earth co-orbital rendezvous missions

Earth co-orbital asteroids present advantages as potential targets for future asteroid rendezvous missions. Their prolonged proximity to Earth facilitates communication, while their Earth-like orbits mean a steady flux of solar power and no significant periodic heating and cooling of the spacecraft throughout the course of the mission. Theoretical studies show that low-inclination co-orbital orbits are more stable than high-inclination orbits. As inclination is the most significant indicator of low delta-v rendezvous orbits, there is the potential for a large population of easily accessible asteroids, with favorable engineering requirements. This study first looks at phase-independent rendezvous orbits to a large number of objects, then looks in more detail at the phase-dependent orbits to the most favorable objects. While rendezvous orbits to co-orbital objects do not have a low delta-v necessarily, some objects present energy requirements significantly less than previous rendezvous missions. Currently we find no ideal co-orbital asteroids for rendezvous missions, although theoretical Earth Trojans present very low-energy requirements for rendezvous.     

High resolution spectroscopy in the far UV: Observations of the interstellar medium by IMAPS on ORFEUS-SPAS

The Interstellar Medium Absorption Profile Spectrograph (IMAPS) is an objectivegrating, echelle spectrograph built to observe the spectra of bright, hot stars over the spectral region 950–1150Å, below the wavelength coverage of HST. This instrument has a high wavelength resolving power, making it especially well suited for studies of interstellar absorption lines. Following a series of sounding rocket flights in the 1980's, IMAPS flew on its first Shuttle-launched orbital mission in September 1993, as a partner in the ORFEUS-SPAS program sponsored by the US and German Space Agencies, NASA and DARA.On ORFEUS-SPAS, IMAPS spent one day of orbital time observing the spectra of 10 O- and early B-type stars. In addition to outlining how IMAPS works, we document some special problems that had an influence on the data, and we explain the specific steps in data reduction that were employed to overcome them. This discussion serves as a basic source of information for people who may use archival data from this flight, as well as those who are interested in some specific properties of the data that will be presented in forthcoming research papers.IMAPS is scheduled to fly once again on ORFEUS-SPAS in late 1996. On this flight, 50% of the observing time available for IMAPS and two other spectrographs on the mission will be available to guest observers.     

The dynamical environment of Dawn at Vesta

Dawn is the first NASA mission to operate in the vicinity of the two most massive asteroids in the main belt, Ceres and Vesta. This double-rendezvous mission is enabled by the use of low-thrust solar electric propulsion. Dawn will arrive at Vesta in 2011 and will operate in its vicinity for approximately one year. Vesta's mass and non-spherical shape, coupled with its rotational period, presents very interesting challenges to a spacecraft that depends principally upon low-thrust propulsion for trajectory-changing maneuvers. The details of Vesta's high-order gravitational terms will not be determined until after Dawn's arrival at Vesta, but it is clear that their effect on Dawn operations creates the most complex operational environment for a NASA mission to date. Gravitational perturbations give rise to oscillations in Dawn's orbital radius, and it is found that trapping of the spacecraft is possible near the 1:1 resonance between Dawn's orbital period and Vesta's rotational period, located approximately between 520 and 580 km orbital radius. This resonant trapping can be escaped by thrusting at the appropriate orbital phase. Having passed through the 1:1 resonance, gravitational perturbations ultimately limit the minimum radius for low-altitude operations to about 400 km, in order to safely prevent surface impact. The lowest practical orbit is desirable in order to maximize signal-to-noise and spatial resolution of the Gamma-Ray and Neutron Detector and to provide the highest spatial resolution observations by Dawn's Framing Camera and Visible InfraRed mapping spectrometer. Dawn dynamical behavior is modeled in the context of a wide range of Vesta gravity models. Many of these models are distinguishable during Dawn's High Altitude Mapping Orbit and the remainder are resolved during Dawn's Low Altitude Mapping Orbit, providing insight into Vesta's interior structure. Ultimately, the dynamics of Dawn at Vesta identifies issues to be explored in the planning of future EP missions operating in close proximity to larger asteroids.     

