Asteroid science

 An IDP (a fragile-looking one)  Brownleeite TEM photo  Comet 26P/Grigg-Skjellerup (pretty sky photo; can do any comet if this specific one is too hard)  Comparison of some small world surfaces at same scales? Itokawa, 67P, Eros?  JSC sample curation facility (ideally, Keiko in her lab)  Hayabusa2 and OSIRIS-REx art [caption] Some IDPs are fragile, have primitive properties, and do not appear to be related to any meteorite. IDPs probably come from collisions among asteroids and from comet jets, but where any specific particle came from is unknown.

Planetary Defense is a complex problem, not well understood by policy makers and the general public. The recent Chelyabinsk incident in Russia created temporary international attention but has failed to effectively stimulate public action. The lack of long-term attention to cosmic hazards has resulted in limited funding to defend our planet. Hence, it is hard to realistically address this challenge and achieve the high test and operational readiness needed for an effective Planetary Defense strategy. To address this problem, we have created a set of recommendations for the development of a Planetary Defense Program, for the purpose of contributing to the protection of Earth from asteroids and comets. The SSP15 READI Project focused on threats for which there is only a short-term warning, specifically a warning of two years or less from detection of the object to impact. We have provided recommendations in five areas of Planetary Defense including detection and tracking, deflection t...

The vast expanse of space holds limitless wealth in the form of platinum-spangled asteroids, floating gold rocks, and other celestial bodies harboring strategic mineral resources worth quintillions of dollars. Water ice, helium-3, platinum, space gold iron, cobalt, and ammonia are just a glimpse of the bounty waiting to be harvested. However, legal uncertainty surrounding space mining hinders the development of this potentially transformative industry.
The Magnificent Handbook of Space Mining Law cuts through the legal fog, offering a groundbreaking interpretation of existing law that paves the way for responsible and commercially viable space mining.
In this book, the author, Dr. Samuel Japhets, challenges the prevailing notion that the 1967 Outer Space Treaty (OST) prohibits all commercial space mining endeavors.
Through a meticulous legal and policy analysis of Articles 1 and 2, 1967 OST, Dr. Sam argues that in its focus on peaceful uses of outer space, the 1967 OST does not prohibit the commercial taking of minerals lodged in celestial bodies. Rather, the OST prohibits any exclusive sovereign territorial claims over those celestial bodies themselves.
Further, Dr. Sam contends that Title IV of the U.S. 2015 Commercial Space Launch Competitiveness Act (CSLCA) provides the proper legal framework for commercial space mining activities because it provides the most persuasive interpretation of the 1967 OST.
The Magnificent Handbook of Space Mining Law thus dismantles the myth of a celestial "no man's land." It emphasizes that the celestial bodies themselves, distinct from the natural resources that reside in them, are not subject to sovereign territorial claims.
Using legal-historical analysis, the author demonstrates that, subject to other international regulations governing resource appropriation in shared spaces, the riches of outer space are fair game for responsible and sustainable commercial ventures.
State and private space investors, stakeholders, or national agencies can locate, characterize, capture, process, concentrate, and transport these resources to points of use in-situ or on planet Earth.
The Magnificent Handbook of Space Mining Law offers a comprehensive roadmap for navigating the legal landscape of commercial space mining, addressing critical issues like: Reconciling the dueling legal perspectives of the 1967 OST with regards to commercial space mining initiatives; Interpreting and applying Title IV of the U.S. 2015 CSLCA Space;  Ecological / Environmental considerations for commercial space mining; Property rights over asteroid or space minerals when extracted from their natural loci; Integration of principles of collaboration, cooperation, and coordination, with self-interested egoism of states in commercial space mining.
By demystifying space mining law and addressing the investor's need for legal certainty and predictability, The Magnificent Handbook of Space Mining Law paves the way for a future where the celestial bounty can be harnessed for private and commercial benefits, ultimately benefiting all of humanity.
This book is an essential resource for lawyers, legal academia, space entrepreneurs, policymakers, and anyone fascinated by the legal and economic implications of the inevitable allure of commercial space mining.

