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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1961

Preliminary Survey of Retrograde Velocities Required for Insertion Into Low-Altitude Lunar Orbits

Closed lunar orbits are envisaged in lunar mission programs. The study described herein was undertaken to obtain an appreciation of the relevant fuel consumption requirements. The retrograde impulses necessary for establishing the orbits were assumed to occur at the point of closest approach of the main earth-moon trajectory; this point, designated as the arrival position, was restricted to a lunar altitude of 5,000 nautical miles or less. The orientation of the arrival position vector relevant to any coplanar radius vector is not constrained, however, and similarly the scalar value of the arrival velocity is unrestrained. Since the arrival altitude is restricted to 5,000 nautical miles or less, the perturbing accelerations of the earth and sun are sufficiently small that the vehicle and moon essentially comprise an isolated two-body system; this is discussed in the report. Retrograde velocities are determined for any required pericynthion position. If the pericynthion orientation requirement is relaxed then a smaller retrograde velocity is in some cases possible. A comparison between minimum retrograde velocities and retrograde velocities necessary for stipulated pericynthion positions is given. Arrival velocities are correlated with feasible earth departure conditions. The equations developed for determining retrograde velocities for desired pericynthion positions are considered useful for estimating essential data for the preliminary planning of lunar missions. Some graphical representation is included herein for immediate familiarization with possible conditions.

Jenkins, Morris V.↗
NASA NTRS2017

The Effect of the Spin-Forbidden Co((sup 1) Sigma plus) plus O((sup 3) P) Yields CO2 (1 Sigma (sub G) plus) Recombination Reaction on Afterbody Heating of Mars Entry Vehicles

Vibrationally excited CO2, formed by two-body recombination from CO((sup 1) sigma plus) and O((sup 3) P) in the wake behind spacecraft entering the Martian atmosphere reaction, is potentially responsible for the higher than anticipated radiative heating of the backshell, compared to pre-flight predictions. This process involves a spin-forbidden transition of the transient triplet CO2 molecule to the longer-lived singlet. To accurately predict the singlet-triplet transition probability and estimate the thermal rate coefficient of the recombination reaction, ab initio methods were used to compute the first singlet and three lowest triplet CO2 potential energy surfaces and the spin-orbit coupling matrix elements between these states. Analytical fits to these four potential energy surfaces were generated for surface hopping trajectory calculations, using Tully's fewest switches surface hopping algorithm. Preliminary results for the trajectory calculations are presented. The calculated probability of a CO((sup 1) sigma plus) and O((sup 3) P) collision leading to singlet CO2 formation is on the order of 10 (sup -4). The predicted flowfield conditions for various Mars entry scenarios predict temperatures in the range of 1000 degrees Kelvin - 4000 degrees Kelvin and pressures in the range of 300-2500 pascals at the shoulder and in the wake, which is consistent with a heavy-particle collision frequency of 10 (sup 6) to 10 (sup 7) per second. Owing to this low collision frequency, it is likely that CO((sup 1) sigma plus) molecules formed by this mechanism will mostly be frozen in a highly nonequilibrium rovibrational energy state until they relax by photoemission.

CO2 recombination↗
NASA NTRS2013

Conceptual Design of a Flight Validation Mission for a Hypervelocity Asteroid Intercept Vehicle

Near-Earth Objects (NEOs) are asteroids and comets whose orbits approach or cross Earth s orbit. NEOs have collided with our planet in the past, sometimes to devastating effect, and continue to do so today. Collisions with NEOs large enough to do significant damage to the ground are fortunately infrequent, but such events can occur at any time and we therefore need to develop and validate the techniques and technologies necessary to prevent the Earth impact of an incoming NEO. In this paper we provide background on the hazard posed to Earth by NEOs and present the results of a recent study performed by the NASA/Goddard Space Flight Center s Mission Design Lab (MDL) in collaboration with Iowa State University s Asteroid Deflection Research Center (ADRC) to design a flight validation mission for a Hypervelocity Asteroid Intercept Vehicle (HAIV) as part of a Phase 2 NASA Innovative Advanced Concepts (NIAC) research project. The HAIV is a two-body vehicle consisting of a leading kinetic impactor and trailing follower carrying a Nuclear Explosive Device (NED) payload. The HAIV detonates the NED inside the crater in the NEO s surface created by the lead kinetic impactor portion of the vehicle, effecting a powerful subsurface detonation to disrupt the NEO. For the flight validation mission, only a simple mass proxy for the NED is carried in the HAIV. Ongoing and future research topics are discussed following the presentation of the detailed flight validation mission design results produced in the MDL.