Orbital and mission planning constraints for the deflection of NEOs impacting on Earth

This paper is the third in a series. Paper 1 presented the results of numerical modeling of deflections of NEOs in route of collision with the Earth. The model was applied to a variety of dynamical cases including both asteroidal and cometary NEOs. Paper 2 introduced the concept of “distributed deflection,” i.e., the possibility to provide the ΔV necessary to deflect an object with a succession of maneuvers each of which would have been insufficient per se to obtain the desired result. In both papers no assumptions were made on the physical composition and structure of the NEO, nor on the details of the possible deflection maneuvers from the point of view of mission analysis. Moreover, ΔV-plots were computed assuming only along-track impulses (both in the positive and negative directions), because it is easy to demonstrate that in general this is energetically the most favorable configuration. Also in the present paper no assumptions were made on the physical composition and structure of the NEO, even if order of magnitude considerations are made on the physical feasibility of a deflection, in terms of the internal strength of the NEO. We present here the results of an investigation on the mission requirements necessary to deflect an object (or contribute to a succession of deflecting maneuvers) in terms of accessibility of the spacecraft terminal orbit from Earth with the current launchers.     

Non-Keplerian orbits for electric sails

An electric sail is capable of guaranteeing the fulfilment of a class of trajectories that would be otherwise unfeasible through conventional propulsion systems. In particular, the aim of this paper is to analyze the electric sail capabilities of generating a class of displaced non-Keplerian orbits, useful for the observation of the Sun’s polar regions. These orbits are characterized through their physical parameters (orbital period and solar distance) and the spacecraft propulsion capabilities. A comparison with a solar sail is made to highlight which of the two systems is more convenient for a given mission scenario. The optimal (minimum time) transfer trajectories towards the displaced orbits are found with an indirect approach.     

Determination of the optimal conditions for inclination maneuvers using a Swing-by

The search for methods to reduce the fuel consumption in orbital transfers is something relevant and always current in astrodynamics. Therefore, the maneuvers assisted by the gravity, also called Swing-by maneuvers, can be an advantageous option to save fuel. The proposal of the present research is to explore the influence of some parameters in a Swing-by of an artificial satellite orbiting a planet with one of the moons of this mother planet, with the goal of changing the inclination of the artificial satellite around the main body of the system. The fuel consumption of this maneuver is compared with the required consumption to perform the same change of inclination using the classical approach of impulsive maneuvers.     

Optimization of interplanetary trajectories for flights to neighboring circumsolar space

The paper deals with the procedure for the generation and optimization of the trajectory plan for missions in neighboring circumsolar space by means of gravity-assist maneuvers near Venus and Earth. An optimum flight trajectory proposed for use in the prospective Intergelio-Zond Russian mission is presented as an example of the described procedure.     

A graph based methodology for mission design

A space mission design methodology is presented, where initial and final orbits are connected through segments of periodic orbits. After a discretization of the solution space, the problem of mission design is transformed into an equivalent combinatorial optimization problem. Specifically, a graph is constructed that represents periodic orbits connected by the execution of impulsive maneuvers. A low computational complexity algorithm for this transformation is introduced. An efficient combinatorial optimization algorithm that solves the shortest path problem is described. Subject to the initial discretization of the solution space, an optimal sequence of coastal arcs is determined for a low total Delta-V mission. Finally, the proposed methodology is applied to the design of a hypothetical Saturn?CTitan system mission.     

Optimal Mars transfers for small payload transportation

Interplanetary transfers represent one of the most interesting themes of astrodynamics, because of its complexity and outcomes for human exploration of the Solar System. A wide number of works concerning different aspects of the interplanetary mission have been developed. The examination of these works leads to the conclusion that, by far, there is not a preferential propulsion system or an optimal trajectory to perform an interplanetary mission, but a precise kind of transfer according to a given mission profile. Here, minimum time trajectories to Mars for small payload transportation with different electric propulsion systems have been analyzed; results have been obtained considering the initial impulse given by the Ariane 5 upper stage. Additionally, an adaptative, multiple shooting optimization algorithm is proposed to solve the problem of optimality in interplanetary transfers with a low continuous thrust. The algorithm searches for the optimal set of initial Lagrange multipliers solving the two point problem by adapting the search intervals according to the unsmooth shape of the augmented cost function.     

The energy transfer process in planetary flybys

We illustrate the energy transfer during planetary flybys as a function of time using a number of flight mission examples. The energy transfer process is rather more complicated than a monotonic increase (or decrease) of energy with time. It exhibits temporary maxima and minima with time which then partially moderate before the asymptotic condition is obtained. The energy transfer to angular momentum is exhibited by an approximate Jacobi constant for the system.We demonstrate this with flybys that have shown unexplained behaviors: (i) the possible onset of the “Pioneer anomaly” with the gravity assist of Pioneer 11 by Saturn to hyperbolic orbit (as well as the Pioneer 10 hyperbolic gravity assist by Jupiter) and (ii) the Earth flyby anomalies of small increases in energy in the geocentric system (Galileo-I, NEAR, and Rosetta, in addition discussing the Cassini and Messenger flybys). Perhaps some small, as yet unrecognized effect in the energy-transfer process can shed light on these anomalies.     

