Third-body Effects Research Articles

Secular dynamics and the lifetimes of lunar artificial satellites under natural force-driven orbital evolution

In this paper, we study the long-term (time scale of several years) orbital evolution of lunar satellites under the sole action of natural forces. In particular, we focus on secular resonances, caused either by the influence of the multipole moments of the lunar potential and/or by the Earth’s and Sun’s third-body effect on the satellite’s long-term orbital evolution. Our study is based on a simplified secular model obtained in ‘closed form’, i.e., without expansions in the satellite’s orbital eccentricity. Contrary to the case of artificial Earth satellites, in which many secular resonances compete in dynamical impact, we give numerical evidence that for lunar satellites only the 2g−resonance (ω̇=0) affects significantly the orbits at secular timescales. We interpret this as a consequence of the strong effect of lunar mascons. We show that the lifetime of lunar satellites is, in particular, nearly exclusively dictated by the 2g resonance. By deriving a simple analytic model, we propose a theoretical framework which allows for both qualitative and quantitative interpretation of the structures seen in numerically obtained lifetime maps. This involves explaining the main mechanisms driving eccentricity growth in the orbits of lunar satellites. In fact, we argue that the re-entry process for lunar satellites is not necessarily a chaotic process (as is the case for Earth satellites), but rather due to a sequence of bifurcations leading to a dramatic variation in the structure of the separatrices in the 2g resonance’s phase portrait, as we move from the lowest to the highest limit in inclination (at each altitude) where the 2g resonance is manifested.

OO Leo: An Active Contact Binary with Possible Solar-like Differential Rotation

With Transiting Exoplanet Survey Satellite (TESS) high-precision photometry and Large Sky Area Multi-object Fiber Spectroscopic Telescope medium-resolution spectra, we present the first light and radial velocity curve analyses for the eclipsing binary OO Leo. The simultaneous solution suggests that OO Leo is a W-subtype contact binary with a relatively low mass ratio (1/q = 0.173) and a moderate degree of contact (f = 28.1%). The asymmetry and continuous changes observed in the TESS light curve were properly modeled by one retrograde cool spot on its secondary surface. A detailed investigation of the Hα line also confirmed that the secondary star had a high level of magnetic activity. The retrograde longitudinal motion of the spot can be explained by a solar-like differential rotation in the secondary component. The orbital period investigation revealed that OO Leo is undergoing a secular decrease and a cyclic variation in its orbital period. The secular decrease may be mainly caused by mass transfer from the more massive secondary star to the less massive primary star. The cyclic period variation can be explained by the light–time effect of an invisible third body or the cyclic magnetic activity of the secondary star. The long-lived spot migration in the longitudinal direction makes OO Leo an excellent target for investigating the differential rotations of contact binaries.

Experimental and chemical kinetic analysis to evaluate CO2 dilution on laminar combustion characteristics of C2H5OH/air blends under normal pressure

Based on a constant volume combustion system, the effect of dilution ratio changes on the laminar combustion characteristics of C2H5OH/air mixture was studied under an initial pressure of 1 bar, initial temperatures of 370 K, 400 K, 450 K, and equivalence ratios of 0.7–1.4. A chemical kinetic mechanism for ethanol-carbon dioxide was established, and the combined physical and chemical effects of carbon dioxide were separated. An independent parameter control method was proposed, introducing virtual species FN2, ICO2, FCO2, and KCO2, to isolate the dilution effect, thermal effect, direct reaction effect, third-body effect, and transport effect. Simulation analysis using the modified chemical kinetic mechanism revealed that various impacts of CO2 reduce the peak progress rate and sensitivity coefficient of key elementary reactions. Furthermore, the dilution effect of CO2 has the greatest influence on the sensitivity coefficients and net progress rates of important elementary reactions. Based on the results of the chemical kinetic simulations, a new global reaction pathway analysis method was created, overcoming the limitations of the Chemkin-pro method. The decomposition pathway of C2H5OH throughout the combustion process was calculated as C2H5OH → SC2H4OH → CH3CHO → CH3CO → CH3 → CH2O → HCO → CO → CO2. Changes in initial temperature and dilution ratio do not alter the main decomposition pathway of C2H5OH. Detailed chemical kinetics and free radical behavior analysis indicate that the LBV of the C2H5OH/CO2/air blends has a linear correlation with [H + O + OH]max.

