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A global grid search is performed to find axi= and doubly=symmetric periodic orbits in the Restricted Three Body Problem using the dimensioned parameters associated with the Jupiter-Europa system.
Distant retrograde orbits (DROs) are stable periodic orbit solutions of the equations of motion in the circular restricted three body problem. Since no closed form expressions for DROs are known, we present methods for approximating a family of planar DROs for an arbitrary, fixed mass ratio. Furthermore we give methods for computing the first and second derivatives of the position and velocity with respect to the variables that parameterize the family. The approximation and derivative methods described allow a mission designer to target specific DROs or a range of DROs with no regard to phasing in contrast to the more limited case of targeting a six-state only.
Due to the nonlinear nature of the Earth-Moon-Sun three-body problem and non-spherical gravity, CEV cislunar targeting algorithms will require many propagations in their search for a desired trajectory. For on-board targeting especially, the algorithm must have a simple, fast, and accurate propagator to calculate a trajectory with reasonable computation time, and still be robust enough to remain stable in the various flight regimes that the CEV will experience. This paper compares Cowell s method with a fourth-order Runge- Kutta integrator (RK4), Encke s method with a fourth-order Runge-Kutta- Nystr m integrator (RKN4), and a method known as Multi-Conic. Additionally, the study includes the Bond-Gottlieb 14-element method (BG14) and extends the investigation of Encke-Nystrom methods to integrators of higher order and with variable step size.
This paper explores the uses of planar, simple-periodic symmetrical families of orbits in mission designs in the Earth-Moon system. This classification is defined as the planar periodic orbits that pierce the x-axis in the rotating frame exactly twice per orbit where each piercing is orthogonal to the x-axis. A continuation method has been used to explore several families of this class of orbit in the Earth-Moon restricted three-body system. The invariant manifolds of the unstable orbits in each of these families are then produced and several mission designs are discussed that take advantage of these manifolds. Focus is given to mission designs that implement resonant orbits that periodically fly by the moon.
Recently, various kinds of planetary explorations have become more feasible, taking the advantage of low thrust propulsion means such as ion engines that have come into practical use. The field of space activity has now been expanded even to the rim of the outer solar system. In this context, the Japan Aerospace Exploration Agency (JAXA) has started investigating a Deep Space Port built at the L2 Lagrange point in the Sun-Earth system. For the purpose of making the deep space port practically useful, there is a need to establish a method to making spaceship depart and return from/to the port. This paper first discusses the escape maneuvers originating from the L2 point under the restricted three-body problem. Impulsive maneuvers from the L2 point are extensively studied here, and using the results, optimal low-thrust escape strategies are synthesized. Furthermore, this paper proposes the optimal escape and acceleration maneuvers schemes using Electric Delta-V Earth Gravity Assist (EDVEGA) technique.
Spacecraft capture trajectories to the periodic orbits of the L1 and L2 points in the restricted Hill three-body problem are studied. The specific focus is on transfer to these vicinities from interplanetary trajectories. This application is motivated by future proposals to place "Deep Space ports" at the Earth and Mars L1 or L2 points. These spaceports are considered as candidate gateways for interplanetary transfers in the future. We utilize stable manifolds for capture trajectories to periodic orbits around the libration points. As a result, the cost of capture into a periodic orbit is also reduced relative to direct capture into a parabolic orbit. The way of linking between interplanetary transfer trajectories and the stable manifold is also discussed.
The collinear libration point L3 of the sun-earth+moon system is an ideal place for some space missions. Although there has been a great amount of work concerning the applications of the other two collinear libration points L1 and L2, little work has been done about the point L3. In this paper, the dynamics of the libration points was briefly introduced first. Then a way to transfer the spacecraft to the collinear libration point L3 via the invariant manifolds of the other two collinear libration points was proposed. Theoretical works under the model of circular restricted three-body problem were done. For the sun-earth+moon system, this model is a good approximation. The results obtained are useful when a transfer trajectory under the real solar system is designed.
