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Navigation Between Geosynchronous and Lunar L1 Orbiters

Linked Autonomous Interplanetary Satellite Orbit Navigation (LiAISON) is a new technique that takes advantage of the asymmetrical gravity field present in a three-body system in order to perform absolute tracking of satellites using only relative satellite-to-satellite observations. Previous studies have demonstrated LiAISON's practical applications for lunar missions, including a satellite in a halo orbit about either the Earth-Moon L1 or L2 point. This paper studies the viability of applying LiAISON measurements between a lunar halo orbiter and a satellite in a geosynchronous orbit. Simulations demonstrate that the absolute positions and velocities of both satellites are observable using only relative measurements with an achieved uncertainty on the order of observation noise.

low-energy↗

Properties of Ground Level Enhancement Events and the Associated Solar Eruptions During Solar Cycle 23

Solar cycle 23 witnessed the most complete set of observations of coronal mass ejections (CMEs) associated with the Ground Level Enhancement (GLE) events. We present an overview of the observed properties of the GLEs and those of the two associated phenomena, viz., flares and CMEs, both being potential sources of particle acceleration. Although we do not find a striking correlation between the GLE intensity and the parameters of flares and CMEs, the solar eruptions are very intense involving X-class flares and extreme CME speeds (average approx. 2000 km/s). An M7.1 flare and a 1200 km/s CME are the weakest events in the list of 16 GLE events. Most (80 %) of the CMEs are full halos with the three non-halos having widths in the range 167 to 212 degrees. The active regions in which the GLE events originate are generally large: 1290 msh (median 1010 msh) compared to 934 msh (median: 790 msh) for SEP-producing active regions. For accurate estimation of the CME height at the time of metric type II onset and GLE particle release, we estimated the initial acceleration of the CMEs using flare and CME observations. The initial acceleration of GLE-associated CMEs is much larger (by a factor of 2) than that of ordinary CMEs (2.3 km/sq s vs. 1 km/sq s). We confirmed the initial acceleration for two events for which CME measurements are available in the inner corona. The GLE particle release is delayed with respect to the onset of all electromagnetic signatures of the eruptions: type II bursts, low frequency type III bursts, soft X-ray flares and CMEs. The presence of metric type II radio bursts some 17 min (median: 16 min; range: 3 to 48 min) before the GLE onset indicates shock formation well before the particle release. The release of GLE particles occurs when the CMEs reach an average height of approx 3.09 R(sub s) (median: 3.18 R (sub s) ; range: 1.71 to 4.01 R (sub s) ) for well-connected events (source longitude in the range W20–W90). For poorly connected events, the average CME height at GLE particle release is ∼66 % larger (mean: 5.18 R (sub s) ; median: 4.61 R (sub s) ; range: 2.75–8.49 R (sub s) ). The longitudinal dependence is consistent with shock accelerations because the shocks from poorly connected events need to expand more to cross the field lines connecting to an Earth observer. On the other hand, the CME height at metric type II burst onset has no longitudinal dependence because electromagnetic signals do not require magnetic connectivity to the observer. For several events, the GLE particle release is very close to the time of first appearance of the CME in the coronagraphic field of view, so we independently confirmed the CME height at particle release. The CME height at metric type II burst onset is in the narrow range 1.29 to 1.8 R(sub s), with mean and median values of 1.53 and 1.47 R(sub s). The CME heights at metric type II burst onset and GLE particle release correspond to the minimum and maximum in the Alfven speed profile. The increase in CME speed between these two heights suggests an increase in Alfvenic Mach number from 2 to 3. The CME heights at GLE particle release are in good agreement with those obtained from the velocity dispersion analysis, including the source longitude dependence. We also discuss the implications of the delay of GLE particle release with respect to complex type III bursts by approx 18 min (median: 16 in; range: 2 to 44 min) for the flare acceleration mechanism. A similar analysis is also performed on the delay of particle release relative to the hard X-ray emission.

