Earth–Mars transfers with ballistic escape and low-thrust capture

In this paper novel Earth–Mars transfers are presented. These transfers exploit the natural dynamics of n-body models as well as the high specific impulse typical of low-thrust systems. The Moon-perturbed version of the Sun–Earth problem is introduced to design ballistic escape orbits performing lunar gravity assists. The ballistic capture is designed in the Sun–Mars system where special attainable sets are defined and used to handle the low-thrust control. The complete trajectory is optimized in the full n-body problem which takes into account planets’ orbital inclinations and eccentricities. Accurate, efficient solutions with reasonable flight times are presented and compared with known results.     

Fast Earth–Moon transfers with ballistic capture

This contribution deals with fast Earth–Moon transfers with ballistic capture in the patched three-body model. We compute ensembles of preliminary solutions using a model that takes into account the relative inclination of the orbital planes of the primaries. The ballistic capture orbits around the Moon are obtained relying on the hyperbolic invariant structures associated to the collinear Lagrangian points of the Earth–Moon system, and the Sun–Earth system portion of the transfers are quasi-periodic orbits obtained by a genetic algorithm. The trajectories are designed to be good initial guesses to search optimal cost-efficient short-time Earth–Moon transfers with ballistic capture in more realistic models.     

Cylindrical isomorphic mapping applied to invariant manifold dynamics for Earth–Moon Missions

Several families of periodic orbits exist in the context of the circular restricted three-body problem. This work studies orbital motion of a spacecraft among these periodic orbits in the Earth–Moon system, using the planar circular restricted three-body problem model. A new cylindrical representation of the spacecraft phase space (i.e., position and velocity) is described, and allows representing periodic orbits and the related invariant manifolds. In the proximity of the libration points, the manifolds form a four-fold surface, if the cylindrical coordinates are employed. Orbits departing from the Earth and transiting toward the Moon correspond to the trajectories located inside this four-fold surface. The isomorphic mapping under consideration is also useful for describing the topology of the invariant manifolds, which exhibit a complex geometrical stretch-and-folding behavior as the associated trajectories reach increasing distances from the libration orbit. Moreover, the cylindrical representation reveals extremely useful for detecting periodic orbits around the primaries and the libration points, as well as the possible existence of heteroclinic connections. These are asymptotic trajectories that are ideally traveled at zero-propellant cost. This circumstance implies the possibility of performing concretely a variety of complex Earth–Moon missions, by combining different types of trajectory arcs belonging to the manifolds. This work studies also the possible application of manifold dynamics to defining a suitable, convenient end-of-life strategy for spacecraft placed in any of the unstable orbits. The final disposal orbit is an externally confined trajectory, never approaching the Earth or the Moon, and can be entered by means of a single velocity impulse (of modest magnitude) along the right unstable manifold that emanates from the Lyapunov orbit at \(L_2\) .     

Sun–Earth L_{1} and L_{2} to Moon transfers exploiting natural dynamics

This paper examines the design of transfers from the Sun–Earth libration orbits, at the \(L_{1}\) and \(L_{2}\) points, towards the Moon using natural dynamics in order to assess the feasibility of future disposal or lifetime extension operations. With an eye to the probably small quantity of propellant left when its operational life has ended, the spacecraft leaves the libration point orbit on an unstable invariant manifold to bring itself closer to the Earth and Moon. The total trajectory is modeled in the coupled circular restricted three-body problem, and some preliminary study of the use of solar radiation pressure is also provided. The concept of survivability and event maps is introduced to obtain suitable conditions that can be targeted such that the spacecraft impacts, or is weakly captured by, the Moon. Weak capture at the Moon is studied by method of these maps. Some results for planar Lyapunov orbits at \(L_{1}\) and \(L_{2}\) are given, as well as some results for the operational orbit of SOHO.     