The National Aeronautics and Space Administration (NASA) solicited proposals in 2006 for an opportunity to include a small secondary payload with the launch of the Lunar Reconnaissance Orbiter (LRO) scheduled for October 2008. The cost cap of the proposal was between $50 and $80M, and the mass cap was 1,000 kilograms. JPL proposed a Lunar Impactor (LI) concept for this solicitation. The mission objective of LI was to impact the permanently shadowed region of a South polar crater ultimately to detect the presence of water. The detection of water ice would prove to be an important factor on future lunar exploration. NASA Ames Research Center also proposed a similar concept, the Lunar Crater observation and Sensing Satellite (LCROSS), which was selected by NASA for the mission. However, in this paper, the trajectory design of the LI proposed by JPL is considered. Since the LI spacecraft was to be launched on the LRO launch vehicle as a secondary payload, its initial trajectory must be diverted at some later time from the LRO trans-lunar trajectory for the subsequent impact. Several such trajectories have been considered, where each trajectory option fields some specific values for the mission parameters. The mission parameters include the availability of LRO instruments at the time of impact for the observation by LRO, the mission duration, the impact velocity, the impact angle, etc. It is possible for the LI to be deflected with a relatively low delta-V to impact a South polar crater at a reasonable impact velocity and impact angle directly with no delay. However, the instruments on-board LRO may not be ready for observation. Thus, several delayed trajectory options have been considered further. The lunar phase at the time of impact may also play an important factor for observation, especially from Earth. Several lunar flyby trajectory maneuvers have been identified to arrive at the Moon for impact at the desired lunar phase. By using a combination of these successive lunar flyby maneuvers, the impact lunar phase may be adjusted to the desired location. A few such trajectories have been suggested. Also, some attempts have been made to maximize the impact velocity by converting the impact trajectory into a retrograde orbit with respect to Earth. Since these types of trajectories take advantage of the Sun-Earth three-body region to minimize the delta-V, the mission duration is relatively long. A few such trajectories are suggested. Also, an attempt has been made to adjust the lunar impact within a desired time period for the optimum Earth observation for the above trajectories. The mission parameters resulting from each trajectory option above are considered and weighed against the cost and robustness of the mission in a brief summary.
This paper reviews progress that has been made in obtaining essentially exact solutions to the nonrelativistic three-body problem for helium by a combination of variational and asymptotic expansion methods. The calculation of relativistic and quantum electrodynamic corrections by perturbation theory is discussed, and in particular, methods for the accurate calculation of the Bethe logarithm part of the electron self energy are presented. As an example, the results are applied to the calculation of isotope shifts for the short-lived 'halo' nucleus He-6 relative to He-4 in order to determine the nuclear charge radius of He-6 from high precision spectroscopic measurements carried out at the Argonne National Laboratory. The results demonstrate that the high precision that is now available from atomic theory is creating new opportunities to create novel measurement tools, and helium, along with hydrogen, can be regarded as a fundamental atomic system whose spectrum is well understood for all practical purposes.
A particular periodic orbit in the Earth-Sun circular restricted three body problem is shown to have the characteristics needed for a ballistic lunar capture transfer. An injection from a circular parking orbit into the periodic orbit serves as an initial guess for a targeting algorithm. By targeting appropriate parameters incrementally in increasingly complicated force models and using precise derivatives calculated from the state transition matrix, a reliable algorithm is produced. Ballistic lunar capture trajectories in restricted four body systems are shown to be able to be produced in a systematic way.
As a fundamental property, the energy budget affects many aspeCts of planets and their moons, such as thermal structure, meteorology, and evolution. We use the observations from two Cassini spectrometers (i.e., CIRS and VIMS) to explore one important component of the energy budget the total emitted power of Jupiter, Saturn, and Titan (Li et al., 2010, 2011, 2012). Key results are: (1) The Cassini observations precisely measure the global-average emitted power of three bodies: 14.l0+/-0.03 Wm(exp -2), 4.952+/-0.035 Wm(exp -2), and 2.834+/-0.012 Wm(exp -2) for Jupiter, Saturn, and Titan, respectively. (2) The meridional distribution of emitted power displays a significant asymmetry between the northern and southern hemispheres on Jupiter and Saturn. On Titan, the meridional distribution of emitted power is basically symmetric around the equator. (3) Comparing with the Voyager measurements, the new Cassini observations reveal a significant temporal variation of emitted power on both Jupiter and Saturn: i) The asymmetry between the two hemisphere shown in the Cassini epoch (2000-2010) is not present in the Voyager epoch (1979-1980); and ii) From the Voyager epoch to the Cassini epoch, the global-average emitted power appeared to increase by approx 3.8% for Jupiter and approx 6.4% for Saturn. (4) Together with previous measurements of the absorbed solar power on Titan, the new Cassini measurements of emitted power provide the first observational evidence of the global energy balance on Titan. The uncertainty in the previous measurements of absorbed solar energy places an upper limit on its energy imbalance of 6.0% on Titan. The exploration of emitted power is the first part of a series of studies examining the temporal variability of the energy budget on the giant planets and Titan. Currently, We are measuring the absorbed solar energy in order to determine new constraints on the energy budgets of Jupiter, Saturn, and Titan.