The two-bodies problem can be fully solved, and was solved by Kepler (1609) and Newton (1687). The general three-body problem is often given as an example of a mathematical problem that 'can't be solved'. So, there is no general analytical solution. This problem can be significant and a special case of this problem is the Circular Restricted Three-Body Problem (CRTBP), which can be applied to the Earth-Moon system with a spacecraft, the Sun-Earth system with an asteroid, etc. In this paper, let's focus on the motion of a test particle near the triangular Lagrange points L 4 and L 5 in the Earth-Moon and the Sun-Earth systems. Studying the movement of an object around these points is especially important for space mission design. To generate a trajectory around these points, the non-linear equations of motion for the circular restricted three-body problem were numerically integrated into MATLAB ® 2023 software and the results are presented in the plane (x, y) and the phase plane (x, v x) and (y, v y). By numerical orbit integration, it is possible to investigate what happens when the displacement is relatively large or short from the Lagrange points. Then the small astronomical body may vibrate around these points. The results in this paper are shown in the rotating and inertia axes. Various initial positions near the Lagrange points and velocities are used to produce various paths the test particle can take. The same examples of numerical studies of trajectories associated with Lagrange points are shown in the inertial and the rotating coordinates system and are discussed. From the results of the numerical tests performed in MATLAB ® 2023, it is possible to saw that there are different types of periodic, quasi-periodic, and chaotic orbits.

Studies of the restricted three interactions in the solar system. The Lagrangian points have important applications in astronautics, since they are equilibrium points of the equation of moti satellite or a space station. Zero velocity curves were plotted for constant values of were used to define areas of the Lagrange points of the Circular Restricted Three equations of mo eigenvalues to investigate the stability. The invariant manifold structures of the collinear libration points for the spatial restricted three dynamical phenomena from a geometric point of view. Earth, Moon and Earth numerically integrated.

In this paper we discuss the position of the libration points and we demonstrate the relationship between curves defined by the Jacobi constant C and the orbital path of the object. This work focuses on the dynamics of a small object (typically an asteroid, a comet, a spacecraft, or just a particle) near the libration points of the Earth-Moon system and a system with the mass ratio µ = 0.0385 (this value is critical). We calculate the position and the Jacobi constant of the libration points for this systems and the threedimensional nonlinear equations of motion were numerically integrated to find the orbital path of the object in three-dimensional Euclidian space. Same orbits are stable, same orbits are unstable and same orbits are chaotic. Chaotic orbits are unpredictable on the long run.

Chapter 1: How to make the electric vehicle viable Friction-less Wind turbine idea: One Idea I had was a slipstream turbine system that could charge the battery as the vehicle went down the road. The wind that naturally moves across a car as it is in motion could be captured in a turbine system that when turned on charges the battery of the car as it sits still or is in motion. Maybe add a feature to the turbine system where the system has a clear channel for maximum airflow as the slipstream goes up and over the car. The system could also allow the air to travel via a channel through the car while moving through friction-less turbine generators generating electricity as the car moves down the road. The vehicle can be designed to create a shape that when in a naturally windy city or town the car can generate electricity as it is sitting still via friction-less wind turbines as ambient wind flows through the turbines.

In order for humans to explore beyond Low Earth Orbit both safely and economically, it will be essential to learn how to make use of in situ materials and energy in an environment much different than on earth. Precursor robotic missions will be necessary to determine what resources will be available and to demonstrate the capabilities for their use. To that end, we have recently been studying acidic Ionic Liquid (IL) systems for use in a low temperature (< 200 C) process to solubilize regolith, and to extract, as water, the oxygen available in metal oxides. Using this method, we have solubilized lunar regolith simulant (JSC-1A), as well as extraterrestrial materials in the form of meteorites, and have extracted up to 80% of the available oxygen. Moreover, by using a hydrogen gas electrode, we have shown that the IL can be regenerated at the anode and metals (e.g. iron) can be plated onto the cathode. These results indicate that IL processing is an excellent candidate for extracti...

Hayabusa2 mission has started as the follow-on mission of Hayabusa. The target asteroid is 1999 JU3, which is a C-type asteroid. The scientific purpose is to study the formation and evolution of the solar system, especially to study the organic matter and water, which existed in the early stage of the solar system formation. The engineering is also important and the spacecraft will be much more robust and reliable with some new technological challenges. The launch of Hayabusa2 is planned at the end of 2014, arriving at the asteroid in the middle of 2018, and it comes back to the earth at the end of 2020. At present, the flight model is under manufacturing.