Investigating the Origins of Hot Neptunes from Radial Velocity Data

Abstract Hot Neptunes are extrasolar planets that are similar in size to Neptune in our solar system but are much closer to their host stars, completing an orbit in 10 days or less. The origin of hot Neptunes is not fully understood. A potential large third body at a distance can lead to the migration of long-period planets to become much closer to the host star, and such a dynamical process helps explain the origin of hot Jupiters. We investigate whether hot Neptunes could share a similar origin by analyzing radial velocity data from multiple sources for a sample of 34 hot Neptune systems. Hot Neptune systems appear to have similar values of linear trend to hot Jupiter systems. We perform a maximum likelihood analysis to constrain the mass and distance distribution of the putative third body. The overall fraction of hot Neptune systems with third bodies is consistent with unity, higher than 71% at the 2σ level. On average, the mass and distance distribution of the third bodies for hot Neptune systems is consistent with that for hot Jupiter systems. Our results suggest that hot-Neptune systems share the same origin mechanism as hot Jupiters, e.g., through the gravitational effect of third bodies.

Formic acid oxidation on different coverages of Bismuth-modified Pt(1 0 0): A detailed voltammetric and FTIR study

The formic acid oxidation reaction (FAOR) on bismuth-modified Pt(100) is studied using electrochemical techniques and FITR spectroscopy at different bismuth coverages and formic acid concentrations. The results clearly show that: (1) The measured currents for the Bi-modified Pt(100) surface contain contributions from both the Pt-Bi ensembles and the Pt sites far from the Bi adatoms. (2) The catalytic effect of bismuth is not linked to the adsorption of formate on Pt sites. (3) The bismuth not only improves the activity of the FAOR through the active intermediate but also inhibits the CO poison by a third-body effect. (4) The experimental results indicate that the catalytic activity is linked to the Pt-Bi ensembles. The active species, formate, adsorbs on the Bi site and the neighboring Pt sites facilitate the cleavage of the C–H bond. (5) From the concentration dependence, the reaction order for formate on bismuth-modified Pt(100) is 1 at low potentials. In contrast, a reaction order of 0.5 is obtained at higher potentials. These results are in agreement with the proposed mechanism.

The effects of steam dilution on flame structure and stability for a H2/air micromix burner

The present work is dedicated to understand the effects of steam dilution on the structure and stability of a micromix H2/air swirl flame. The flame structure and stability were obtained through numerical simulations using Large Eddy Simulation (LES) with the Eddy-Dissipation-Concept (EDC) combustion model. In addition, OH-PLIF images and temperature distribution were used to verity the computed results. The experimental and simulated OH distributions show that great part of OH distributes on midstream and downstream of the flame. From the numerical results, it can be seen that the thermal-dilution effect of steam has the biggest impact on flame temperature. Detailed analysis show that the thermal-dilution effect of steam lowers the OH mass fraction, which is the same as third-body effect, however, the OH mass fraction is increased by the direct chemical effect due to decrease the net reaction rate of R4 (H2 + OH = H2O + H). The stability of the micromix hydrogen flame could be reduced due to the thermal-dilution effect, but the direct chemical effect could slightly improve the stability of the micromix hydrogen flame which is the same as third-body effect.

Dynamical perturbations around an extreme mass ratio inspiral near resonance

Extreme mass ratio inspirals (EMRIs) -- systems with a compact object orbiting a much more massive (e.g., galactic center) black hole -- are of interest both as a new probe of the environments of galactic nuclei, and their waveforms are a precision test of the Kerr metric. This work focuses on the effects of an external perturbation due to a third body around an EMRI system. This perturbation will affect the orbit most significantly when the inner body crosses a resonance with the outer body, and result in a change of the conserved quantities (energy, angular momentum, and Carter constant) or equivalently of the actions, which results in a subsequent phase shift of the waveform that builds up over time. We present a general method for calculating the changes in action during a resonance crossing, valid for generic orbits in the Kerr spacetime. We show that these changes are related to the gravitational waveforms emitted by the two bodies (quantified by the amplitudes of the Weyl scalar $\psi_4$ at the horizon and at $\infty$) at the frequency corresponding to the resonance. This allows us to compute changes in the action variables for each body, without directly computing the explicit metric perturbations, and therefore we can carry out the computation by calling an existing black hole perturbation theory code. We show that our calculation can probe resonant interactions in both the static and dynamical limit. We plan to use this technique for future investigations of third-body effects in EMRIs and their potential impact on waveforms for LISA.