Geomagnetic Storms↗

Probing Pre-Galactic Metal Enrichment with High-Redshift Gamma-Ray Bursts

We explore high-redshift gamma-ray bursts (GRBs) as promising tools to probe pre-galactic metal enrichment. We utilize the bright afterglow of a Population III (Pop III) GRB exploding in a primordial dwarf galaxy as a luminous background source, and calculate the strength of metal absorption lines that are imprinted by the first heavy elements in the intergalactic medium (IGM). To derive the GRB absorption line diagnostics, we use an existing highly resolved simulation of the formation of a first galaxy which is characterized by the onset of atomic hydrogen cooling in a halo with virial temperature approximately greater than10(exp 4) K.We explore the unusual circumburst environment inside the systems that hosted Pop III stars, modeling the density evolution with the self-similar solution for a champagne flow. For minihalos close to the cooling threshold, the circumburst density is roughly proportional to (1 + z) with values of about a few cm(exp −3). In more massive halos, corresponding to the first galaxies, the density may be larger, n approximately greater than100 cm(exp −3). The resulting afterglow fluxes are weakly dependent on redshift at a fixed observed time, and may be detectable with the James Webb Space Telescope and Very Large Array in the near-IR and radio wavebands, respectively, out to redshift z approximately greater than 20. We predict that the maximum of the afterglow emission shifts from near-IR to millimeter bands with peak fluxes from mJy to Jy at different observed times. The metal absorption line signature is expected to be detectable in the near future. GRBs are ideal tools for probing the metal enrichment in the early IGM, due to their high luminosities and featureless power-law spectra. The metals in the first galaxies produced by the first supernova (SN) explosions are likely to reside in low-ionization stages (C II, O I, Si II and Fe II). We show that, if the afterglow can be observed sufficiently early, analysis of the metal lines may distinguish whether the first heavy elements were produced in a pair-instability supernova or a core-collapse (Type II) SN, thus constraining the initial mass function of the first stars.

Metal↗

The Contribution of z < or Approx. 6 Sources to the Spatial Coherence in the Unresolved Cosmic Near-Infrared and X-Ray Backgrounds

A spatial clustering signal has been established in Spitzer/IRAC measurements of the unresolved cosmic near-infrared background (CIB) out to large angular scales, approx. 1deg. This CIB signal, while significantly exceeding the contribution from the remaining known galaxies, was further found to be coherent at a highly statistically significant level with the unresolved soft cosmic X-ray background (CXB). This measurement probes the unresolved CXB to very faint source levels using deep near-IR source subtraction.We study contributions from extragalactic populations at low to intermediate redshifts to the measured positive cross-power signal of the CIB fluctuations with the CXB. We model the X-ray emission from active galactic nuclei (AGNs), normal galaxies, and hot gas residing in virialized structures, calculating their CXB contribution including their spatial coherence with all infrared emitting counterparts. We use a halo model framework to calculate the auto and cross-power spectra of the unresolved fluctuations based on the latest constraints of the halo occupation distribution and the biasing of AGNs, galaxies, and diffuse emission. At small angular scales (1), the 4.5microns versus 0.5-2 keV coherence can be explained by shot noise from galaxies and AGNs. However, at large angular scales (approx.10), we find that the net contribution from the modeled populations is only able to account for approx. 3% of the measured CIB×CXB cross-power. The discrepancy suggests that the CIB×CXB signal originates from the same unknown source population producing the CIB clustering signal out to approx. 1deg.

unresolved cosmic near infrared background (CIB)↗

Shock Heating of the Merging Galaxy Cluster A521

A521 is an interacting galaxy cluster located at z = 0.247, hosting a low-frequency radio halo connected to an eastern radio relic. Previous Chandra observations hinted at the presence of an X-ray brightness edge at the position of the relic, which may be a shock front. We analyze a deep observation of A521 recently performed with XMM-Newton in order to probe the cluster structure up to the outermost regions covered by the radio emission. The cluster atmosphere exhibits various brightness and temperature anisotropies. In particular, two cluster cores appear to be separated by two cold fronts. We find two shock fronts, one that was suggested by Chandra and that is propagating to the east, and another to the southwestern cluster outskirt. The two main interacting clusters appear to be separated by a shock-heated region, which exhibits a spatial correlation with the radio halo. The outer edge of the radio relic coincides spatially with a shock front, suggesting that this shock is responsible for the generation of cosmic-ray electrons in the relic. The propagation direction and Mach number of the shock front derived from the gas density jump, M = 2.4 +/- 0.2, are consistent with expectations from the radio spectral index, under the assumption of Fermi I acceleration mechanism.