The NASA Discovery Stardust spacecraft flew by the main belt asteroid 5535 Annefrank at a distance of 3100 km and a speed of 7.4 km/s in November 2002 to test the encounter sequence developed for its primary science target, the comet 81P/Wild 2. During this testing, over 70 images of Annefrank were obtained, taken over a phase angle range from 40 to 140 deg. This viewing showed that Annefrank was at least 6.6 × 5.0 × 3.4 km in size (diameters), with its shortest dimension normal to its orbit plane. Annefrank is highly angular, with flat appearing surfaces, possibly planes formed when it was fractured off of a larger parent body. For the limited part of the surface seen, Annefrank resembles a triangular prism for the main body, with smaller, rounder bodies, possibly accreted through contact.

Experimental results for solar metallurgy, solar powder metallurgy of titanium, solar surface treatment of titanium and titanium welding are briefly reviewed. Most of them were performed at Plataforma Solar de Almeria Spain using solar furnaces SF5 and SF40 in gas/vacuum furnace. Generally, it was observed that the time to achieve required sample temperature is very short when concentrated solar power used. Thanks to use of renewable solar energy these technologies starts to be attractive for industrial production of titanium in Earth solar belt. It can be expected that the obtained results and approaches are similar also in Space. According to the obtained knowledge, the possible solutions/necessary changes for solar furnaces on Moon, Mars and in main asteroids belt are discussed.

The asteroid 101955 Bennu is the target asteroid of the ongoing asteroid sample return mission OSIRIS-REx from NASA. In the mission, the spacecraft is scheduled to rendezvous with Bennu in August 2018. Investigating the dynamics of surface motion can offer guidance for further hopping landers or even sample return missions regarding Bennu or similarly irregular-shaped asteroids. This paper presents the free motion of sample particles on and above the surface of Bennu. The concepts and equations that govern the motion of a particle on and above the surface of an asteroid are briefly introduced. Trajectories of a number of particles' free motion are numerically calculated by considering four scenarios with different restitution coefficients. Initial positions of those particles are all randomly given on the surface of Bennu and their initial velocities are set as zero. The distribution of final locations of those sample particles is summarized and analyzed. Both the gravitational potential and its effective potential on the surface of Bennu are calculated to give a possible reason for the distributing characteristics.

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 L4 and L5 and the collinear point L3 of the CRTBP (circular restricted three-body problem) in the Sun-Earth system. These trajectories could serve as channels through where material can be transported from L5 to L3 by performing small maneuvers at the departure of the Trojan orbit. The size of these maneuvers at L5 is between 299 m/s and 730 m/s depending on the transfer time of the trajectory and does not need any deterministic maneuvers at L3. Our results suggest that material may also be transported from the Trojan orbits to quasi-satellite orbits or even displaced quasi-satellite orbits.

Interest on Large Space Structures (LSS), orbiting in strategic and possibly long-term stable locations, is nowadays increasing in the space community. LSS can serve as strategic outpost to support a variety of manned and unmanned mission, or may carry scientific payloads for astronomical observations. The paper focuses on analysing LSS in the Earth-Moon system, exploring dynamical structures that are available within a multi-body gravitational environment. Coupling between attitude and orbital dynamics is investigated, with particular interest on the gravity gradient torque exerted by the two massive attractors. First, natural periodic orbit-attitude solutions are obtained; a LSS that exploits such solutions would benefit of a naturally periodic body rotation synchronous with the orbital motion, easing the effort of the attitude control system to satisfy pointing requirements. Then, the solar radiation pressure is introduced into the fully coupled dynamical model and its effects investigated, discovering novel periodic attitude solu

Missions to rendezvous with or capture an asteroid present significant interest both from a geophysical and safety point of view. They are key to the understanding of our solar system are as well stepping stones for interplanetary human flight. In this paper, we focus on a rendezvous mission with 2006RH 120 , an asteroid classified as a Temporarily Captured Orbiter (TCO). TCOs form a new population of near Earth objects presenting many advantages toward that goal. Prior to the mission, we consider the spacecraft hibernating on a Halo orbit around the Earth-Moon's L 2 libration point. The objective is to design a transfer for the spacecraft from the parking orbit to rendezvous with 2006RH 120 while minimizing the fuel consumption. Our transfers use indirect methods, based on the Pontryagin Maximum Principle, combined with continuation techniques and a direct method to address the sensitivity of the initialization. We demonstrate that a rendezvous mission with 2006RH 120 can be accomplished with low delta-v. This exploratory work can be seen as a first step to identify good candidates for a rendezvous on a given TCO trajectory.

