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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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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Application of the pseudostate theory to the three-body Lambert problem

The pseudostate theory, which approximates three-body trajectories by overlapping the conic effects of both massive bodies on the third body, has been used to solve boundary-value problems. Frequently, the approach to the secondary is quite close, as in interplanetary gravity-assist or satellite-tour trajectories. In this case, the orbit with respect to the primary is radically changed so that perturbation techniques are time consuming, yet higher accuracy than point-to-point conics is necessary. This method reduces the solution of the three-body Lambert problem to solving two conic Lambert problems and inverting a 7 x 7 matrix, the components of which are all found analytically. Typically 90-95 percent of the point-to-point conic error, with respect to an integrated trajectory, is eliminated.

Byrnes, Dennis V.↗
NASA NTRS1979

Application of the pseudostate theory to the three-body Lambert problem

The pseudostate theory, which approximates three-body trajectories by overlapping the conic effects of both massive bodies on the third body, has been used to solve boundary value problems. Frequently, the approach to the secondary is quite close, as in interplanetary gravity assist trajectories or satellite tour trajectories. In this case the orbit with respect to the primary is radically changed so that perturbation techniques are time consuming, yet higher accuracy than point-to-point conics (V-infinity matching) is necessary. This method reduces the solution of the three-body Lambert problem to solving two conic Lambert problems and inverting a 7 x 7 matrix, the components of which are all found analytically. Typically 90-95% of the point-to-point conic error with respect to an integrated trajectory is eliminated.

Byrnes, D. V.↗
DOE OSTI2021

Tunable Three-Body Loss in a Nonlinear Rydberg Medium

Long-range Rydberg interactions, in combination with electromagnetically induced transparency (EIT), give rise to strongly interacting photons where the strength, sign, and form of the interactions are widely tunable and controllable. Such control can be applied to both coherent and dissipative interactions, which provides the potential for generating novel few-photon states. Recently it has been shown that Rydberg-EIT is a rare system in which three-body interactions can be as strong or stronger than two-body interactions. In this work, we study three-body scattering loss for Rydberg-EIT in a wide regime of single and two-photon detunings. We report our numerical simulations of the full three-body wave function and analytical estimates based on Fermi’s golden rule strongly suggest that the observed features in the outgoing photonic correlations are caused by the resonant enhancement of the three-body losses.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1962

The Restricted Three-Body-Problem as a Perturbation of Euler's Problem of Two Fixed Centers and Its Application to Lunar Trajectories

The restricted Three-Body-Problem considers the motion of an infinitesimal mass under the gravitational attraction of two finite masses, which revolve about their common center of gravity in coplanar circles. It is well known that Euler's problem of two fixed centers, consisting of the motion of an infinitesimal mass under the gravitational attraction of two finite masses fixed in space, can be solved by elliptic functions. The idea presented here is to take the solution of Euler's problem as the solution of the restricted Three-Body-Problem by allowing the initial values to be functions of time now. Differential equations for the perturbed initial values are established. These equations can be given in closed form by using the fact that the transformation to the perturbed initial values of Euler's problem is canonical. Thus, an approximation can be obtained for the solution of the restricted Three-Body-Problem. The method can also be used to represent classes of neighboring trajectories for guidance purposes.

Euler equation↗
NASA NTRS2008

Subregions of Motion and Elliptic Halo Orbits in the Elliptic Restricted Three-Body Problem

In this paper we present regions of motion and periodic orbits in the spatial elliptic restricted three body problem (ER3BP). Periodic orbits and regions of motion are fundamental keys to understand any dynamical system; for this reason the Hill's surfaces or the families of halo orbits have been extensively studied in the frame of the circular restricted three body problem. It is our opinion that their natural extensions to the ER3BP have not been studied enough. We divide the position space into forbidden subregions, subregions of motion and low-velocity subregions.We use these notions to define necessary condition for a transfer trajectory in the ER3BP. Also we compute branches of elliptic halo orbits bifurcating from halo orbits in the circular restricted three body problem. The new periodic orbits have principal periods and stability properties different from those of the originating halo orbit.

mission design↗
NASA NTRS1966

Numerical integration of periodic orbits in the elliptic restricted three-body problem

The problem of finding periodic orbits in the circular restricted three-body problem has been very extensively studied in celestial mechanics. It is well known that continuous families of periodic orbits exist, for which the period varies in a continuous way. However, all the applications which are found in the solar system correspond to cases with non-zero eccentricities, and the elliptic restricted three-body problem is thus a better approximation than the circular one. For instance, for the motion of a satellite in the Earth-Moon system, as a first approximation, we may assume that the Moon moves around the Earth in circular motion; but as a much better approximation, we can also assume that the Moon moves in an elliptic orbit around the Earth.

NUMERICAL INTEGRATION↗
NASA NTRS1980

Central configurations and hyperbolic-elliptic motion in the three-body problem

A refined classification of motion for the planar three-body problem with zero-sum total energy is presented. The structure and dimensions of the sets of initial conditions leading to parabolic expansion or hyperbolic-elliptic motion are found. Attention is given to the use of the Hamiltonian of the system and to the two- and three-dimensional problem. It is verified that the new coordinates of position and linear momentum approaches limits as t (time) approaches infinity, and that these limits constitute equilibrium solutions to the three-body problem representing control configurations.

Hulkower, N. D.↗
DOE OSTI2020

Three-body Förster resonance of a new type in Rydberg atoms

The three-body Förster resonances 3 × nP{sub 3/2}(|M|) →nS{sub 1/2} + (n + 1)S{sub 1/2} + nP{sub 3/2}(|M*|), controlled by a constant electric field, were realised earlier by the authors in an ensemble of several cold Rydberg Rb atoms. One of the drawbacks of such resonances for potential application in three-qubit quantum gates is the proximity of the two-body Förster resonance 2 × nP{sub 3/2} → nS{sub 1/2} + (n + 1)S{sub 1/2}, as well as the possibility of their implementation only for states with values of the principal quantum numbers n ⩽38. A three-body resonance of a new type, 3 × nP{sub 3/2} → nS{sub 1/2} + (n + 1)S{sub 1/2} + nP{sub 1/2}, which can be realised for arbitrary n, is proposed and analysed. Its specific feature is also that the third atom transits into a state with a different total angular momentum J = 1/2, which has no Stark structure, so that the two-body resonance is completely absent. Numerical calculations showed that for not too strong interaction, it is possible to observe coherent three-body oscillations of the populations of collective states, which is of interest for developing new schemes of three-qubit quantum gates controlled by an electric field. (paper)

74 ATOMIC AND MOLECULAR PHYSICS↗