Bourdin, H.↗

Ensemble Forecasting of Coronal Mass Ejections Using the WSA-ENLIL with CONED Model

The combination of the Wang-Sheeley-Arge (WSA) coronal model, ENLIL heliospherical model version 2.7, and CONED Model version 1.3 (WSA-ENLIL with CONED Model) was employed to form ensemble forecasts for 15 halo coronal mass ejections (halo CMEs). The input parameter distributions were formed from 100 sets of CME cone parameters derived from the CONED Model. The CONED Model used image processing along with the bootstrap approach to automatically calculate cone parameter distributions from SOHO/LASCO imagery based on techniques described by Pulkkinen et al. (2010). The input parameter distributions were used as input to WSA-ENLIL to calculate the temporal evolution of the CMEs, which were analyzed to determine the propagation times to the L1 Lagrangian point and the maximum Kp indices due to the impact of the CMEs on the Earth's magnetosphere. The Newell et al. (2007) Kp index formula was employed to calculate the maximum Kp indices based on the predicted solar wind parameters near Earth assuming two magnetic field orientations: a completely southward magnetic field and a uniformly distributed clock-angle in the Newell et al. (2007) Kp index formula. The forecasts for 5 of the 15 events had accuracy such that the actual propagation time was within the ensemble average plus or minus one standard deviation. Using the completely southward magnetic field assumption, 10 of the 15 events contained the actual maximum Kp index within the range of the ensemble forecast, compared to 9 of the 15 events when using a uniformly distributed clock angle.

coronal mass↗

Lunar Phase Function at 1064 Nm from Lunar Orbiter Laser Altimeter Passive and Active Radiometry

We present initial calibration and results of passive radiometry collected by the Lunar Orbiter Laser Altimeter onboard the Lunar Reconnaissance Orbiter over the course of 12 months. After correcting for time- and temperature-dependent dark noise and detector responsivity variations, the LOLA passive radiometry measurements are brought onto the absolute radiance scale of the SELENE Spectral Profiler. The resulting photometric precision is estimated to be 5%. We leverage the unique ability of LOLA to measure normal albedo to explore the 1064 nm phase function's dependence on various geologic parameters. On a global scale, we find that iron abundance and optical maturity (quantified by FeO and OMAT) are the dominant controlling parameters. Titanium abundance (TiO2), surface roughness on decimeter to decameter scales, and soil thermo- physical properties have a smaller effect, but the latter two are correlated with OMAT, indicating that exposure age is the driving force behind their effects in a globally-averaged sense. The phase function also exhibits a dependence on surface slope at approximately 300 m baselines, possibly the result of mass wasting exposing immature material and/or less space weathering due to reduced sky visibility. Modeling the photometric function in the Hapke framework, we find that, relative to the highlands, the maria exhibit decreased backscattering, a smaller opposition effect (OE) width, and a smaller OE amplitude. Immature highlands regolith has a higher backscattering fraction and a larger OE width compared to mature highlands regolith. Within the maria, the backscattering fraction and OE width show little dependence on TiO2 and OMAT. Variations in the phase function shape at large phase angles are observed in and around the Copernican-aged Jackson crater, including its dark halo, a putative impact melt deposit. Finally, the phase function of the Reiner Gamma Formation behaves more optically immature than is typical for its composition and OMAT, suggesting the visible-to-near-infrared spectrum and phase function respond differently to the unusual regolith evolution and properties at this location. The phase difference map revealed additional geologically-influenced variations in the phase function's shape. In particular, variations were observed associated with the dark halo around Jackson crater, the impact ejecta of Copernicus and Giordano Bruno, and the Reiner Gamma Formation. For the latter, we 915 found that the phase function behaves more optically immature than the global phase function for its composition and OMAT, suggesting a difference in how the visible-to-near-IR spectrum and phase function respond to the unusual regolith evolution and properties at this location.

moon↗

Transfer Trajectory Options for Servicing Sun-Earth-Moon Libration Point Missions

Future missions to the Sun-Earth Libration L1 and L2 regions will require scheduled servicing to maintain hardware and replenish consumables. While there have been statements made by various NASA programs regarding servicing of vehicles at these locations or in Cis-lunar space, a practical transfer study has not been extensively investigated in an operational fashion to determine the impacts of navigation and maneuver errors. This investigation uses dynamical systems and operational models to design transfer trajectories between the Sun-Earth Libration region (QuasiHalo orbit) and the Earth-Moon vicinity (Distant Retrograde Orbit, QuasiHalo Orbit, Halo Orbit, and Near Rectilinear Halo Orbit). We address the total delta V cost of transfers between each pair of locations using a Monte Carlo analysis.

