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Lagrange points in the Earth-Moon system The three-body problem In 1722, Leonard Euler proved the existence of the collinear libration point. In 1765, Lagrange found the triangular libration point L4 and L5 [4, Fig. 2]. In 1899, Henri Poincaré proved that the restricted problem was unsolvable and analytic, differentiable function of both the initial conditions and the time. Solving this problem is infinitely complex because of its many nonlinear dynamical systems which still have no closed form solution [5].
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This paper describes the results of a study to find possible Near Earth Asteroids (NEA) capable of being captured using upcoming rocketry for the purposes of space-based mining, combining reusable rockets such as SpaceX's Big Falcon Rocket (i.e. BFR) and refueling capabilities. This work introduces a relatively low-cost option with higher Delta V,...
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... used to perform feasibility analysis of multiple asteroid retrieval missions (MARM) and the return of NEOs for the purposes of space based refining and construction. Moreover, the tool can be used dynamically to predict different MARM projects based on different parameters from upcoming updates from SpaceX, NASA, JPL and the science community. Fig. 2]. In 1899, Henri Poincaré proved that the restricted problem was unsolvable and analytic, differentiable function of both the initial conditions and the time. Solving this problem is infinitely complex because of its many nonlinear dynamical systems which still have no closed form solution ...
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![Figure 4. SpaceX's Starship payload delivery [13].](profile/Gustavo-Gargioni/publication/343803212/figure/fig4/AS:945374344790024@1602406216943/SpaceXs-Starship-payload-delivery-13_Q320.jpg)
This paper aims to analyze the feasibility of a space-mining operation by estimating hardware acquisition and refueling operations expenses for a 30-year Multiple Asteroid Retrieval Mission (MARM). The study builds on previous work on possible Near-Earth Asteroids (NEA) capable of being captured using upcoming rocketry for space-based mining. It co...
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... Asteroid mining studies from Elvis [13][14][15], Craig [16] and Gargioni [17][18][19] used analytical models to provide high-level discussion for asteroid mining, where no detailed trajectories were used. Some studies used more detailed trajectories, whether through the analytical [20,21] or numerical approach [22][23][24][25][26], for mining mission planning. ...
This paper presents a generic framework for Near-Earth Asteroid (NEA) mining campaign design and analysis. It integrates various modules that cover the target selection, trajectory generation, mission opportunity search, economic analyses and campaign scheduling and optimization. Each module is independent and can be exchanged for various mission scenarios and fidelity levels. The use of the framework is first illustrated in the Bennu mining campaign design. For the Bennu water mining campaign with the impulsive propulsion, three mining seasons are observed. During a mining season, the Net Present Value (NPV) could reach $2,000 M, while the NPV outside the mining season is about $500 M. The framework is also utilized in the sensitivity analysis. Several key factors deciding the profitability of NEA mining campaigns are studied. Lastly, using the proposed framework, mining campaigns are numerically designed. Based on the observation of periodic changes of economic returns, NEA mining seasons are identified and categorized into three major types based on their feasibility for mining. Targets with different types of mining seasons have different levels of constraints on mission windows, and different mining strategies can be made accordingly.
... Note that transfers to L 4 are beyond the scope of the investigation in this paper. The fundamental objective of this study is thus to harness the natural dynamics of a spacecraft about L 4 to produce a stable periodic orbit that permits the study of LO [28]. Additionally, for Solar corona observations, the SPO family falls within the umbra of the Moon every synodic period. ...
This paper proposes a framework for a satellite mission with the goal to perform Lunar Occultations within the context of the circular restricted three-body problem (CR3BP) of the Earth-Moon system. This is achieved by exploiting the geometrical relationships between the Earth, Moon, and a spacecraft orbiting around L4. Additionally, it examines the viability of a linear state-feedback control policy to stabilize short-period orbits under the presence of the gravitational effect of the Sun, Solar radiation pressure, and the Lunar orbital eccentricity, which is not accounted for in the CR3BP dynamics. Given the unprecedented NUV angular resolution achieved by a spacecraft at L4, this research proposes a framework for a remote sensing observatory for Solar activity, thereby enabling the monitoring of the entire hemisphere of Solar radiation, and to study different astrophysical issues via Lunar Occultations.
... Equilibrium points of the CR3BP[42]. ...