Combined low-thrust propulsion and invariant manifold trajectories to capture NEOs in the Sun–Earth circular restricted three-body problem

In this paper, a method to capture near-Earth objects (NEOs) incorporating low-thrust propulsion into the invariant manifolds technique is investigated. Assuming that a tugboat-spacecraft is in a rendez-vous condition with the candidate asteroid, the aim is to take the joint spacecraft-asteroid system to a selected periodic orbit of the Sun–Earth restricted three-body system: the orbit can be either a libration point periodic orbit (LPO) or a distant prograde periodic orbit (DPO) around the Earth. In detail, low-thrust propulsion is used to bring the joint spacecraft-asteroid system from the initial condition to a point belonging to the stable manifold associated to the final periodic orbit: from here onward, thanks to the intrinsic dynamics of the physical model adopted, the flight is purely ballistic. Dedicated guided and capture sets are introduced to exploit the combined use of low-thrust propulsion with stable manifolds trajectories, aiming at defining feasible first guess solutions. Then, an optimal control problem is formulated to refine and improve them. This approach enables a new class of missions, whose solutions are not obtainable neither through the patched-conics method nor through the classic invariant manifolds technique.     

A study of halo orbits at the Sun–Mars L1 Lagrangian point in the photogravitational restricted three-body problem

Photogravitational Restricted Three-Body Problem (PGRTBP) is considered and halo orbits are generated in the vicinity of the Sun–Mars L₁ Lagrangian point. Deviation of properties such as time period, size and velocity variation in the halo orbits with Sun as a source of radiation are discussed. With increase in solar radiation pressure, the halo orbits are found to elongate and move towards the Sun and the time period of the halo orbits is found to increase. The variation in the behaviour of invariant manifolds with change in radiation pressure is also computed and it is found that as the radiation pressure increases, the transition from Mars-centric path to heliocentric path is delayed. Certain implications of the velocity profile of the invariant manifolds are also discussed.     

Extension of fast periodic transfer orbits from the Earth–Moon RTBP to the Sun–Earth–Moon Quasi-Bicircular Problem

Starting from 80 families of low-energy fast periodic transfer orbits in the Earth–Moon planar circular Restricted Three Body Problem (RTBP), we obtain by analytical continuation 11 periodic orbits and 25 periodic arcs with similar properties in the Sun–Earth–Moon Quasi-Bicircular Problem (QBCP). A novel and very simple procedure is introduced giving the solar phases at which to attempt continuation. Detailed numerical results for each periodic orbit and arc found are given, including their stability parameters and minimal distances to the Earth and Moon. The periods of these orbits are between 2.5 and 5 synodic months, their energies are among the lowest possible to achieve an Earth–Moon transfer, and they show a diversity of circumlunar trajectories, making them good candidates for missions requiring repeated passages around the Earth and the Moon with close approaches to the last.     

Power law distribution of pressure drops in dust devils: Observation techniques and Earth–Mars comparison

Data from the Pathfinder and Phoenix landers on Mars show transient pressure drops (～1–4 per day) attributed to nearby encounters with dust devils or dust-free vortices. The distribution of pressure drop amplitudes is consistent with a truncated power law distribution with a slope of ?2, similar to that suggested previously for the optical diameters of dust devils. Comparable data from terrestrial field observations are very sparse: the only published dataset is half a century old and lists only 19 pressure drops. That dataset is too small to permit a robust comparison with Mars and likely suffers from a low detection efficiency at small dust devil sizes. Observed pressure drops in these fixed-station Mars datasets (30–300 μbar) are 10× lower than those typically observed on Earth (0.3–3 mbar): some higher drops have been reported for large terrestrial devils sampled by pursuing vehicles. The needed terrestrial data for comparison with Mars in-situ data (soon to be augmented, we hope, by the Mars Science Laboratory mission) is noted. Prospects for obtaining such data via field campaigns using new data acquisition technology, and with microbarographs for nuclear test monitoring, are discussed.     