Linked Autonomous Interplanetary Satellite Orbit Navigation (LiAISON) is a new technique that takes advantage of the asymmetrical gravity field present in a three-body system in order to perform absolute tracking of satellites using only relative satellite-to-satellite observations. Previous studies have demonstrated LiAISON's practical applications for lunar missions, including a satellite in a halo orbit about either the Earth-Moon L1 or L2 point. This paper studies the viability of applying LiAISON measurements between a lunar halo orbiter and a satellite in a geosynchronous orbit. Simulations demonstrate that the absolute positions and velocities of both satellites are observable using only relative measurements with an achieved uncertainty on the order of observation noise.
This investigation is focused specifically on transfers from Earth-Moon L(sub 1)/L(sub 2) libration point orbits to Mars. Initially, the analysis is based in the circular restricted three-body problem to utilize the framework of the invariant manifolds. Various departure scenarios are compared, including arcs that leverage manifolds associated with the Sun-Earth L(sub 2) orbits as well as non-manifold trajectories. For the manifold options, ballistic transfers from Earth-Moon L(sub 2) libration point orbits to Sun-Earth L(sub 1)/L(sub 2) halo orbits are first computed. This autonomous procedure applies to both departure and arrival between the Earth-Moon and Sun-Earth systems. Departure times in the lunar cycle, amplitudes and types of libration point orbits, manifold selection, and the orientation/location of the surface of section all contribute to produce a variety of options. As the destination planet, the ephemeris position for Mars is employed throughout the analysis. The complete transfer is transitioned to the ephemeris model after the initial design phase. Results for multiple departure/arrival scenarios are compared.
Insertion of astronauts into microgravity induces a cascade of physiological adaptations, notably including a cephalad fluid shift. Longer-duration flights carry an increased risk of developing Visual Impairment and Intracranial Pressure (VIIP) syndrome, a spectrum of ophthalmic changes including posterior globe flattening, choroidal folds, distension of the optic nerve sheath, kinking of the optic nerve and potentially permanent degradation of visual function. The slow onset of changes in VIIP, their chronic nature, and the similarity of certain clinical features of VIIP to ophthalmic findings in patients with raised intracranial pressure strongly suggest that: (i) biomechanical factors play a role in VIIP, and (ii) connective tissue remodeling must be accounted for if we wish to understand the pathology of VIIP. Our goal is to elucidate the pathophysiology of VIIP and suggest countermeasures based on biomechanical modeling of ocular tissues, suitably informed by experimental data, and followed by validation and verification. We specifically seek to understand the quasi-homeostatic state that evolves over weeks to months in space, during which ocular tissue remodeling occurs. This effort is informed by three bodies of work: (i) modeling of cephalad fluid shifts; (ii) modeling of ophthalmic tissue biomechanics in glaucoma; and (iii) modeling of connective tissue changes in response to biomechanical loading.
Many academic studies in spaceflight dynamics rely on simplified dynamical models, such as restricted three-body models or averaged forms of the equations of motion of an orbiter. In practice, the end result of these preliminary orbit studies needs to be transformed into more realistic models, in particular to generate good initial guesses for high-fidelity trajectory optimization tools like Mystic. This paper reviews and extends some of the approaches used in the literature to perform such a task, and explores the inherent trade-offs of such a transformation with a view toward automating it for the case of ballistic arcs. Sample test cases in the libration point regimes and small body orbiter transfers are presented.
The problem of a low-thrust spacecraft controlled to a reference orbit is addressed in this paper. A simple and explicit low-thrust guidance scheme with constrained thrust magnitude is developed by combining the fundamental equations of motion for constrained systems from analytical dynamics with a Lyapunov-based method. Examples are given for a spacecraft controlled to a reference trajectory in the circular restricted three body problem.
Various researchers have proposed the use of electrodynamic tethers for power generation and capture from interplanetary transfers. The effect of tether forces on periodic orbits in Jupiter-satellite systems are investigated. A perturbation force is added to the restricted three-body problem model and a series of simplifications allows development of a conservative system that retains the Jacobi integral. Expressions are developed to find modified locations of equilibrium positions. Modified families of Lyapunov orbits are generated as functions of tether size and Jacobi integral. Zero velocity curves and stability analyses are used to evaluate the dynamical properties of tether-modified orbits.
Investigation of new orbit geometries exhibits a very attractive behavior for a spacecraft to monitor space weather coming from the Sun. Several orbit transfer mechanisms are analyzed as potential alternatives to monitor solar activity such as a sub-solar orbit or quasi-satellite orbit and short and long heteroclinic and homoclinic connections between the triangular points L(sub 4) and L(sub 5) and the collinear point L(sub 3) of the Circular Restricted Three-Body Problem (CRTBP) in the Sun-Earth system.