... 17 The overarching objective of the investigation is to leverage the natural dynamics between L 4 and the Moon and come up with a stable periodic orbit that is useful to observe the Solar corona. 18 The Sun, Earth, Moon, and L 4 all share geometric relationships that may be exploited to discover the proper positioning of a given s/c in the periodic orbit such that the necessity of stationkeeping is reduced. 19 If properly designed, the periodic orbit may require minimal adjustments to orbital perturbations and instability. ...
There is a significant interest in studying the Solar corona to gather information
about the Sun. This investigation provides an efficient approach to observe the So-
lar corona by using the Moon as an occulter to suppress the blinding luminosity of
the Sun’s surface. Another objective is an analysis and comparison of diffraction
patterns created by Lunar occultations (LO) from L4 and from Earth. By exploit-
ing the Libration point L4 within the Cislunar region, a spacecraft (s/c) would be
within proper position to observe the Solar corona every sidereal month.
... O projeto, antes de ser cancelado em 2017 devido a cortes no orçamento na NASA (NASA, 2017), tinha por objetivo a captura de NEAs para fins de pesquisa e exploração comercial.A consutoria de negócios Morgan Stanley acredita que a indústria espacial triplicará até 2040, alcançando valores acima de USD 1 trilhão (STANLEY, 2020), devido a dois fatores: novas tecnologias e novos conhecimentos adquiridos. De acordo comGargioni et al. (2019), astrônomos do Lincoln Near-Earth Asteroid Research Lab estimam, por exemplo, que o asteroide Ryugu valha algo em torno de USD 82 bilhões em minerais, sendo composto principalmente de níquel, ferro, cobalto, água, nitrogênio, hidrogênio e amônia.Esse pequeno asteroide de pouco menos de 2 km de extensão foi visitado pela sonda Hayabusa-2, da Agência Espacial Japonesa (JAXA). A missão concluiu com êxito o primeiro objetivo de trazer para a Terra o material coletado, obtido por meio de breve contato da sonda com o asteroide em 2019. ...
The use of resources from asteroids was introduced more than 100 years ago by Konstantin Tsiolkovsky. In order for this to be possible, it is necessary that these objects are inserted into orbits close to Earth so that they can be explored and researched. Transporting these to Distant Retrograde Orbits (DROs) in the cislunar region has been proposed in the past. Pires e Winter (2020) mapped stable DROs in the cislunar region that can be used for this purpose. This work presents an analysis of determining optimal transfer orbits from an LEO to stable DROs. Transfer optimal conditions are determined through a semi-analytical method performed with the Rebound integrator. The optimal transfers are geocentric Keplerian orbits in which the total specific impulse ∆v of the maneuvers is minimized. The actual orbit of simulated transfer under the N-body problem (PNC) Sun + Earth + Moon + spacecraft diverges slightly from the theoretical Keplerian orbit. Such divergence is quantified by calculating the distance between the position in the real orbit and the respective position in the theoretical Keplerian orbit for the same instant of time. Among a total of 427 cislunar DROs stable for 103 years mapped, a subset of 43 was selected with initial conditions uniformly distributed in a region initially 15% to 20% of the Earth-Moon distance from the Moon. For each of the conditions analyzed, the method determined dozens of optimal transfer orbits in different points of the DRO characterizing multiple optimal transfer options, i.e. each consists of a local minimum point. It is observed that the insertion points of these multiple options, when mapped in the Earth-Moon rotating frame, are not evenly distributed but concentrated on 2 very specific islands. The analysis also revealed that among the dozens of optimal orbits determined for each initial condition, those with the smallest ∆v are localized mainly on one of the 2 mentioned regions. Applying in the context of asteroid exploration, these selected DROs are potential parking orbits for these objects to be inserted, requiring low energy to be reached by a spacecraft departing from Earth.
... Equilibrium points of the CR3BP[39] ...
The work proposes a systematic method to compute an optimal transfer trajectory between two non-Keplerian halo orbits in the Circular Restricted Three body formulation of the Earth-Moon dynamics. The paper exploits the knowledge of the natural non-linear dynamics and the primer vector theory applied to the Circular Restricted Three Body Problem to design optimal Halo-to-Halo transfers with fixed and limited, compared with the rest of the literature, Time of flight, from every point of the departure orbit to every point of the arrival orbit. With the goal
... For each scenario for which the optimization found no solution, meaning that the non-linear constraints could not be satisfied, no information is given. For scenarios involving Earth-based resources (first column), ∆V I is the ∆V from the parking orbit (at 185 km [45]) to the destination, because there is only a cargo spacecraft directly from LEO, without a mining phase, as discussed in Section 2.1. ...
