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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 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.↗
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 NTRS1975

A two parameter survey of periodic orbits in the restricted problem of three bodies

Within the context of the restricted problem of three bodies the effects caused by varying the mass ratio of the primaries and the eccentricity of their orbits, upon periodic orbits of the infinitesimal mass which are numerical continuations of circular orbits in the ordinary problem of two bodies are shown. A recursive power series technique is used to numerically integrate the equations of motion as well as the first variational equations in order to generate a two parameter family of perodic orbits and identify the linear stability characteristics. Seven such families are investigated with equally spaced mass ratios from 0.0 to 1.0 and eccentricities of the orbits of the primaries in a range 0.0 to 0.6. Stable orbits are associated with large distances of the infinitesimal mass from the perturbing primary, nearly circular motion of the primaries, and small mass ratios of the primaries. Unstable orbits for the infinitesimal mass are associated with small distances from the perturbing primary, highly elliptic orbits of the primaries and large mass ratios.

Shelus, P. J.↗
NASA NTRS1971

Calculation of trajectories using constant and slowly varying functions

A method is presented for calculating trajectories for the restricted problem of three bodies which utilizes conic propagation of the state vector with frequency correction of position and velocity by means of a constant or slowly varying function. This method of calculating trajectories was applied to the planar circular restricted three body problem, the planar elliptic restricted problem, and the ephemeral restricted problem. Two methods (the refined method and the straight forward method) of determining the direction of the position correction are presented for the circular restricted problem and the elliptic restricted problem of three bodies. Only the straight forward method was used with the ephemeral restricted problem. The earth, the moon, and a space vehicle comprise the restricted three body model that is used.

Culpepper, B. K.↗
NASA NTRS1967

Regularization of the restricted problem of four bodies.

Regularization of restricted three-body problem extended to case where three primaries of any mass revolve in circular orbits around common center of mass and fourth body of infinitesimal mass moves in their field

CIRCULAR ORBIT↗
NASA NTRS1981

Periodic solutions about the collinear Lagrangian solution in the general problem of three bodies

The article describes the solutions near Lagrange's circular collinear configuration in the planar problem of three bodies with three finite masses. The article begins with a detailed review of the properties of Lagrange's collinear solution. Lagrange's quintic equation is derived and several expressions are given for the angular velocity of the rotating frame. The equations of motion are then linearized near the circular collinear solution, and the characteristic equation is also derived in detail. The different types of roots and their corresponding solutions are discussed. The special case of two equal outer masses receives special attention, as well as the special case of two small outer masses. Finally, the fundamental family of periodic solutions is extended by numerical integration all the way up to and past a binary collision orbit. The stability and the bifurcations of this family are briefly enumerated.

Broucke, R.↗
NASA NTRS1971

The topology of the regularized integral surfaces of the 3-body problem

Momentum, angular momentum, and energy of integral surfaces in the planar three-body problem are considered. The end points of orbits which cross an isolating block are identified. It is shown that this identification has a unique extension to an identification which pairs the end points of orbits entering the block and which end in a binary collision with the end points of orbits leaving the block and which come from a binary collision. The problem of regularization is that of showing that the identification of the end points of crossing orbits has a continuous, unique extension. The regularized phase space for the three-body problem was obtained, as were regularized integral surfaces for the problem on which the three-body equations of motion induce flows. Finally the topology of these surfaces is described.

Easton, R.↗
NASA NTRS1974

Stability regions for quasiperiodic motion in the restricted problem of three bodies

Surfaces of section, plotted in configuration space, have been computed for the motion of the massless particle in the restricted problem of three bodies. Nine mass ratios and a wide variety of Jacobi constants were investigated; over four thousand orbits were computed, about half of which were finally used. The plots of surface of section have been reduced to plots of stability regions, following a method due to Henon (1965a, 1965b, 1966b, 1969). Sample surfaces of section are also given. The complete set of 276 surfaces of section has been published as a report (Jefferys, 1971) and is available upon request from the author.

Jefferys, W. H.↗