Earth↗

Dynamics of Asteroid 2006 RH120: Pre-Capture and Escape Phases

Asteroid 2006 RH120 was the first natural object captured by the Earth to be observed called a Minimoon. In this work, we show that the invariant manifolds of the orbits around the L1 and L2 Lagrange points play a significant role in the capture of the asteroid around Earth and its eventual escape from the Earth approximately 1 year later. This is similar to the Temporary Capture of comets around Jupiter. We determined that the asteroid was in a 27:29 mean motion resonance with the Earth and approached the Earth through the stable manifold of an L1 Northern Halo Orbit. After the Temporary Capture, the asteroid escaped the Earth through the unstable manifold of an L2 Southern Halo orbit and into a 21:20 resonant orbit with the Earth. The asteroid travelled through a series of resonant orbits before and after the capture. These resonant transitions are similar to the orbits of Galileo and Cassini during their touring phase, using resonant orbits to reduce mission ∆V requirements.

NEO↗

Transfer Trajectory Options for Servicing Sun-Earth-Moon Libration Point Missions

Future missions to the Sun-Earth Libration L1 and L2 regions will require scheduled servicing to maintain hardware and replenish consumables. While there have been statements made by various NASA programs regarding servicing of vehicles at these locations or in Cis-lunar space, a practical transfer study has not been extensively investigated in an operational fashion to determine the impacts of navigation and maneuver errors. This investigation uses dynamical systems and operational models to design transfer trajectories between the Sun-Earth Libration region (QuasiHalo orbit) and the Earth-Moon vicinity (Distant Retrograde Orbit, QuasiHalo Orbit, Halo Orbit, and Near Rectilinear Halo Orbit). We address the total ΔV cost of transfers and operational considerations between each pair of locations using a Monte Carlo analysis.

Folta, David C.↗

A Flexible Lunar Architecture for Exploration (FLARE) Supporting NASA’s Artemis Program

The Flexible Lunar Architecture for Exploration (FLARE) is a concept to deliver four crew to the lunar surface for a minimum of seven days and then return them safely to Earth. FLARE can be implemented whenever the component vehicles are operational. FLARE was developed as an alternative to NASA’s Human Landing System (HLS) reference architecture from the Design Analysis Cycle (DAC) #2 created in 2019. The DAC2 guidelines required utilization of the Gateway vehicle in a Near- Rectilinear Halo Orbit (NRHO). Instead, FLARE chooses a Low Lunar Frozen Polar Orbit (LLFPO) for lunar rendezvous of components, and an optional Gateway vehicle. The LLFPO provides a stable orbit that overflies the south pole every 2 h, ensuring easy access to the lunar surface for surface aborts with a much lower propellant requirement than NRHO. The minimum FLARE concept uses one Space Launch System (SLS) launch, one Orion, one European Service Module (ESM), and one human lander (launched on commercial vehicle(s)). FLARE adds the SpaceTug, based upon the mature and successful ULA “Common” Centaur Upper Stage vehicle, with modifications to create an Earth-Moon transfer vehicle. In the FLARE baseline mission, the SpaceTug provides propulsion needed to return the Orion + ESM from LLFPO to Earth. The SpaceTug also provides propulsion to deliver the separate human lander components – the Descent Element (DE) and the Ascent Element (AE) - from Low Earth Orbit (LEO) to LLFPO. The SLS Block 1 then launches the Orion + ESM and completes a rendezvous with the mated DE + AE components in LLFPO. FLARE offers optional phases beyond the baseline mission. The SpaceTug can deliver components of the planned Gateway, including the Power and Propulsion Element (PPE) and the Habitable and Logistics Outpost (HALO), to LLFPO. FLARE provides an option to deliver precursor equipment to the lunar surface to enhance and extend the human mission. With these components, including an inflatable habitation module and airlock, individual crew mobility vehicle(s), an In-Situ Resource Utilization (ISRU) demonstration, and science and technology experiments, the crew can explore and conduct science on the lunar surface for up to 14 days.

Moon 2024↗

A Disc-Dominated and Clumpy Circumgalactic Medium of the Milky Way Seen in X-Ray Emission

The Milky Way galaxy is surrounded by a circumgalactic medium (CGM) that may play a key role in galaxy evolution as the source of gas for star formation and a repository of metals and energy produced by star formation and nuclear activity. The CGM may also be a repository for baryons seen in the early universe, but undetected locally. The CGM has an ionized component at temperatures near 2 x 10^6 K studied primarily in the soft X-ray band. Here we report a survey of the southern Galactic sky with a soft X-ray spectrometer optimized to study diffuse soft X-ray emission. The X-ray emission is best fit with a disc-like model based on the radial profile of the surface density of molecular hydrogen, a tracer of star formation, suggesting that the X-ray emission is predominantly from hot plasma produced via stellar feedback. Strong variations in the X-ray emission on angular scales of ~10 degrees indicate that the CGM is clumpy. Addition of an extended, and possibly massive, halo component is needed to match the halo density inferred from other observations.