The theorem of mirror trajectories was proven almost six decades ago by Miele, and states that for a given path in the restricted problem of three bodies (with primaries in mutual circular orbits) there exists a mirror trajectory (in two dimensions) and three mirror paths (in three dimensions). This theorem regards feasible trajectories and proved extremely useful for investigating the natural spacecraft dynamics in the circular restricted problem of three bodies. Several trajectories of crucial importance for mission analysis and design can be identified by using the theorem of mirror trajectories, i.e. (a) free return paths, (b) periodic orbits, and (c) homoclinic connections. Free return paths have been designed and flown in the Apollo missions, because they allow safe ballistic return toward the Earth in case of failure of the main propulsive system. These trajectories belong to the class of mirror paths with a single orthogonal crossing of the axis that connects the Earth and the Moon in the synodic reference system. Instead, if two orthogonal crossings of the same axis exist, then the resulting path is a periodic orbit. A variety of such orbits can be found, encircling either both primaries, a single celestial body, or a collinear libration point. In all cases, periodic orbits represent repeating trajectories that can be traveled indefinitely, (ideally) without any propellant expenditure. Homoclinic connections are special paths that belong to both the stable and the unstable manifold associated with a periodic orbit. These trajectories depart asymptotically from a periodic orbit and can encircle both primaries (even with close approaches) before converging asymptotically toward the initial periodic orbit. After almost six decades, the theorem of mirror trajectories, which clarified the fundamental symmetry properties related to the motion of a third body (or, more concretely, a space vehicle), still excerpts a considerable influence in space mission analysis and design.

Near the Tunguska River in Siberian on 30 June 1908 occurred the explosion in/over the central vent of a paleovolcano, which was associated with a mantle plume. The probability of such an exact hit in the volcanic target for comets/asteroids is close to zero. As a result of hundreds of expeditions to the disaster area, no craters or traces of cosmic substance corresponding to the explosion energy were found. Supporters of comet/asteroid hypotheses concluded that according to barograms and the fall of forest trees at the epicenter, the explosion over the Tunguska paleovolcano could have occurred 5-7 km above the surface. A fragile comet would not penetrate the Earth's atmosphere to such a depth, and an asteroid, in turn, would leave a 2-cm layer of own fragments on the ground [1]. I show that the reason for the 1908 Tunguska event was the joint activity of the Sun and the Moon, starting in the summer of 1907, and especially reinforced from 27 to 30 June 1908, including the time of the solar eclipse on 28 June 1908. The result was a tectonic earthquake of the entire East Siberian platform. This is confirmed, among other things, by registrations by Prof. Weber at the Kiel Observatory of magnetic pulsations from the Tunguska epicenter on 27-30 June 1908. Immersion of stones, i.e. the rise of the surface observed in Tasmania from the beginning of June 1908 and which ceased immediately after the explosion at Tunguska on the morning of 30 June, I attribute to the pressure of underground fluids/gases of the recently discovered Cosgrove's volcanoes in Tasmania. Comets or asteroids could not have caused the surface's uplift in Tasmania. Hence, the hypothesis of an explosion of a cosmic body during the 1908 Tunguska event can be excluded. The boundaries of the observed optical anomalies over Eurasia in the 1908 summer were connected and corresponded to the seismic Perm anomaly, which is located atop the Earth's outer core (LLSVPs Anomaly).

The theorem of mirror trajectories was proven almost six decades ago by Miele, and states that for a given path in the restricted problem of three bodies (with primaries in mutual circular orbits) there exists a mirror trajectory (in two dimensions) and three mirror paths (in three dimensions). This theorem regards feasible trajectories and proved extremely useful for investigating the natural spacecraft dynamics in the circular restricted problem of three bodies. Several trajectories of crucial importance for mission analysis and design can be identified by using the theorem of mirror trajectories, i.e. (a) free return paths, (b) periodic orbits, and (c) homoclinic connections. Free return paths have been designed and flown in the Apollo missions, because they allow safe ballistic return toward the Earth in case of failure of the main propulsive system. These trajectories belong to the class of mirror paths with a single orthogonal crossing of the axis that connects the Earth and the Moon in the synodic reference system. Instead, if two orthogonal crossings of the same axis exist, then the resulting path is a periodic orbit. A variety of such orbits can be found, encircling either both primaries, a single celestial body, or a collinear libration point. In all cases, periodic orbits represent repeating trajectories that can be traveled indefinitely, (ideally) without any propellant expenditure. Homoclinic connections are special paths that belong to both the stable and the unstable manifold associated with a periodic orbit. These trajectories depart asymptotically from a periodic orbit and can encircle both primaries (even with close approaches) before converging asymptotically toward the initial periodic orbit. After almost six decades, the theorem of mirror trajectories, which clarified the fundamental symmetry properties related to the motion of a third body (or, more concretely, a space vehicle), still excerpts a considerable influence in space mission analysis and design.