Using wavelet approximation to study the influence of Jupiter on the orbital evolution of a distant satellite of Saturn

We suggest a nonstandard methodology for studying the influence of Jupiter on the secular orbital evolution of a distant satellite of Saturn. This influence is tangible only in short time spans near the times of the smallest separation between Jupiter and Saturn, i.e., when the heliocentric longitudes of the two planets coincide. These times are spaced about 20 years apart. To describe the jumplike behavior of perturbations, we suggest approximating the principal part of the perturbing function averaged over the satellite’s motion by a two-parameter exponential wavelet-type (burst) function. The subsequent averaging (smoothing) of the perturbing function allows us to eliminate the 20-year-period terms and obtain an approximate analytical solution in a special case of the problem. The results are illustrated by plots of the variations in the averaged perturbing function and the orbital eccentricity of Saturn’s outer satellite S/2000 S1, which is most strongly perturbed by Jupiter.     

Systematics of superoutbursts in dwarf novae

Photometric properties of known and suspected members of the SU UMa subclass of dwarf novae are tabulated and discussed. The precessing disc model of superoutbursts gives a satisfactory quantitative explanation of the periods of superhumps and their changes during superoutburst. The systems such as WZ Sge and HV Vir that have very long intervals between superoutbursts are deduced to be beyond the orbital period minimum, and have degenerate secondaries. The systems such as V1159 Ori that have extremely short recurrence times have high rates of mass transfer and are the equivalent of the Z Cam subclass that occurs at longer orbital periods.A simplified analytical approach to the theory of accretion discs is able to explain the correlations between normal and superoutburst recurrence times. It also explains the slope of the plateau region of superoutbursts, and why the slope is shallower in the very short recurrence time systems.     

Primeval substance delivery from Phobos to the Earth—the Phobos-Soil project: Ballistics,navigation, and flight control

This paper is concerned with the problems of ballistics, navigation, and flight control of the space craft (SC) in the Phobos-Grunt mission. We consider an insertion into the Earth-Mars transfer trajectory, the Earth-Mars transfer, the strategy of corrections, and the accuracy of the insertion of the SC into Martian orbit. During the orbital maneuvering stage in the sphere of influence of Mars, we set up a scheme that allows for the insertion of the SC, with the prescribed accuracy, into a point 80-km above the Phobos surface over the theoretical landing area. We specify the sequence for a controlled landing and provide methods for solving the problems of navigation and control during a self-c ontained landing. We also consider the liftoff from Phobos, insertion into the parking orbit, and the Mars-Earth transfer.     

Target selection and accessibility for rendezvous with a Near-Earth asteroid mission

Mission to asteroids and comets has been the hot spot of deep space exploration in the new century. The choice of a suitable target, which involves both scientific value and technical feasibility, becomes a difficult task to accomplish due to limited energy and technology. The aim of this paper is to provide an approach to selecting a target and evaluating accessibility for rendezvous with a Near-Earth Asteroid mission, taking into account scientific value and engineering feasibility. Firstly, according to the orbital characteristics and physical properties of Near-Earth asteroids, we make a summary of some of the most frequent factors influencing the target selection of scientific significance. When selecting the target for a space mission, these factors can be regarded as the scientific motivations. Then in order to avoid the possibility that some high priority targets for science would be discarded due to requiring too high an energy budget by using a classical direct transfer strategy, we calculate the transfer trajectory for rendezvous with candidates by using the planetary swingby technique and the global optimal two-impulse method. Finally, through a comparison between the scientific relevance of each possible target and the corresponding estimate of energy needed for rendezvous missions, the ranking of some candidates is identified.     

Trajectory optimization by making use of the closed solution of constant thrust-acceleration motion

The problem of fuel optimal rendezvous and transfer maneuvers in a central gravitational field is considered. By using analytical results and a parametrization of the control functions, the original optimal control problem can be solved by a sequence of mathematical programming problems. After introducingg KS-variables and piecewise-constant thrust accelerations, all necessary trajectory integrations are performed in closed form. This optimization procedure leads to a considerable reduction in computing time and allows the solution of a wide class of problems: The propulsion system may be thrust-limited or power-limited, one may consider rendezvous or transfer maneuvers with fixed or free final time. A numerical example for a 3-dimensional maneuver is included.