P Kaaret↗

Navigation between geosynchronous and lunar L₁ orbiters

Linked Autonomous Interplanetary Satellite Orbit Navigation (LiAISON) is a new technique that takes advantage of the asymmetrical gravity field present in a three-body system in order to perform absolute tracking of satellites using only relative satellite-to-satellite observations. Previous studies have demonstrated LiAISON’s practical applications for lunar missions, including a satellite in a halo orbit about either the Earth-Moon L₁or L₂ point. This paper studies the viability of applying LiAISON measurements between a lunar halo orbiter and a satellite in a geosynchronous orbit. Simulations demonstrate that the absolute positions and velocities of both satellites are observable using only relative measurements with an achieved uncertainty on the order of observation noise.

Anderson, Rodney L.↗

Heliophysics Environmental & Radiation Measurement Experiment Suite (HERMES): A Small External Payload for the Lunar Gateway with Big Challenges

Currently scheduled for liftoff in 2024, Gateway will be an outpost orbiting the moon for astronauts headed to and from the lunar surface and serve as a staging point for deep space exploration. In January of 2020 NASA headquarters contacted Goddard Space Flight Center to request that they develop a Heliophysics instrumentation package for Gateway. This package would later become known as HERMES-Heliophysics Environmental & Radiation Measurement Experiment Suite. HERMES consists of a Miniaturized Electron pRoton Telescope (MERIT), an Electron Electrostatic Analyzer (EEA), Solar Probe Analyzers (SPAN)-A-ions, and Noise Eliminating Magnetometer Instrument in a Small Integrated System (NEMISIS), which consists of one fluxgate and two Magneto-Inductive Magnetometers. From the beginning the HERMES mission faced a number of Challenges. It was constrained to fit in a small, half meter, cube and it was required to weigh no more than 25kg. A new boom design for the magnetometer would be required and for safety reasons it must be able to retract autonomously with power removed. To complicate matters the location of the SORI-Small ORU- (Orbital Replacement Unit) Robotics Interface, the primary interface for the HERMES platform to the Gateway elements, was undetermined. Also, the mechanical, thermal and electrical interfaces are not fully defined. The Canadian Space Agency is still in process of designing the version of the SORI that will be flown on the Power and Propulsion Element (PPE) and Habitation and Logistics Outpost (HALO) elements, each of which are being developed by different contractors. At the time of initiating the HERMES project, neither of the Gateway module providers were under contract. Additionally, we would later learn the ISS heritage SORI modules were not originally designed for launching on the Gateway elements with a payload directly attached but rather were intended to be brought up on a separate carrier outfitted with launch locks and specialized launch structures from which the robotic arm on Gateway would then be used to detach the payload and install it on the SORI adapters while on orbit. Launching the integrated Payload/SORI on the PPE and HALO elements complicates the stiffness requirements and coupled loads analysis. Adding to this are serious constraints on Field-Of-View (FOV) for solar viewing and severe radiation exposure considerations brought on by slowly raising the orbit through the Van Allen Belts. Just to make things a little more challenging the budget for the entire project was intended to be a low-cost tailored Class-D mission approach. Plus, the effects of Corona VIrus Disease 2019 (COVID-19) were not factored in from the beginning. This paper will discuss what’s being done to overcome these challenges and put HERMES on track for a 2024 Launch Readiness Date (LRD).

Irving Joseph Burt↗

Thermal Analysis of NRHO Entry Lunar Flyby Maneuver

NASA’s Gateway will serve as a platform for sustained human lunar exploration and an opportunity to gain experience with long duration deep-space architectures. The first two Gateway modules, the Power and Propulsion Element (PPE) and the Habitation and Logistics Outpost (HALO) are scheduled to launch together as a Co-Manifested Vehicle (CMV) in 2024. To reach the destination Near-Rectilinear Halo Orbit (NRHO), the CMV will perform a low-thrust electric propulsion spiral and a final transfer maneuver that will include a low altitude flyby of the lunar surface. This flyby thermal environment is more adverse than that expected during the NRHO itself and risks temperature exceedances on various spacecraft components. The highly transient nature of the flyby also required a different approach than the typical worst-case dissipation margins used to size the spacecraft thermal control systems. This paper presents analyses on the relative severity of different minimum perilune altitudes and results of an integrated CMV thermal model built in Thermal Desktop.