Regions outside the reach of traditional propulsion systems or the ones that require significant propellant, may be reached by harnessing the solar radiation pressure and leveraging coupled dynamics to maneuver a sail-based spacecraft. Earth-trailing orbits have recently been investigated for getting a unique perspective of the Sun while maintaining the spacecraft in close proximity to Earth. Vertical orbits trailing the Earth exhibit the additional capability to view the Sun from above and below the ecliptic plane. In this work, families of sail-based orbits are explored for varying Earth-trailing angles and Z amplitudes in the Sun-Earth circular restricted three-body problem. Optimization is carried out to ensure that the non-traditional vertical orbits exhibit a constant pitch angle control history, as well as symmetry across the X-Y plane. The stability of the resulting orbit families is assessed using an extension of Flouquet theory to Differential Algebraic Equations. Results indicate that sail-based Earth-trailing vertical orbits can be more stable than traditional sub-L 1 sail-based vertical orbits.

Lagrangian points are essentially points in space with a certain equilibrium. Where satellites or observation telescopes can be parked in a stable orbit. The determination of these Lagrange points corresponds to the three-body gravitational problem, which is difficult to solve analytically. For points L1 and L2, however, a certain formula can be assigned on the basis of certain simplifications, which, depending on the given conditions in the Sun-Earth and Earth-Moon system, yields an acceptable result.

This document reflects the effort of constructing a basis for understanding attitude motion within a multi-body problem with application to spacecraft flight dynamics. The circular restricted three-body problem (CR3BP) is employed as a model for the orbital motion. Then, attitude dynamics is discussed within the CR3BP. Conditions for bounded attitude librations and techniques for the identification of such behavior are presented: initially for a spacecraft fixed at an orbital equilibrium point, and later for a vehicle that moves on non-linear periodic orbit. While previous works focus on specific challenges, this analysis serves to create a more general framework for attitude dynamics within the CR3BP. A larger framework enables additional observations. For example, a linkage is noted between regions of bounded motion that may appear on an attitude grid search map and families of periodic attitude solutions. Finally, coupling effects between attitude and orbit dynamics within the CR3BP, ones that enable new options for trajectory design, are considered an important opportunity, and should be included in a general framework. As a proof of that concept, sailcraft trajectories are generated within a coupled orbit-attitude model only using a sequence of constant commands for the attitude actuators.

The National Aeronautics and Space Administration (NASA) is currently studying an option for the Asteroid Redirect Robotic Mission (ARRM) that would capture a multi-ton boulder (typically 2-4 meters in size) from the surface of a large (~100+ meter) Near-Earth Asteroid (NEA) and return it to cislunar space for subsequent human and robotic exploration. This alternative mission approach, designated the Robotic Boulder Capture Option (Option B), has been investigated to determine the mission feasibility and identify potential differences from the initial ARRM concept of capturing an entire small NEA (4-10 meters in size), which has been designated the Small Asteroid Capture Option (Option A). Compared to the initial ARRM concept, Option B allows for centimeter-level characterization over an entire large NEA, the certainty of target NEA composition type, the ability to select the boulder that is captured, numerous opportunities for mission enhancements to support science objectives, additional experience operating at a low-gravity planetary body including extended surface contact, and the ability to demonstrate future planetary defense strategies on a hazardous-size NEA. Option B can leverage precursor missions and existing Agency capabilities to help ensure mission success by targeting wellcharacterized asteroids and can accommodate uncertain programmatic schedules by tailoring the return mass.