Barbee, Brent W.↗
DOE OSTI2022

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron–electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. In conclusion, the transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Prompt-delayed γ-ray spectroscopy of neutron-rich 119.121 In isotopes

The Z = 50 shell closure, near N = 82, is unique in the sense that it is the only shell closure with the spin-orbit partner orbitals, π g 9 / 2 and π g 7 / 2 , enclosing the magic gap. The interaction of the proton hole/particle in the above-mentioned orbitals with neutrons in the νh 11/2 orbital is an important prerequisite to the understanding of the nuclear structure near N = 82 and the νπ interaction. To explore the structural similarity between the high-spin isomeric states in In ( Z = 49), Sn ( Z = 50), and Sb ( Z = 51) isotopes from a microscopic point of view. In addition, to understand the role of a proton hole or particle in the spin-orbit partner orbitals, π g 9 / 2 and π g 7 / 2 , respectively, with neutron holes in the ν h 11 / 2 orbital on these aforementioned isomers. The fusion and transfer induced fission reaction Be 9 ( U 238 , f ) with 6.2 MeV/u beam energy, using a unique setup consisting of AGATA, VAMOS++, and EXOGAM detectors, was used to populate through the fission process and study the neutron-rich In 119 , 121 isotopes. This setup enabled the prompt-delayed γ -ray spectroscopy of isotopes in the time range of 100 ns – 200 μ s . In the odd- A In 119 , 121 isotopes, indications of a short half-life 19/2 - isomeric state, in addition to the previously known 25/2 + isomeric state, were observed from the present data. Further, new prompt transitions above the 25/2 + isomer in In 121 were identified along with reevaluation of its half-life. The experimental data were compared with the theoretical results obtained in the framework of large-scale shell-model calculations in a restricted model space. Furthermore, the ( π g 9 / 2 ν h 11 / 2 ; I | H ^ | π g 9 / 2 ν h 11 / 2 ; I ) two-body matrix elements of residual interaction were modified to explain the excitation energies and the B ( E 2) transition probabilities in the neutron-rich In isotopes. The (i) decreasing trend of E (29/2 + ) - E (25/2 + ) in odd-In (with dominant configuration π g 9 / 2 - 1 ν h 11 / 2 - 2 and maximum aligned spin of 29/2 + ) and (ii) increasing trend of E (27/2 + ) - E (23/2 + ) in odd-Sb (with dominant configuration π g 7 / 2 + 1 ν h 11 / 2 - 2 and maximum aligned spin of 27/2 + ) with increasing neutron number could be understood as a consequence of hole-hole and particle-hole interactions, respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2013

NASA Tech Briefs, Februrary 2013

Topics covered include: Measurements of Ultra-Stable Oscillator (USO) Allan Deviations in Space; Gaseous Nitrogen Orifice Mass Flow Calculator; Validation of Proposed Metrics for Two-Body Abrasion Scratch Test Analysis Standards; Rover Low Gain Antenna Qualification for Deep Space Thermal Environments; Automated, Ultra-Sterile Solid Sample Handling and Analysis on a Chip; Measuring and Estimating Normalized Contrast in Infrared Flash Thermography; Spectrally and Radiometrically Stable, Wideband, Onboard Calibration Source; High-Reliability Waveguide Vacuum/Pressure Window; Methods of Fabricating Scintillators With Radioisotopes for Beta Battery Applications; Magnetic Shield for Adiabatic Demagnetization Refrigerators (ADR); CMOS-Compatible SOI MESFETS for Radiation-Hardened DC-to-DC Converters; Silicon Heat Pipe Array; Adaptive Phase Delay Generator; High-Temperature, Lightweight, Self-Healing Ceramic Composites for Aircraft Engine Applications; Treatment to Control Adhesion of Silicone-Based Elastomers; High-Temperature Adhesives for Thermally Stable Aero-Assist Technologies; Rockballer Sample Acquisition Tool; Rock Gripper for Sampling, Mobility, Anchoring, and Manipulation; Advanced Magnetic Materials Methods and Numerical Models for Fluidization in Microgravity and Hypogravity; Data Transfer for Multiple Sensor Networks Over a Broad Temperature Range; Using Combustion Synthesis to Reinforce Berms and Other Regolith Structures; Visible-Infrared Hyperspectral Image Projector; Three-Axis Attitude Estimation With a High-Bandwidth Angular Rate Sensor Change_Detection.m; AGATE: Adversarial Game Analysis for Tactical Evaluation; Ionospheric Simulation System for Satellite Observations and Global Assimilative; Modeling Experiments (ISOGAME); An Extensible, User- Modifiable Framework for Planning Activities; Mission Operations Center (MOC) - Precipitation Processing System (PPS) Interface Software System (MPISS); Automated 3D Damaged Cavity Model Builder for Lower Surface Acreage Tile on Orbiter; Mixed Linear/Square-Root Encoded Single-Slope Ramp Provides Low-Noise ADC with High Linearity for Focal Plane Arrays; RUSHMAPS: Real-Time Uploadable Spherical Harmonic Moment Analysis for Particle Spectrometers; Powered Descent Guidance with General Thrust-Pointing Constraints; X-Ray Detection and Processing Models for Spacecraft Navigation and Timing; and Extreme Ionizing-Radiation-Resistant Bacterium