Comparative study on the effect of initial temperatures and pressures on the laminar flame speed of the heavily carbonaceous syngas containing water vapor via reaction kinetics simulation

To study the chemical and thermodynamic effects on the laminar flame speed (Su) of heavily carbonaceous syngas (CO/H2/CO2/N2/Air) applied in actual industries under different conditions with water addition, reaction kinetics simulation is employed by varying the ratio of CO/H2 mixture from 20:1 to 80:1 under various initial pressures and different initial temperatures. By comparing a large number of experimental data with the calculated data of six mechanisms, the most appropriate mechanism is selected to study. As for the syngas with higher carbon content, results show that the Su is more sensitive to the variation of humidity. The third-body effect of water in the key reactions H + O2(+M) ↔ HO2(+M) and H + OH + M ↔ H2O + M are identified through the reaction rate evaluation and sensitivity analysis, demonstrating the unique role of HO2 radicals in the combustion of the humid heavily carbonaceous syngas. Finally, by comparing the variation of Su under different temperatures and pressures, two primary paths to generating OH radicals in heavily carbonaceous syngas are put forward. This work would provide theoretical analysis and data support for advancing the combustion efficiency of heavy-carbonaceous-related fuels in industrial manufacture.

The effects of N2 and steam dilution on NO emission for a H2/Air micromix flame

The different effects of N2 and water steam dilution on the NO emission from a micromix H2/air flame were experimentally and numerically studied. NO emission was measured using Fourier transform infrared spectroscopy gas analyzer (FTIR). Numerical simulation of the H2/air flame was carried out with realizable k-ε model and the Eddy Dissipation Concept (EDC) model. Two pseudo species were introduced in the simulations to numerically isolate the thermal-dilution, direct chemical and third-body effect of the steam. The experimental and numerical results show that NO emission with steam dilution is about 20%∼50% of the emission with N2 dilution at the same equivalence ratio (φ) and dilution ratio (D). The present simulation results show that the thermal-dilution and direct chemical effects of steam account for 50.8%∼92.1% and 5.8%∼15.8% of the total NO emission, respectively, while the third-body effect of steam shows less impact on NO emission. Specifically, the third-body effect slightly promotes the formation of H and NO at lower φ (0.6–0.8) and suppresses the formation of H and NO at higher φ (0.9–1.0) through inhibiting the third-body reaction of H + O2 + M ⇔ HO2 + M. In addition, the direct chemical and third-body effects of steam always decrease the formation of NO from the NNH route.

NO mechanisms of syngas MILD combustion diluted with N2, CO2, and H2O

The NO mechanism under the moderate or intense low-oxygen dilution (MILD) combustion of syngas has not been systematically examined. This paper investigates the NO mechanism in the syngas MILD regime under the dilution of N2, CO2, and H2O through counterflow combustion simulation. The syngas reaction mechanism and the counterflow combustion simulation are comprehensively validated under different CO/H2 ratios and strain rates. The effects of oxygen volume fraction, CO/H2 ratio, pressure, strain rate, and dilution atmosphere are systematically investigated. For all the MILD cases, the contribution of the prompt and NO-reburning routes to the overall NO emission is less than 0.1% due to the lack of CH4 in fuel. At atmospheric pressure, the thermal route only accounts for less than 20% of the total NO emission because of the low reaction temperature. Moreover, at atmospheric pressure, the contribution of the NNH route to NO emission is always larger than 55% in the N2 atmosphere. The N2O-intermediate route is enhanced in CO2 and H2O atmospheres due to the increased third-body effects of CO2 and H2O through the reaction N2 + O (+M) ↔ N2O (+M). Especially in the H2O atmosphere, the N2O-intermediate route contributes to 60% NO at most. NO production is reduced with increasing CO/H2 ratio or pressure, mainly due to decreased NO formation from the NNH route. Importantly, a high reaction temperature and low NO emission are simultaneously achieved at high pressure. To minimize NO emission, the reactions should be operated at high values of CO/H2 ratios (i.e., >4) and pressures (e.g., P > 10 atm), low oxygen volume fractions (e.g., XO2 < 15%), and using H2O as a diluent. This study provides a new fundamental understanding of the NO mechanism of syngas MILD combustion in N2, CO2, and H2O atmospheres.

