Trans-Lunar Cruise Trajectory Design of GRAIL (Gravity Recovery and Interior Laboratory) Mission

Chung, Min-Kun; Hatch, Sara J.; Kangas, Julie A.; Long, Stacia M.; Roncoli, Ralph B.; Sweetser, Theodore H.

doi:10.2514/6.2010-8384

Cited by 15 publications

(5 citation statements)

References 2 publications

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“…Focusing on impulsive transfers, the complexity of these ranges from simple Hohmann transfers in a two-body model to weak stability boundary transfers with ballistic capture at the Moon in more complete astrodynamical models (Belbruno and Miller 1993;Hatch et al 2010). Particularly, an initial flyby at the Moon was proved to be a key feature to obtain an Earth-Moon transfer with a cost approaching the theoretical minimum of 3726 m/s, as estimated by Sweetser (1991).…”

Section: Introductionmentioning

confidence: 99%

On optimal three-impulse Earth–Moon transfers in a four-body model

Grossi,

Buonagura,

Giordano

et al. 2024

Celest Mech Dyn Astron

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Within the emerging age of lunar exploration, optimizing transfer trajectories is a fundamental measure toward achieving more economical and efficient lunar missions. This study addresses the possibility of reducing the fuel cost of two-impulse Earth–Moon transfers in a four-body model with the Earth, the Moon, and the Sun as primaries. Lawden’s primer vector theory is applied within this framework to derive a set of necessary conditions for a fuel-optimal trajectory. These conditions are used to identify which trajectories from an existing database could benefit from the insertion of an additional intermediate impulse. More than 10,000 three-impulse transfers are computed with a direct numerical optimization method. These solutions contribute to enriching the database of impulsive trajectories, useful to perform trade-off analyses. While the majority of trajectories exhibit only marginal improvements, a significant breakthrough emerges for transfers featuring an initial gravity assist at the Moon. Implementing a corrective maneuver after the lunar encounter yields substantial reductions in fuel costs.

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Section: Introductionmentioning

confidence: 99%

On optimal three-impulse Earth–Moon transfers in a four-body model

Grossi,

Buonagura,

Giordano

et al. 2024

Celest Mech Dyn Astron

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“…The spacecraft performs small trajectory correction maneuvers, but otherwise coasts ballistically during the transfer. The GRAIL mission 1,2,3 is implementing a low-energy transfer 4 that is operationally similar to the direct transfer; that is, it involves a large maneuver to depart the Earth, a large maneuver to insert into orbit at the Moon, and a ballistic coast. The transfer requires less fuel, given the same propulsion system, though it requires 2-3 additional months of transfer duration.…”

Section: Introductionmentioning

confidence: 99%

“…From there they perform a series of maneuvers to transition into their science orbit. 3 In order to compare the GRAIL trajectory with those surveyed in this paper, and with the Apollo transfer discussed above, each GRAIL spacecraft would have a velocity of approximately 2.30 km/s at an altitude of 100 km if they did not initiate their orbit insertion before that point. A hypothetical impulsive orbit insertion maneuver would require a ΔV of approximately 0.67 km/s to insert each spacecraft into similar circular 100-km lunar orbits.…”

Section: Introductionmentioning

confidence: 99%

Surveying Ballistic Transfers to Low Lunar Orbit

Parker

Anderson

Peterson

2013

Journal of Guidance, Control, and Dynamics

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A simple strategy is identified to generate ballistic transfers between the Earth and Moon, i.e., transfers that perform two maneuvers: a trans-lunar injection maneuver to depart the Earth and a Lunar Orbit Insertion maneuver to insert into orbit at the Moon. This strategy is used to survey the performance of numerous transfers between varying Earth parking orbits and varying low lunar target orbits. The transfers surveyed include short 3-6 day direct transfers, longer 3-4 month lowenergy transfers, and variants that include Earth phasing orbits and/or lunar flybys.

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“…Exploiting BC grants several benefits in terms of both cost reduction (Belbruno and Miller, 1993) and mission versatility (Belbruno and Carrico, 2000;Topputo and Belbruno, 2015), in general at the cost of longer transfer times (Circi and Teofilatto, 2001;Ivashkin, 2002). In the past, the BC mechanism was used to rescue Hiten (Belbruno and Miller, 1990), and to design insertion trajectories in lunar missions like SMART-1 (Racca et al, 2002) and GRAIL (Chung et al, 2010). In the near future, BepiColombo will exploit BC orbits to be weakly captured by Mercury (Benkhoff et al, 2021;Schuster and Jehn, 2014).…”

mentioning

confidence: 99%

Stable sets mapping with Taylor differential algebra with application to ballistic capture orbits around Mars

Caleb

Merisio

Lizia

et al. 2022

Celest Mech Dyn Astron

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Ballistic capture orbits offer safer Mars injection at longer transfer time. However, the search for such an extremely rare event is a computationally-intensive process. Indeed, it requires the propagation of a grid sampling the whole search space. This work proposes a novel ballistic capture search algorithm based on Taylor differential algebra propagation. This algorithm provides a continuous description of the search space compared to classical grid sampling research and focuses on areas where the nonlinearities are the largest. Macroscopic analyses have been carried out to obtain cartography of large sets of solutions. Two criteria, named consistency and quality, are defined to assess this new algorithm and to compare its performances with classical grid sampling of the search space around Mars. Results show that differential algebra mapping works on large search spaces, and automatic domain splitting captures the dynamical variations on the whole domain successfully. The consistency criterion shows that more than 87% of the search space is guaranteed as accurate, with the quality criterion kept over 80%.Ballistic capture (BC) allows a spacecraft to approach a planet and enter a temporary orbit about it without requiring maneuvers in between. As part of the low-energy transfers, it is a valuable alternative to Keplerian approaches. Exploiting BC grants several benefits in terms of both cost reduction (Belbruno and Miller, 1993) and mission versatility (Belbruno and Carrico, 2000;Topputo and Belbruno, 2015), in general at the cost of longer transfer times (Circi and Teofilatto, 2001;Ivashkin, 2002). In the past, the BC mechanism was used to rescue Hiten (Belbruno and Miller, 1990), and to design insertion trajectories in lunar missions like SMART-1 (Racca et al, 2002) and GRAIL (Chung et al, 2010). In the near future, BepiColombo will exploit BC orbits to be weakly captured by Mercury (Benkhoff et al, 2021;Schuster and Jehn, 2014). BC is an event occurring in extremely rare occasions and requires acquiring a proper state (position and velocity) far away from the target planet (Topputo and Belbruno, 2015). In fact, massive numerical simulations are required to find the specific conditions that support capture (Topputo and Belbruno, 2009) and only approximately 1 out of 10 000 states lead to capture (Luo and Topputo, 2015). In a first effort to reduce the computational burden, the variational theory for

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Trans-Lunar Cruise Trajectory Design of GRAIL (Gravity Recovery and Interior Laboratory) Mission

Cited by 15 publications

References 2 publications

On optimal three-impulse Earth–Moon transfers in a four-body model

On optimal three-impulse Earth–Moon transfers in a four-body model

Surveying Ballistic Transfers to Low Lunar Orbit

Stable sets mapping with Taylor differential algebra with application to ballistic capture orbits around Mars

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