Source record↗
DOE OSTI2020

From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)

We recently introduced in [9] a boundary-to-bound dictionary between gravitational scattering data and observables for bound states of non-spinning bodies. In this paper, we elaborate further on this holographic map. We start by deriving the following — remarkably simple — formula relating the periastron advance to the scattering angle: $ΔΦ(J,ε)=χ(J,ε)+χ(-J,ε)$, via analytic continuation in angular momentum and binding energy. Using explicit expressions from [9], we confirm its validity to all orders in the Post-Minkowskian (PM) expansion. Furthermore, we reconstruct the radial action for the bound state directly from the knowledge of the scattering angle. The radial action enables us to write compact expressions for dynamical invariants in terms of the deflection angle to all PM orders, which can also be written as a function of the PM-expanded amplitude. As an example, we reproduce our result in [9] for the periastron advance, and compute the radial and azimuthal frequencies and redshift variable to two-loops. Agreement is found in the overlap between PM and Post-Newtonian (PN) schemes. Last but not least, we initiate the study of our dictionary including spin. We demonstrate that the same relation between deflection angle and periastron advance applies for aligned-spin contributions, with J the (canonical) total angular momentum. Explicit checks are performed to display perfect agreement using state-of-the-art PN results in the literature. Using the map between test- and two-body dynamics, we also compute the periastron advance up to quadratic order in spin, to one-loop and to all orders in velocity. We conclude with a discussion on the generalized ‘impetus formula’ for spinning bodies and black holes as ‘elementary particles’. Our findings here and in [9] imply that the deflection angle already encodes vast amount of physical information for bound orbits, encouraging independent derivations using numerical and/or self-force methodologies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Spinning black hole scattering at $ \mathcal{O} $(G 3 S 2 )(G 3 S 2 ): Casimir terms, radial action and hidden symmetry

We resolve subtleties in calculating the post-Minksowskian dynamics of binary systems, as a spin expansion, from massive scattering amplitudes of fixed finite spin. In particular, the apparently ambiguous spin Casimir terms can be fully determined from the gradient of the spin-diagonal part of the amplitudes with respect to S 2 = −s(s+1)ħ 2 , using an interpolation between massive amplitudes with different spin representations. From two-loop amplitudes of spin-0 and spin-1 particles minimally coupled to gravity, we extract the spin Casimir terms in the conservative scattering angle between a spinless and a spinning black hole at $ \mathcal{O} $(G 3 S 2 ), finding agreement with known results in the literature. This completes an earlier study [Phys. Rev. Lett. 130 (2023), 021601] that calculated the non-Casimir terms from amplitudes. We also illustrate our methods using a model of spinning bodies in electrodynamics, finding agreement between scattering amplitude predictions and classical predictions in a root-Kerr electromagnetic background up to $ \mathcal{O} $(α 3 S 2 ). For both gravity and electrodynamics, the finite part of the amplitude coincides with the two-body radial action in the aligned spin limit, generalizing the amplitude-action relation beyond the spinless case. Surprisingly, the two-loop amplitude displays a hidden spin-shift symmetry in the probe limit, which was previously observed at one loop. We conjecture that the symmetry holds to all orders in the coupling constant and is a consequence of integrability of Kerr orbits in the probe limit at the first few orders in spin.