Adaptability of different mechanisms and kinetic study of methane combustion in steam diluted environments

The chemical kinetics of methane oxidation in a steam-diluted environment are studied in the present study. Various well-validated mechanisms for methane combustion are adopted and compared with experimental data. Ignition delay, laminar flame speed, and emissions for CH4 combustion with steam dilution are discussed. Cumulative relative error parameter was determined for all mechanisms considered in this study to evaluate the prediction level in quantifiable terms. Reaction pathways under no and steam-diluted environments are analyzed, and key elementary reactions and species are identified in these conditions. The analysis gives a relative idea of the applicability of some of the reduced mechanisms for the diluted steam conditions. This study aims to guide future computational fluid dynamics simulations to accurately predict combustion characteristics in these conditions. Computations of laminar flame speed from GRI-3.0, Aramco3.0, Curran, and San Diego mechanisms were the most precise under diluted steam conditions. Similarly, for the calculation of ignition delay of methane under the steam dilution, the Aramco mechanism and the Curran’s mechanism were able to predict the experimentally observed values most closely. Sensitivity study for the OH concentrations shows that the H-abstraction of methane from OH radicals has an opposing trend with dilution for Aramco and GRI-3.0 mechanism. On the other hand, CO and NO emissions were reduced significantly, with the dilution increased from 0 to 20%. The third-body effect of steam is observed to dominate the deviation observed between the detailed and reduced mechanism. For low operating pressure conditions, the GRI-3.0 mechanism gives an excellent prediction, whereas, for applications like gas turbines and furnaces, Aramco-3.0 and Curran mechanisms can be adopted to give good results. The San Diego mechanism can be chosen for low computational facility purposes as it shows very good predictions for ignition delay and laminar flame speed computations.

Experimental and Numerical Study on the Combustion Characteristics of a Laminar Non-Premixed Methane Jet Flame in Oxygen/Carbon Dioxide Coflow

The combustion characteristics of laminar non-premixed CH4 jet flame in an O2/CO2 coflows with different oxygen mole fractions were studied experimentally. The flame heights at different oxygen concentrations and fuel jet velocity were obtained. The experimental observation shows that the luminosity of the CH4 jet flame in O2/CO2 coflow is different from that of the flame in air stream. A two-dimensional numerical study of a laminar non-premixed CH4 jet flame in the O2/CO2 coflow with the O2 mole fraction of 0.35 was conducted to analyze the effects of CO2 dilution on the flame. The distribution of OH radicals in the flame was measured experimentally using planar laser-induced fluorescence (PLIF) to validate the computational method adopted in this work, and the computational and experimental results of the OH distributions showed good consistency at various fuel flow velocities. Three artificial species were created in the numerical experiment to analyze the effects of the chemical reactions, third-body collisions, and transport properties of CO2 on the height, width, and temperature distribution of the flame. The results showed that CO2 participation in chemical reactions exerts significant effects on the flame. However, the influences of the third-body effects and transport properties of CO2 on the jet flame are unremarkable. The global reaction pathways and distributions of important species in the laminar non-premixed CH4 jet flame were analyzed in detail to investigate the influence mechanisms of CO2 on the flame height and temperature. The entire flame can be divided into two oxidation parts, which separated by the boundary of the HCCO. The H, O, and OH concentrations and distributions in different parts of the flame were influenced by CO2 dilution, resulting in different flame heights and temperature distributions.

New insights into methanol and formic acid electro-oxidation on Pt: Simultaneous DEMS and ATR-SEIRAS study under well-defined flow conditions and simulations of CO spectra.

Methanol and formic acid electro-oxidation on Pt has been studied under well-defined flow conditions by a spectroscopic platform that combines differential electrochemical mass spectrometry (DEMS) and attenuated total reflection-Fourier transform infrared (ATR-FTIR) spectroscopy. The volatile soluble products from methanol and formic acid oxidation on Pt have been detected by DEMS, while adsorbed intermediates have been identified with ATR-FTIR spectroscopy. Besides CO2 and methylformate, which were detected by DEMS, other non-volatile soluble intermediates such as formaldehyde and formic acid were also generated during methanol oxidation on Pt. Besides water adsorption bands, linearly bonded CO, bridge-bonded CO, adsorbed formate, adsorbed formic acid, and adsorbed CHO bands were observed by ATR-FTIR spectroscopy during methanol and formic acid oxidation on Pt. Formic acid adsorption suppressed the formate and water adsorption. Our results suggest that formate could be an inactive adsorbed species, rather than an active intermediate, for both methanol and formic acid oxidation. Pb modification of Pt significantly enhanced formic acid oxidation through the direct pathway due to the third-body effect and electronic effects. Formic acid oxidation took place mainly at Pb modified low-coordinated defect sites at low potentials. Formic acid decomposition to form adsorbed CO occurred only in the hydrogen region, and Pb modification also slightly enhanced the successive oxidation of adsorbed CO. A double-peak infrared band was observed for linearly bound CO on the Pt film and was simulated with the Fresnel equations and Bruggeman effective medium theory.