Malcolm Macdonald, Thierry Appourchaux, Vincenzo Andretta, Frédéric Auchère, Frédéric Baudin, Patrick Boumier, Allan Sacha Brun, Thierry Corbard, Andrew N. Fazakerley, Silvano Fineschi, Wolfgang Finsterle, Louise Harra, Richard A. Harrison, Donald Hassler , John Leibacher , Chris J. Owen, Milan Maksimović, Valentín Martínez Pillet, Neil Murphy, Giampiero Naletto, Pierre Rochus, Marco Romoli, Werner Schmutz, Takashi Sekii, Daniele Spadaro

Two problems are considered connected with the use of solar sails on spacecraft (s/c) moving in the vicinity of solar-terrestrial libration points L1 and L2. First problem is related to the exploration of s/c trajectories modification under influence of solar radiation pressure in case with comparatively big solar sails are mounted on s/c. In this case trajectory is shifted further from the Earth and closer to the Sun along Sun-Earth line. The shift may reach one million km or more. Simultaneously its size and shape are also changed. The dependence of these variations upon the mass to area ratio is determined. Such trajectories are interesting for solar wind shock waves investigations because it allows earlier detection of these waves as compared with use of “usual” motion of the s/c in L1 proximity. The other problem explored in the paper is s/c motion control using variation of forces produced by solar radiation pressure. The following approach for this variation is supposed: the ...

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 L4 and L5 and the collinear point L3 of the CRTBP (circular restricted three-body problem) in the Sun-Earth system. These trajectories could serve as channels through where material can be transported from L5 to L3 by performing small maneuvers at the departure of the Trojan orbit. The size of these maneuvers at L5 is between 299 m/s and 730 m/s depending on the transfer time of the trajectory and does not need any deterministic maneuvers at L3. Our results suggest that material may also be transported from the Trojan orbits to quasi-satellite orbits or even displaced quasi-satellite orbits.

The Russian Ministry of Education and Science has awarded us a "megagrant" to study planetary protection from potentially hazardous asteroids. Primarily, this involves developing ideas for surveys to find objects that pass close to the Earth, and develop strategies for deflecting any object found to be on a collision course with the Earth. Various ways are proposed in published works describing how to change an asteroid's orbit in order to prevent its collision with the Earth: Changing the reflection characteristics (albedo) of asteroid's surface to alter the small Yarkovsky acceleration; the use of a "gravitational tractor", when the asteroid's trajectory is changed due to the spacecraft's gravitational effects; targeting a spacecraft to an asteroid to collide with it (kinetic impact). In all these cases, the change in the asteroid's orbital parameters is quite small, generally comparable to the size of the asteroid's orbit determination errors. In this paper plans are discussed to develop a method of asteroid deflection, which is radically different from those mentioned above.

This paper addresses the computation of the required trajectory correction maneuvers (TCM) for a halo orbit space mission to compensate for the launch velocity errors introduced by inaccuracies of the launch vehicle. By combining dynamical systems theory with optimal control techniques, we produce a portrait of the complex landscape of the trajectory design space. This approach enables parametric studies not available to mission designers a few years ago, such as how the magnitude of the errors and the timing of the first TCM affect the correction ∆V. The impetus for combining dynamical systems theory and optimal control in this problem arises from design issues for the Genesis Discovery mission being developed for NASA by the Jet Propulsion Laboratory.

We extend the analysis, started in a previous work [1], concerning the formation of lunar impact craters due to low-energy trajectories. First, we adopt the Circular Restricted Three-Body Problem and consider different choices of initial conditions inside the stable invariant manifold associated with the central invariant one in the neighborhood of the L 2 equilibrium point in the Earth-Moon system. Then we move to the Bicircular Restricted Four-Body Problem to study the effect of the Sun on the distribution of impacts on the Moon's surface.

A primary challenge of low-thrust mission design is the development of an initial guess for the state and control history of a trajectory. To address this challenge, one technique assembles dynamical structures, such as periodic orbits and their associated manifolds, into discontinuous chains that are corrected to locally optimal transfer solutions via direct transcription. In this investigation, dynamical structures that leverage a low-thrust force in a multi-body regime are incorporated into the orbit chain to expand the options available for construction of an initial guess and to guide the direct transcription algorithm toward different categories of locally optimal solutions. The properties and structures of the low-thrust model that facilitate orbit chain construction are demonstrated in representative transfer scenarios. Direct transcription is applied to converge upon locally optimal transfer trajectories in both simplified and ephemeris models. Results indicate that low-thr...