Space resource utilization (SRU) can be a catalyst for a growing space economy. Significant reductions in cost, launch mass and risk for human and robotic activities beyond Earth can be achieved. Commercial entities will have the opportunity to generate revenue through economic development, allowing for a decreased dependency on governmental agencies for the exploration of space. A wide variety of materials can be found on planetary and small solar system bodies, which are potentially of great use to customers in space. This paper conducts a comparison of the economic and commercial potential of SRU on the surface of the Moon, Mars, a representative near-Earth asteroid and a representative main-belt asteroid. In particular, mining of water will be considered which will be electrolyzed into hydrogen and oxygen using solar power. Coupled economic and trajectory optimization then results in the minimum specific cost to deliver propellant (LOX/LH2) from these bodies to a number of customer locations. Customers on the surface of or in orbit around the Earth, Moon, and Mars are investigated, along with Psyche, a large metallic main-belt asteroid. Using a cost model that considers technology maturation to allow current aviation-like costs to be used for development and manufacturing, missions are optimized. Results show that for customers beyond low-Earth orbit, SRU should be used instead of launching water-derived resource directly from the Earth. In particular, near-Earth asteroids are shown to be in an attractive location for mining, processing and delivering a large quantity of LOX/LH2 at a low specific cost, for customers in the vicinity of the Earth and the Moon, including nearby collinear Lagrange points. Exceptions are customers on the surface of the Earth and the Moon, who, together with customers on the surface of Mars, are better off mining and processing on that same surface. A sensitivity analysis shows that, for all investigated customers except Psyche, there are near-Earth asteroids available which can be used to deliver water-derived resources for a lower specific cost than the most ideal main-belt asteroid. Only once these near-Earth asteroids have been depleted, mining main-belt asteroids and transporting resources back to a customer in the vicinity of the Earth is worth considering.
... Current work focuses on asteroid classification (Bus and Binzel, 2003), developing architectures and designing missions for asteroid mining (Andrews et al., 2015;Dorrington and Olsen, 2019), compiling sets of attainable target asteroids (Sanchez and McInnes, 2011;Yárnoz et al., 2013), trajectory optimization to NEAs (Tan et al., 2018;Peloni et al., 2016;Mingotti et al., 2014;Sánchez and Yárnoz, 2016), employing reusable launch vehicles (e.g., SpaceX BFR (Gargioni et al., 2019)) for asteroid mining missions or employing solar sails for sample return and mining missions (Dachwald and Seboldt, 2005;Hughes et al., 2006;McInnes, 2017;Peloni et al., 2016;Grundmann et al., 2019) and the economic modelling of asteroid mining ventures (Sonter, 1997;Ross, 2001;Hein et al., 2020;Gertsch and Gertsch, 2005;Andrews et al., 2015;Oxnevad, 1991;Dorrington and Olsen, 2019). While this addresses many issues important during the design of a profitable asteroid mining mission, little research has been done on integrating economical modelling into the optimization of trajectories to NEAs. ...
... • Chemical propulsion: launch to LEO (185 km) using the SpaceX BFR (Gargioni et al., 2019), which is used at its maximum allowable payload capacity (150 tons (Musk, 2018), i.e., 136 metric tonnes) with the cargo spacecraft and a kick stage, both including propellant. The kick stage will bring the cargo spacecraft from LEO to an escape trajectory with C 3 = 0 km 2 /s 2 . ...
... • Solar sail: launch to LEO (185 km) using the SpaceX BFR (Gargioni et al., 2019), which is again used at its maximum allowable payload capacity (136 metric tonnes (Musk, 2018)) with a fleet of mid-term solar sails (lightness number β 0 = 0.1 (Dachwald, 2005)) and a kick stage including propellant used to inject the stowed sails to an Earth escape trajectory with C 3 = 0 km 2 /s 2 . A fleet is used to ensure that the sails are of reasonable size, rather than one very large sail. ...
Asteroid mining has the potential to greatly reduce the cost of in-space manufacturing, production of propellant for space transportation and consumables for crewed spacecraft, compared to launching the required resources from the Earth’s deep gravity well. This paper discusses the top-level mission architecture and trajectory design for these resource-return missions, comparing high-thrust trajectories with continuous low-thrust solar-sail trajectories. The paper focuses on maximizing the economic Net Present Value, which takes the time-cost of finance into account and therefore balances the returned resource mass and mission duration. The different propulsion methods are compared in terms of maximum economic return and sets of attainable target asteroids. Results for transporting resources to geostationary orbit show that the orbital parameter hyperspace of suitable target asteroids is considerably larger for solar sails, allowing for more flexibility in selecting potential target asteroids. Also, results show that the Net Present Value that can be realized is larger when employing solar sailing instead of chemical propulsion. In addition, it is demonstrated that a higher Net Present Value can be realized when transporting volatiles to the Lunar Gateway instead of geostationary orbit. The paper provides one more step towards making commercial asteroid mining an economically viable reality by integrating trajectory design, propulsion technology and economic modelling.