Classical Theories of Gravity↗
DOE OSTI2020

Self-interaction error overbinds water clusters but cancels in structural energy differences

Here, we gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi–Löwdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew–Burke–Ernzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a density-driven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction–corrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/ H 2 O from about 42 meV/ H 2 O for SCAN. By decomposing the total binding energy into many-body components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN and self-interaction–corrected SCAN. These findings suggest that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Neutron-unbound states in 31 Ne

Background: The Island of Inversion near the N = 20 shell gap is home to nuclei with reordered single-particle energy levels compared to the spherical shell model. Studies of 31 Ne have revealed that its ground state has a halo component, characterized by a valence neutron orbiting a deformed 30 Ne core. This lightly-bound nucleus with a separation energy of only S n = 170 keV is expected to have excited states that are neutron unbound. Purpose: The purpose of this experiment was to investigate the low-lying excited states in 31 Ne that decay by the emission of a single neutron. Methods: An 89 MeV/u 33 Mg beam impinged on a segmented Be reaction target. Neutron unbound states in 31 Ne were populated via a two-proton knockout reaction. The 30 Ne fragment and associated neutron from the decay of 31 Ne were detected by the MoNA-LISA-Sweeper experimental setup at the National Superconducting Cyclotron Laboratory. Invariant mass spectroscopy was used to reconstruct the two-body decay energy ( 30 Ne + n). Results: The two-body decay energy spectrum exhibits two features: a low-lying peak at 0.30 ± 0.17 MeV and a broad enhancement at 1.50 ± 0.33 MeV, each fit with an energy-dependent asymmetric Breit-Wigner line shape representing a resonance in the continuum. Accompanying shell model calculations using the FSU interaction within NuShellX, combined with cross-section cal culations using the eikonal reaction theory, indicate that these peaks in the decay energy spectrum are caused by multiple resonant states in 31 Ne. Conclusions: In this study, excited states in 31 Ne were observed for the first time. Transitions from calculated shell model final states in 31 Ne to bound states in 30 Ne are in good agreement with the measured decay energy spectrum. Cross-section calculations for the two-proton knockout populating 31 Ne states as well as spectroscopic factors pertaining to the decay of 31 Ne into 30 Ne are used to examine the results within the context of the shell model expectations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Quantum field theory, worldline theory, and spin magnitude change in orbital evolution

A previous paper [Z. Bern et al., Binary dynamics through the fifth power of spin at 𝑂⁡(𝐺 2 ), Phys. Rev. Lett. 130, 201402 (2023)] identified a puzzle stemming from the amplitudes-based approach to spinning bodies in general relativity: additional Wilson coefficients appear compared to current worldline approaches to conservative dynamics of generic astrophysical objects, including neutron stars. In this paper we clarify the nature of analogous Wilson coefficients in the simpler theory of electrodynamics. We analyze the original field-theory construction, identifying definite-spin states some of which have negative norms, and relating the additional Wilson coefficients in the classical theory to transitions between different quantum spin states. We produce a new version of the theory which also has additional Wilson coefficients, but no negative-norm states. We match, through 𝒪⁡(𝛼 2 ) and 𝒪⁡(𝑆 2 ), the Compton amplitudes of these field theories with those of a modified worldline theory with extra degrees of freedom introduced by releasing the spin supplementary condition. We build an effective two-body Hamiltonian that matches the impulse and spin kick of the modified field theory and of the worldline theory, displaying additional Wilson coefficients compared to standard worldline approaches. The results are then compactly expressed in terms of an eikonal formula. Our key conclusion is that, contrary to standard approaches, while the magnitude of the spin tensor is still conserved, the magnitude of the spin vector can change under conserved Hamiltonian dynamics and this change is governed by the additional Wilson coefficients. For specific values of Wilson coefficients the results are equivalent to those from a definite spin obeying the spin supplementary condition, but for generic values they are physically inequivalent. These results warrant detailed studies of the corresponding issues in general relativity.

classical black holes↗
NASA NTRS1970

On the matrizant of the two-body problem

Matrizant of two body problem or integrable dynamic system for applications to computing perturbations and differential correction of orbits with observations

Broucke, R. A.↗
NASA NTRS1976

The development of the Poincare-similar elements with true anomaly as the independent variable

In reference 1, the Hamiltonian of the unperturbed two-body problem in extended phase space is established. Depending on the type of time transformation, eight canonical elements were developed with the true anomaly or the eccentric anomaly as the independent variable. These two new sets, DS(phi) and DS(u), however contain singularities for small eccentricities and inclinations. In reference 2, these singularities are removed by a transformation from DS(u) to eight canonical PS(u) elements. In reference 3, the DS(phi) variables are transformed to the PS(phi) elements to remove the singularities. However, no direct relation was established between the eight canonical PS(phi) elements and the Cartesian coordinates. It is the purpose of this report to establish those relations and to develop the perturbed equations of motion in the PS(phi) space. This report also demonstrates the accuracy of this new set when it is applied to numerical orbit prediction problems.