Methane emissions from Earth’s degassing: Implications for Mars

The presence of methane on Mars is of great interest, since one possibility for its origin is that it derives from living microbes. However, CH₄ in the martian atmosphere also could be attributable to geologic emissions released through pathways similar to those occurring on Earth. Using recent data on methane degassing of the Earth, we have estimated the relative terrestrial contributions of fossil geologic methane vs. modern methane from living methanogens, and have examined the significance that various geologic sources might have for Mars.Geologic degassing includes microbial methane (produced by ancient methanogens), thermogenic methane (from maturation of sedimentary organic matter), and subordinately geothermal and volcanic methane (mainly produced abiogenically). Our analysis suggests that ～80% of the “natural” emission to the terrestrial atmosphere originates from modern microbial activity and ～20% originates from geologic degassing, for a total CH₄ emission of ～28.0×10⁷ tonnes year^?1.Estimates of methane emission on Mars range from 12.6×10¹ to 57.0×10⁴ tonnes year^?1 and are 3–6 orders of magnitude lower than that estimated for Earth. Nevertheless, the recently detected martian, Northern-Summer-2003 CH₄ plume could be compared with methane expulsion from large mud volcanoes or from the integrated emission of a few hundred gas seeps, such as many of those located in Europe, USA, Mid-East or Asia. Methane could also be released by diffuse microseepage from martian soil, even if macro-seeps or mud volcanoes were lacking or inactive. We calculated that a weak microseepage spread over a few tens of km², as frequently occurs on Earth, may be sufficient to generate the lower estimate of methane emission in the martian atmosphere.At least 65% of Earth’s degassing is provided by kerogen thermogenesis. A similar process may exist on Mars, where kerogen might include abiogenic organics (delivered by meteorites and comets) and remnants of possible, past martian life. The remainder of terrestrial degassed methane is attributed to fossil microbial gas (～25%) and geothermal-volcanic emissions (～10%). Global abiogenic emissions from serpentinization are negligible on Earth, but, on Mars, individual seeps from serpentinization could be significant. Gas discharge from clathrate-permafrost destabilization should also be considered.Finally, we have shown examples of potential degassing pathways on Mars, including mud volcano-like structures, fault and fracture systems, and major volcanic edifices. All these types of structures could provide avenues for extensive gas expulsion, as on Earth. Future investigations of martian methane should be focused on such potential pathways.     

Indirect transfer to the Earth–Moon L1 libration point

The Earth–Moon L1 libration point is proposed as a human gateway for space transportation system of the future. This paper studies indirect transfer using the perturbed stable manifold and lunar flyby to the Earth–Moon L1 libration point. Although traditional studies indicate that indirect transfer to the Earth–Moon L1 libration point does not save much fuel, this study shows that energy efficient indirect transfer using the perturbed stable manifold and lunar flyby could be constructed in an elegant way. The design process is given to construct indirect transfer to the Earth–Moon L1 libration point. Simulation results show that indirect transfer to the Earth–Moon L1 libration point saves about 420 m/s maneuver velocity compared to direct transfer, although the flight time is about 20 days longer.     

The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System

Starting from the four-body problem a generalization of both the restricted three-body problem and the Hill three-body problem is derived. The model is time periodic and contains two parameters: the mass ratio ν of the restricted three-body problem and the period parameter m of the Hill Variation orbit. In the proper coordinate frames the restricted three-body problem is recovered as m → 0 and the classical Hill three-body problem is recovered as ν → 0. This model also predicts motions described by earlier researchers using specific models of the Earth–Moon–Sun system. An application of the current model to the motion of a spacecraft in the Sun perturbed Earth–Moon system is made using Hill's Variation orbit for the motion of the Earth–Moon system. The model is general enough to apply to the motion of an infinitesimal mass under the influence of any two primaries which orbit a larger mass. Using the model, numerical investigations of the structure of motions around the geometric position of the triangular Lagrange points are performed. Values of the parameter ν range in the neighborhood of the Earth–Moon value as the parameter m increases from 0 to 0.195 at which point the Hill Variation orbit becomes unstable. Two families of planar periodic orbits are studied in detail as the parameters m and ν vary. These families contain stable and unstable members in the plane and all have the out-of-plane stability. The stable and unstable manifolds of the unstable periodic orbits are computed and found to be trapped in a geometric area of phase space over long periods of time for ranges of the parameter values including the Earth–Moon–Sun system. This model is derived from the general four-body problem by rigorous application of the Hill and restricted approximations. The validity of the Hill approximation is discussed in light of the actual geometry of the Earth–Moon–Sun system. This revised version was published online in July 2006 with corrections to the Cover Date.     

Carbon dioxide glaciers on Mars: Products of recent low obliquity epochs (?)

Three localized sets of small arcuate ridges associated with slopes in the northern polar area of Mars (∼70°N latitude) are morphologically similar to sets of drop moraines left by episodes of advance and retreat of cold-based glaciers. Comparison with other glacial features on Mars shows that these features differ in important aspects from those associated with water–ice flow. Instead, we interpret these features to be due to perennial accumulation and flow of solid carbon dioxide during recent periods of very low spin-axis obliquity.     