... For the cost, it considers the acquisition of a fleet and 30-year refueling launch operations. By dividing the total mass of the 33 asteroids, the resulting cost was estimated per kg to be at USD 902/kg [2]. Although the feasibility of acquisition and its cost may be close to proper valuation, many technical challenges remain, see [3]. ...
... CNEOS provides almost a million predictions of close approaches (CAs). Utilizing the on-line tool from previous work [2], we combine and retrieve data from CAs and the asteroid classical orbital elements (COEs) into a single and vast matrix, or spreadsheet. In this matrix, rows represent CAs, and columns represent a field compressing a piece of information relative to the close approach. ...
... where m o " 1, 640, 000kg is the gross mass of the customized Starship from previous work [2], g is the gravity at the Earth's sea level, and Isp is the specific impulse of the Raptor engines on the Starship, from section 4. Third, the collected portion of the asteroid adds mass to the spacecraft during return. Equating the ∆V for departure and return, and recognizing that g and Isp are the same the following equation is obtained ...
This paper aims to analyze the feasibility of a space-mining operation by estimating hardware acquisition and refueling operations expenses for a 30-year Multiple Asteroid Retrieval Mission (MARM). The study builds on previous work on possible Near-Earth Asteroids (NEA) capable of being captured using upcoming rocketry for space-based mining. It combines the re-usability of rocket architecture with refueling capabilities to reduce costs. Furthermore, it expands the mission requirements to include a variable retrieval mass, whereas previous work only considered missions that allowed for the entirety of an asteroid to be retrieved. This paper developed a high-level point of view of the mining industry, which proposes to constrain the operation under an estimated amount of investment and logistical cost. Asteroid Retrieval Missions (ARMs) depart from L2 Halo orbit. The time window for the space mining operation is proposed to be three decades, starting in 2030. The logistics of fuel from the Earth's surface to L2 Halo is presented to refueled each ARM. Previously developed data mining online tool that searches for Near-Earth Asteroids (NEA) close approach database from JPL and the small body database from NASA was used as a dataset for possible candidates. The final solution was the retrieval of 60,430 metric tons with the cost per kg of USD 333.44. It reflects an 87.62% reduction in cost per kg compared to previous work.
... Moreover, asteroid resources could provide bulk material in (Earth) orbit, for example for propellant for crewed deep space exploration missions or material for the fabrication of space-based habitats. [2][3][4][5][6] Many important issues for the success of asteroid mining missions are being addressed: classification of near-Earth asteroids (NEAs), 7 trajectory optimisation to and from NEAs, [8][9][10][11][12][13] mining equipment [14][15][16] and economic modelling of these missions. [4][5][6]17,18 For economic modelling, many assumptions must be made concerning a range of elements of the mission. ...
A range of resources can be extracted from asteroids, for example volatiles for propellant and consumables for (crewed) spacecraft, semi-conductors and metals for in-space manufacturing or platinum group metals for terrestrial use. One of the key justifications for in-situ manufacturing/resource utilisation is the high costs incurred during launch from the Earth’s deep gravity well. However, selling asteroid-derived resources in Earth orbit at a price competitive with launching the same resources from the Earth’s surface is largely dependent on specific launch costs, especially for low value-to-mass resources such as volatiles and construction materials. This paper investigates the influence of the cost and payload capacity of launch vehicles on asteroid mining profitability. Results demonstrate that for resources delivered to GEO, if the launch cost decreases, the specific launch cost (per kg) decreases in such a way that the decrease in total cost is smaller than the decrease in revenue, resulting in a less profitable mission. Similarly, when the payload capacity increases and therefore the specific launch cost decreases, the resulting mission also generates less profit. Sensitivity analyses show that for an example mission with two round trips to the same asteroid, profits increase with the increased number of trips, if the asteroid has not been fully depleted. Similarly, a further sensitivity analysis demonstrates that by changing the destination orbit for the processed resources to the Lunar Gateway, increased profit margins can be realised.