Mueller, A.↗
NASA NTRS1987

The effect of atmospheric drag on position and velocity errors of orbiting spacecraft

A model, in closed form, of position and velocity changes due to atmospheric drag of a spacecraft in orbit about a planetary body is presented, considering primarily the effects of a two-body force field. Calculations for both elliptical and circular geometries indicate that the simplifying assumptions in the analysis make the theory more accurate (to less than 1 percent error) for lengthier mappings, when the drag effect becomes quite significant. The downtrack error demonstrates a quadratic growth, while the radial error demonstrates a linear growth.

Russell, R. Kent↗
NASA NTRS1986

Orbital resonances, unusual configurations and exotic rotation states among planetary satellites

The origin of orbital resonances is shown in the demonstration of the evolution of a pair of planetary satellites through a commensurability of the mean motions by a sequence of diagrams of constant energy curves in a two-dimensional phase space; the closed curve corresponding to the motion in each successive diagram is identified by its adiabatically conserved area. It is found that two-body resonances serve as a basis in the solution of the problem of the origin and evolution of the three-body Laplace resonance among the Galilean satellites of Jupiter. The unusual rotation state of Saturn's satellite Hyperion which is expected to tumble chaotically for an indefinite amount of time is discussed.

Peale, S. J.↗
NASA NTRS1989

A gravity assist primer

An account is given of the method by which the 'energy gain' accruing to a spacecraft as a result of its 'gravity-assist', parabolic-trajectory flyby of a massive body, such as a planet. The procedure begins with the solution of the two-body portion of the problem, and the results thus obtained are used to calculate changes with respect to the other massive body in the overall scenario, namely the sun. Attention is given to the 'vector diagram' often used to display the gravity-assist effect. The present procedure is noted to be reasonably accurate for flybys in which the plane of the spacecraft's trajectory is approximately the same as that of the planet's orbit around the sun, or the ecliptic plane; this reduces the problem to one in two dimensions.

Cesarone, R. J.↗
NASA NTRS2009

Simulation of Attitude and Trajectory Dynamics and Control of Multiple Spacecraft

Agora software is a simulation of spacecraft attitude and orbit dynamics. It supports spacecraft models composed of multiple rigid bodies or flexible structural models. Agora simulates multiple spacecraft simultaneously, supporting rendezvous, proximity operations, and precision formation flying studies. The Agora environment includes ephemerides for all planets and major moons in the solar system, supporting design studies for deep space as well as geocentric missions. The environment also contains standard models for gravity, atmospheric density, and magnetic fields. Disturbance force and torque models include aerodynamic, gravity-gradient, solar radiation pressure, and third-body gravitation. In addition to the dynamic and environmental models, Agora supports geometrical visualization through an OpenGL interface. Prototype models are provided for common sensors, actuators, and control laws. A clean interface accommodates linking in actual flight code in place of the prototype control laws. The same simulation may be used for rapid feasibility studies, and then used for flight software validation as the design matures. Agora is open-source and portable across computing platforms, making it customizable and extensible. It is written to support the entire GNC (guidance, navigation, and control) design cycle, from rapid prototyping and design analysis, to high-fidelity flight code verification. As a top-down design, Agora is intended to accommodate a large range of missions, anywhere in the solar system. Both two-body and three-body flight regimes are supported, as well as seamless transition between them. Multiple spacecraft may be simultaneously simulated, enabling simulation of rendezvous scenarios, as well as formation flying. Built-in reference frames and orbit perturbation dynamics provide accurate modeling of precision formation control.

Stoneking, Eric T.↗
NASA NTRS2014

Analysis of Petal Rotation Trajectory Characteristics

In this study, the characteristics of petal rotation trajectories are explored in both the two-body and circular restricted three-body problem (CRTBP) models. Petal rotation trajectories alternate long and short resonances of different kinds to rotate the line of apsides. They are typically computed using the patched conic model, and they are used in a number of different missions and mission concepts including Cassini, JUICE, and Europa mission concepts. Petal rotation trajectories are first analyzed here using the patched conic model to quantify their characteristics and search for cases with fast rotation of the line of apsides. When they are computed in the CRTBP, they are unstable periodic orbits with corresponding stable and unstable manifolds. The characteristics of these orbits are explored from a dynamical systems perspective in the second phase of the study.

Resonance↗