In this paper we consider how 'near' term solar sails can be used in formation above the ecliptic plane to provide platforms for accurate and continuous remote sensing of the polar regions of the Earth. The dynamics of the solar sail elliptical restricted three-body problem (ERTBP) are exploited for formation flying by identifying a family of periodic orbits above the ecliptic plane. Moreover, we find a family of 1 year periodic orbits where

Introduction: Space exploration missions are dependent on large vehicles launched from Earth even when the payloads are small. Even though staging would increae the efficiency of missions to other planets and celectial bodies, the massive launch vehicles needed for the completion of such missions make them practically infeasible. If propellants can be produced and stored on the Moon, Mars, etc., the need for these massive systems disappears, making space exploration more feasible (technically and economically) and safe because redundant and emergency systems can then be created at lower costs and shorther times. Background: Obviously, the availability of resources plays a mayor role as it does the performance of the current rocket engines. When studying the Moon and Mars there are two clear choices: oxygen/hydrogen, and oxygen/methane propulsion systems. We have chosen to use data from the Apollo missions to asses the availability of resources o the Moon and other data from NASA mis...

In this paper, an adaptive control algorithm is presented to enable a spacecraft to track desired trajectories near the Lz Lagrange point in the Sun-Earth system. An adaptive full-state feedback control law, designed using a Lyapunov-type analysis, exhibits globally asymptotic position tracking in the presence of the unknown spacecraft mass. The control law is simulated for a Lyapunov orbit in the vicinity of the LZ Lagrange point as the periodic reference trajectory.

While no known asteroid poses a threat to Earth for at least the next century, the catalog of near-Earth asteroids is incomplete for objects whose impacts would produce regional devastation 1,2. Several approaches have been proposed to potentially prevent an asteroid impact with Earth by deflecting or disrupting an asteroid 1-3. A test of kinetic impact technology was identified as the highest priority space mission related to asteroid mitigation 1. NASA's Double Asteroid Redirection Test (DART) mission is the first full-scale test of kinetic impact technology. The mission's target asteroid was Dimorphos, the secondary member of the S-type binary near-Earth asteroid (65803) Didymos. This binary asteroid system was chosen to enable ground-based telescopes to quantify the asteroid deflection caused by DART's impact 4. While past missions have utilized impactors to investigate the properties of small bodies 5,6 , those earlier missions were not intended to deflect their targets and did not achieve measurable deflections. Here we report the DART spacecraft's autonomous kinetic impact into Dimorphos and reconstruct the impact event, including the timeline leading to impact, the location and nature of the DART impact site, and the size and shape of Dimorphos. The successful impact of the DART spacecraft with Dimorphos and the resulting change in Dimorphos's orbit 7 demonstrates that kinetic impactor technology is a viable technique to potentially defend Earth if necessary.

Asteroids and comets are of strategic importance for science in an effort to uncover the formation, evolution and composition of the Solar System. Near-Earth objects (NEOs) are of particular interest because of its accessibility from Earth, but also because of their speculated wealth of resources. The exploitation of these resources has long been discussed as a means to lower the cost of future space endeavours. In this paper, we analyze the possibility of retrieving entire objects from accessible heliocentric orbits and moving them into the Earth's neighbourhood. The asteroid retrieval transfers are sought from the continuum of low energy transfers enabled by the dynamics of invariant manifolds; specifically, the retrieval transfers target planar, vertical Lyapunov and halo orbit families associated with the collinear equilibrium points of the Sun-Earth Circular Restricted Three Body problem. The judicious use of these dynamical features provides the best opportunity to find extremely low energy Earth transfers for asteroidal material. With the objective to minimise transfer costs, a global search of impulsive transfers connecting the unperturbed asteroid's orbit with the stable manifold phase of the transfer is performed. A catalogue of asteroid retrieval opportunities of currently known NEOs is presented here. Despite the highly incomplete census of very small asteroids, the catalogue can already be populated with 12 different objects retrievable with less than 500 m/s of Δv. All, but one, of these objects have an expected size and transfer requirements that can be met by current propulsion technologies. Moreover, the methodology proposed represents a robust search for future retrieval candidates that can be automatically applied to a growing survey of NEOs. I. Recently, significant interest has been devoted to the understanding of minor bodies of the Solar System, including near-Earth and main belt asteroids and comets. NASA, ESA and JAXA have conceived a series of missions to obtain data from such bodies, having in mind that their characterisation not only provides a deeper insight into the Solar System, but also represents a technological challenge for space exploration. Near Earth Objects (NEO), in particular, have also stepped into prominence because of two important aspects: they are among the easiest celestial bodies to reach from the Earth and they may represent a threat to our planet.