Gullies and their relationships to the dust–ice mantle in the northwestern Argyre Basin,Mars

We investigated gullies and their relationships to the atmospherically derived dust–ice mantle and aeolian features in the northwestern part of the Argyre basin. A detailed morphologic map of the Argyre study region allowed us to constrain the stratigraphic relationships and relative ages of gullies. In addition, we investigated the morphologic characteristics and orientations of all gullies in the Argyre study region. Maximum absolute ages for gullies were determined with crater size–frequency distribution measurements of the dust–ice mantle, which is the source material of gullies in the study area. Gullies only evolve from this mantle probably by melting of its ice content. Two different morphologies of pristine and degraded gullies were identified, mostly occurring on pole- and equatorward-facing slopes, respectively. We conclude that the morphologies and orientations were initiated either by a more rapid and extensive erosion of equatorward-facing gullies or by at least two generations of gullies with generally older gullies on equatorward-facing slopes and younger ones on pole-facing slopes. Different intensities of solar insolation on equator- and pole-facing slopes might be responsible for the different development of pristine and degraded gullies. Gullies in the study area generally have ages ?20 Ma. Some uncratered (and thus very young) aeolian dunes are superposed by a few gullies in some locations, indicating another even younger generation of gullies with an upper limit absolute model age of about <500 ka.     

The Sun–Earth saddle point: characterization and opportunities to test general relativity

The saddle points are locations where the net gravitational accelerations balance. These regions are gathering more attention within the astrophysics community. Regions about the saddle points present clean, close-to-zero background acceleration environments where possible deviations from General Relativity can be tested and quantified. Their location suggests that flying through a saddle point can be accomplished by leveraging highly nonlinear orbits. In this paper, the geometrical and dynamical properties of the Sun–Earth saddle point are characterized. A systematic approach is devised to find ballistic orbits that experience one or multiple passages through this point. A parametric analysis is performed to consider spacecraft initially on \(L_{1,2}\) Lagrange point orbits. Sun–Earth saddle point ballistic fly-through trajectories are evaluated and classified for potential use. Results indicate an abundance of short-duration, regular solutions with a variety of characteristics.     

Transfers from the Earth to $$L_2$$ L 2 Halo orbits in the Earth–Moon bicircular problem

Celestial Mechanics and Dynamical Astronomy - The Cassini spacecraft discovered many close-in small satellites in Saturnian system, and several of them exhibit exotic orbital states due to...     

Mars: Topographic control of clouds, 1907–1973

Mariner 9 high-resolution photos and topographic information were used to make a topographic analysis of “blue” and “red” cloud positions reported over a 66-year period in Lowell Observatory records. A sample of 77 “blue” cloud sites lay preferentially at the highest Martian elevations; 60% centered precisely on the seven major volcanic mountain peaks (unknown when the clouds were observed); another 16% lay on substantial slopes or contacts between cratered terrain and lower plains. The median altitude of blue cloud sites was 2.1 km above the global topographic median. These results agree with other evidence that most Earth-detected blue clouds are orographic uplift clouds, composed of condensates. Over half of 131 sporadic yellowish or red clouds were associated with blue clouds or volcanoes, and thus probably did not represent dust storm phenomena, contrary to a commonly held belief. Of 88 “possible dust clouds” (chosen by additional criteria), about two-thirds occur at borders between light and dark areas, in the light regions. These sites may have thin veneers of dust, and current depositional or denudational activity. Median altitude of “possible dust cloud” sites was 0.5 km below the global topographic median. Major dust storms begin in a few “core areas,” two of which associate with major basins Hellas and Isidis, probable reservoirs of mobile dust; but exact topographic control and causes of dust storms are unclear.     

Earth–Moon Separation Problem In The Motion Of Near Earth Asteroids

The analysis of application of two dynamical models (``Earth–Moon' and``barycentre' model) in the motion of Near Earth Asteroids was performed. Mainaim was the quantitative estimation of the influence of lunar perturbations on the motionof NEA. Additionally, basic tests of application of numerical methods weremade (RMVS3 and B–S methods). The orbits of 1083 Apollo–Aten–Amor and 7selected AAA objects were adopted as test particles in numerical integrationof the motion. The comparison between results obtained by both dynamicalmodels is discussed in detail. In specific cases, the application of the``Earth–Moon' dynamical model is very important and cannot be neglected incomputations of orbits.