New catalysts for formic acid fuel cells

Thallium adatoms deposited at under-potentials have shown the catalytic effect during the electrooxidation of formic acid on platinum ruthenium alloys. At Pt/Ru with an optimal coverage degree with adatoms Tl, HCOOH is oxidized at nearly 180 mV more negative potential than at Pt/Ru electrodes. The catalytic effect of modified Pt/Ru electrodes is plausibly caused by interaction of the Tl adatoms, located at Pt atoms with OH species of adjacent Ru atoms. These interactions stabilize Ru-OH species and allows for their formation at more negative potentials than at the Pt/Ru electrodes. The Ru-OH species oxidize firmly bound intermediates COad and thus release the Pt atoms for the oxidation of subsequent HCOOH molecules. The catalytic effect is probably caused by the third-body effect.

The effect of third bodies on wear and friction at the wheel-rail interface

The friction forces between the wheel and rail depend on a number of variables including the third body layer at the wheel–rail interface, the wheel and rail profiles, and the train dynamics. The third body layer significantly influences the damage mechanisms at the wheel-rail interface, especially wear, rolling contact fatigue (RCF), corrugations and other surface defects that then require maintenance. The introduction of additional constituents at the wheel–rail interface in the form of an additive with anti-wear and anti-crack properties can reduce the wear and RCF. In general, such an additive also reduces the friction. However, it is important to avoid the friction coefficient between the wheel tread and the top of the rail falling below 0.3 because the result would be wheel slip and long braking distances. Measuring friction coefficients accurately is still a challenge, as most existing tribometers are unable to replicate the wheel-rail contact conditions, specifically the contact pressure and sliding speed. The present study used a newly designed handheld tribometer that is able to match the typical contact pressure. Results obtained with the handheld tribometer have been compared with values extracted from the traction-force measurement system of a locomotive. The tribometer field measurements have shown that by using a top-of-rail friction modifier (TOR-FM), both the wear and the friction coefficients can be reduced, but also that heavy TOR-FM films may cause unacceptably low friction. Comparing the results of field and laboratory tests confirms that weather and realistic third bodies present on the track have a significant effect on friction and wear.

The Third Body Effect of Carbon Dioxide on N-heptane Ignition Delay Characteristics under O2/CO2 Conditions

ABSTRACT In order to study the impact of CO2 during n-heptane ignition delay under O2/CO2 conditions, this study presents a numerical and experimental study in four cases (40 mol.% O2/60 mol.% CO2, 50 mol.% O2/50 mol.% CO2, 57 mol.% O2/43 mol.% CO2 and 65 mol.% O2/35 mol.% CO2). Firstly, a third body effect (TBE) model is presented, which considers the third body efficiency of CO2. Secondly, the TBE model adds the third body efficiency into a one-step global mechanism and obtains an ignition delay time formula according to the auto-ignition theory. Thirdly, experiments are carried out in a constant volume combustion chamber (CVCC) test system. Furthermore, the experiment and simulation results are compared and discussed. In addition, two parameters (α and β) are defined to study the third body effect and the chemical effect of CO2 respectively. Finally, chemical kinetic analyses are used to study the CO2 effect. The results show that the TBE model is in agreement with the experiment and the maximum difference is 8.94% under the 57 mol.% O2/43 mol.% CO2 condition. The third body effect is the main effect of CO2 and it can decrease small molecule intermediates and radicals. Besides, C3H6O is the most affected species by the third body effect of CO2 among four prominent intermediate species. Furthermore, the third body effect of CO2 inhibits most paths of OH production. H+ O2→O+ OH (R11) is the most affected pathway whose peak rate of production (ROP) decreases by 51.5%.