The coupled orbit and attitude motion of a spacecraft in three dimensional (halo) reference orbits is explored in this investigation within the context of the Circular Restricted Three Body Problem (CR3BP). The motion of a spacecraft, comprised of two rigid bodies connected by a single degree of freedom joint, is examined. The nonlinear variational form of the equations of motion is employed to mitigate numerical effects caused by large discrepancies in the length scales. Several nonlinear, periodic reference orbits in the vicinity of the collinear libration points are selected for case studies and the effects of the orbit on the orientation, as well as the orientation on the orbit, are examined. Additionally, the model is extended to include solar radiation pressure and the motion of a solar sail type spacecraft is considered.

A key challenge in low-thrust trajectory design is generating preliminary solutions that simultaneously specify the spacecraft position and velocity vectors, as well as the thrust history. To mitigate this difficulty, dynamical structures within a combined low-thrust circular restricted 3-body problem (CR3BP) are investigated as candidate solutions to seed initial low-thrust trajectory designs. The addition of low-thrust to the CR3BP modifies the locations and stability of the equilibria, offering novel geometries for mission applications. Transfers between these novel equilibria are constructed by leveraging the associated stable and unstable manifolds and insights from the low-thrust CR3BP.

The NASA Discovery Stardust spacecraft flew by the main belt asteroid 5535 Annefrank at a distance of 3100 km and a speed of 7.4 km/s in November 2002 to test the encounter sequence developed for its primary science target, the comet 81P/Wild 2. During this testing, over 70 images of Annefrank were obtained, taken over a phase angle range from 40 to 140 deg. This viewing showed that Annefrank was at least 6.6 Â 5.0 Â 3.4 km in size (diameters), with its shortest dimension normal to its orbit plane. Annefrank is highly angular, with flat appearing surfaces, possibly planes formed when it was fractured off of a larger parent body. For the limited part of the surface seen, Annefrank resembles a triangular prism for the main body, with smaller, rounder bodies, possibly accreted through contact.

Malcolm Macdonald, Thierry Appourchaux, Vincenzo Andretta, Frédéric Auchère, Frédéric Baudin, Patrick Boumier, Allan Sacha Brun, Thierry Corbard, Andrew N. Fazakerley, Silvano Fineschi, Wolfgang Finsterle, Louise Harra, Richard A. Harrison, Donald Hassler , John Leibacher , Chris J. Owen, Milan Maksimović, Valentín Martínez Pillet, Neil Murphy, Giampiero Naletto, Pierre Rochus, Marco Romoli, Werner Schmutz, Takashi Sekii, Daniele Spadaro

Without additional attitude and orbital control systems, such as thrusters, solar-sail trajectories are controlled by the orientation of the sailcraft. The sail attitude is employed to target the sailcraft to some future state along the reference trajectory. In a "turnand-hold" strategy, the attitude profile consists of at least three orientations between an initial and future, target state along the trajectory. Because of orbit-knowledge, control, and turn-modeling errors, a look-ahead control strategy is generated, one in which only the first turn from the profile is performed, and then a new profile is constructed based on updated orbit knowledge. The initial hold intervals, along with the number of turns, used to generate an attitude profile is automatically adapted to improve convergence of the algorithm. This technique is generally successful when applied to reference trajectories generated in an Earth-Moon-Sun ephemeris regime.

Despite numerous successful missions to small celestial bodies, the gravity field of such targets has been poorly characterized so far. Gravity estimates can be used to infer the internal structure and composition of small bodies and, as such, have strong implications in the fields of planetary science, planetary defense, and in-situ resource utilization. Current gravimetry techniques at small bodies mostly rely on tracking the spacecraft orbital motion, where the gravity observability is low. To date, only lower-degree and order spherical harmonics of small-body gravity fields could be resolved. In this paper, we evaluate gravimetry performance for a novel mission architecture where artificial probes repeatedly hop across the surface of the small body and perform low-altitude, suborbital arcs. Such probes are tracked using optical measurements from the mothership's onboard camera and orbit determination is performed to estimate the probe trajectories, the small body's rotational kinematics, and the gravity field. The suborbital motion of the probes provides dense observations at low altitude, where the gravity signal is stronger. We assess the impact of observation parameters and mission duration on gravity observability. Results suggest that the gravitational spherical harmonics of a small body with the same mass as the asteroid Bennu, can be observed at least up to degree 40 within months of observations. Measurement precision and frequency are key to achieve high-performance gravimetry.