lunar flyby maneuver↗

Solar Absorptivity Degradation of Spacecraft Materials Due to UV and Charged Particles in the Gateway Environment

The Gateway Passive Thermal Control System (PTCS) Group has identified charged particle and UV degradation of Gateway materials as a knowledge gap for the Near Rectilinear Halo Orbit (NRHO) and transit environment. Candidate materials and coatings were subjected to expected mission UV and charged particle environments at NASA Goddard Space Flight Center (GSFC). In situ change in reflectivity was observed at specified intervals during testing such that change in solar absorptivity could be plotted as a function of time of solar exposure. Gateway will be an outpost in cislunar space designed to survive a 15-year mission to support human moon landings and future deep space exploration. The Gateway Passive Thermal Control System (PTCS) Group has identified charged particle and UV degradation of potential Gateway materials as a knowledge gap for the Near Rectilinear Halo Orbit (NRHO) and transit environment, especially the slow spiral transit planned for the first two modules. Solar absorptivity degradation is important to quantify because the end-of-life absorptivity impacts thermal performance of the system. To address this, ground testing is being completed at NASA Goddard Space Flight Center in which potential Gateway materials, including radiators, multi-layer insulation (MLI), and structural materials are subjected to the expected transit plus 15-year on-orbit charged particle fluence (9.86x1015 protons/cm2 at 2.5 keV and 3.1x1016 electrons/cm2 at 10 keV) and up to 5000 Equivalent Solar Hours (ESH). Reflectivity of a single sample of each material was measured in atmosphere and in vacuum inside the chamber after exposure to incremental levels of ESH and charged particle fluence. Increase in absorptivity of most samples were seen throughout the test including large differences in absorptivity of materials of the same category. Future testing will validate these results and include additional materials of interest.

materials in the space environment↗

Attitude Profile Reference for the Earth Orbit Raising Phase of NASA Gateway’s Co-Manifested Vehicle

As part of NASAs lunar exploration Artemis program, the agency is designing a Gateway to orbit8near the moon and provide long term support of a sustained lunar presence at the moon’s south pole.9The first element launched for the Gateway is the Co-Manifested Vehicle (CMV), comprised of the10Power and Propulsion Element (PPE) and Habitation and Lunar Outpost (HALO). The PPE Mission11Design team of McGuire & et. al (2021) has developed a Design Reference Mission (DRM) trajectory12for CMV’s Earth Orbit Raising (EOR) mission phase, which provides the vehicle’s 3 degrees of freedom13(DoF) trajectory information during the approximately yearlong spiral out from low Earth orbit and14into the lunar near-rectilinear halo orbit (NRHO). In tandem, the PPE GN&C team is developing a15high-fidelity and fine temporal resolution 6DoF model of the CMV spacecrafts GN&C performance16for delivery to the Gateway team; this work acts to bridge the gap between Mission Designs 3DoF17reference and detailed GN&Cs attitude simulation.

Guidance Navigation and Control↗

Optimal Low Thrust Orbit Transfers for Space Telescope Refueling at SEL2

The James Webb Space Telescope (JWST), a ten billion-dollar infrared telescope with a 6.5m primary mirror to be launched in 2021, is designed to operate in a Halo orbit around the second Sun-Earth Lagrange point (SEL2) for five to ten years. At that point fuel for station keeping and attitude maneuvers will run out. Refueling missions to JWST, as well as to similar space telescope missions proposed for SEL2, could greatly enhance the “science-per-dollar” value and promote a more sustainable use of space assets. In this paper, we present a novel approach to designing fuel optimal trajectories that will allow the refueling spacecraft to arrive at the SEL2 Halo orbit with maximum final mass (i.e. fuel payload). The low thrust optimal control problem is formulated using an indirect optimization method, leading to a two-point boundary value problem with a bang-bang control structure. We make use of a hyperbolic tangent smoothing technique for performing continuation on the thrust magnitude to reduce the sharpness of the control switches in early iterations and, thus, promote convergence. The problem is posed and solved in the circular restricted three-body problem. In this dynamical system, invariant manifolds exist that can be utilized to reduce fuel consumption. The here presented methodology to this challenging and important problem in astrodynamics demonstrates a significant potential for low-cost refueling mission design.

Woollands, Robyn↗