Study of the chemical effect of steam dilution on NO formation in laminar premixed H2/Air flame at normal and elevated pressure

To promote the understanding and development of the steam diluted H2/air combustion technology, the chemical effect of steam dilution on NO formation in 1D laminar premixed H2/air flame is numerically studied over a wide range of conditions. The importance and the influence path of the chemical effect of steam dilution are analyzed, and the impact of working conditions is explored. This research makes up for the deficiencies in understanding the chemical effect of steam dilution, and has significant reference value for optimizing working conditions in practical application. Results show that the importance of steam dilution's chemical effect on NO formation highly depends on the dilution rate and pressure. In this study, the chemical effect of steam accounts for −16.3%–20.1% of the total NO reduced by steam dilution. The direct chemical effect of steam is the main cause of NO change. It reduces the H and O concentration by inhibiting the reaction OH+H2<=>H+H2O and H+O2<=>OH+O. However, the third-body effect of steam increases the O concentration and then slightly promotes NO formation. Increasing pressure causes the direct chemical effect to gradually turns to promote the NO generation at low dilution rates.

Dynamical properties of the Molniya satellite constellation: Long-term evolution of orbital eccentricity

The aim of this work is to analyze the orbital evolution of the mean eccentricity given by the Two-Line Elements (TLE) set of the Molniya satellites constellation. The approach is bottom-up, aiming at a synergy between the observed dynamics and the mathematical modeling. Being the focus the long-term evolution of the eccentricity, the dynamical model adopted is a doubly-averaged formulation of the third-body perturbation due to Sun and Moon, coupled with the oblateness effect on the orientation of the satellite. The numerical evolution of the eccentricity, obtained by a two-degree-of-freedom time dependent model assuming different orders in the series expansion of the third-body effect, is compared against the mean evolution given by the TLE. The results show that, despite being highly elliptical orbits, the second order expansion catches extremely well the behavior. Also, the lunisolar effect turns out to be non-negligible for the behavior of the longitude of the ascending node and the argument of pericenter. Finally, a frequency series analysis is proposed to show the main contributions that can be detected from the observational data.

Modeling third-body effects in the thermal decomposition of H2O2

The thermal decomposition of hydrogen peroxide (H2O2) in seven bath gases (M = He, Ar, H2, N2, CO, CH4, and H2O) has been studied by classical trajectory calculations of the collisional energy transfer processes and master equation analyses of the pressure-dependent rate constants. The energy transfer processes are modeled with the range parameter of the exponential down model and collision frequency for energy transfer. Both of the two quantities are calculated from the collisional trajectories propagated on the potential energy surfaces directly evaluated by the optimized spin-component-scaled MP2 method. The master equation calculations using these parameters were found to give reasonable descriptions of the rate constants at low pressures. The calculated relative third-body efficiencies agree well with the available experimental data for M = He, Ar, and N2 but the efficiency calculated for M = H2O appears to be overestimated at low temperature. The calculated rate constants are represented by the limiting high-pressure rate constant of k∞ = 6.7 × 1014 exp(−24800 K/T) s−1, limiting low-pressure rate constants for M = Ar and N2 of k0(Ar) = 3.65 × 108 (T/K)−4.691 exp(−26470 K/T) cm3 molecule−1 s−1 and k0(N2) = 8.21 × 109 (T/K)−5.034 exp(−26600 K/T) cm3 molecule−1 s−1, the center broadening factor of Fcent = 0.7 exp(− T/3400 K), and the tabulated relative third-body efficiencies. The pressure-dependent rate constants calculated for multicomponent bath gases are reasonably reproduced by the traditional linear mixture rule, whereas the mixture rule based on the reduced pressure is found to provide a more precise description.

Low-thrust trajectory design in low-energy regimes using variational equations

This paper proposes a novel description of the equations of motion for low-thrust trajectory design in the presence of a third-body perturbation. The framework is formulated using Gauss’ Variational Equations (GVE) with two distinct accelerations: the one produced by the electric engine and the disturbing term of the third-body effect, which is computed using the disturbing potential of the previously studied Keplerian Map. The presented GVE third-body (GVE-3B) framework allows for a simple and intuitive description of the low-thrust optimisation problem. It is accurate until very close to the sphere of influence of the perturbing body, and thus can be used to target trajectories in low-energy regimes. Together with the framework, this paper develops a methodology to generate low-energy first-guess solutions for low-thrust trajectories. Both the methodology and the framework are showcased in the design of two distinct missions: a rendezvous with asteroid 2017 SV19 during its next Earth encounter, after departing from the unstable invariant manifold of the L2 point in the Sun-Earth system, and the capture of asteroid 2018 AV2 to a stable invariant manifold of the same point.