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A SYMMETRIC REPRESENTATION FOR THREE-BODY PROBLEMS. I. MOTION IN A PLANE
Three-body problem - a symmetric representation - motion in a plane
The capture problem in the three-body restricted orbital problem
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TWO FIXED CENTER APPROXIMATIONS TO THE RESTRICTED PROBLEM
Perturbation theory of two-fixed-center problem leading to approximation of three-body problem
THE EXISTENCE OF PERIODIC SOLUTIONS PASSING NEAR BOTH MASSES OF THE RESTRICTED THREE BODY PROBLEM
Periodic solutions passing near both masses of the restricted three-body problem - keplerian ellipses
REMARKS ON HILL'S LUNAR THEORY. PART I
Hill lunar theory modifications and computer application for solution of three-body problems
Velocity Modification for Earth Capture of An Astronomical Body in the Solar System
In studying the possible capture of an astronomical body that is orbiting around the sun, two questions are encountered: How near must it approach the earth before it could be captured? How could we make it approach as near to the earth as required? This paper answers the first question by using the results of the restricted three-body problem, and partially answers the second question by estimating the order of magnitude of the velocity modification needed to change the orbit of the body and make capture possible.
Three-Dimensional Lunar Mission Studies
Some three-dimensional lunar trajectories have been calculated by integration of the equations of motion of the classical restricted three-body problem of celestial mechanics. The calculations have been used for analysis of several aspects of lunar flight including requirements for achieving lunar impact and for establishment of a close lunar satellite. The allowable errors in initial conditions for lunar missions are strongly dependent on the values of the initial injection velocity and the injection angle. There can be large differences in results obtained from two-dimensional analyses (in which the vehicle trajectory is assumed to remain always in the earth-moon plane) and those obtained from three-dimensional analyses. Some of the accuracy tolerances can be fairly well estimated by use of a two-body analysis which considers the inclination of the plane of the vehicle trajectory to the earth-moon plane. Satisfactory orbits for a relatively close lunar satellite can be obtained with accuracies in the initial conditions approximately equal to those required for lunar impact.
A SYMMETRIC REPRESENTATION FOR 3-BODY PROBLEMS
A symmetric representation for 3-body problems
ASTRONOMICAL ASPECTS OF THE EXPLORATION OF SPACE. I
Astronomical aspects of space exploration - astronomer and engineer relationship, astronomical units, and three body problem
A SYMMETRIC REPRESENTATION FOR 3-BODY PROBLEMS. I. MOTION IN A PLANE
A symmetric representation for 3-body problems motion in a plane
PERIODIC SOLUTIONS OF THE RESTRICTED THREE BODY PROBLEM REPRESENTING ANALYTIC CONTINUATIONS OF KEPLERIAN ELLIPTIC MOTIONS
Periodic solution of restricted three body problem as analytic continuation of keplerian elliptical motions
THE RESTRICTED THREE BODY PROBLEM. I. THE SURFACES OF ZERO VELOCITY IN REGULARIZED COORDINATES. 2. THE EULER PROBLEM BY GRAPHICAL ANALYSIS
Three body problem zero velocity curves - euler two center problem by graphical analysis - guidance systems
THE HAMILTON-JACOB I FORMULATION OF THE RESTRICTED THREE BODY PROBLEM IN TERMS OF THE TWO FIXED CENTER PROBLEM
Three body problem by hamilton-jacobi perturbation theory - guidance systems
Lunar Flight Study Series: Volume 6. A Study of Geometrical and Terminal Characteristics of Earth-Moon Transits Embedded in the Earth-Moon Plane
This report represents the results of a study of coplanar earth-moon transits. The study was initiated to provide information concerning coplanar geometrical characteristics of earth-moon trnasits. The geometrical aspects of transit behavior are related to variations injection conditions. The model of the earth-moon system used in this investigation is the Jacobian model of the restricted three body problem. All transits considered in this study are restricted to the moon-earth plane (MEP).
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.
DETERMINATION AND SURVEY OF PERIODIC TROJAN ORBITS IN THE RESTRICTED PROBLEM OF THREE BODIES
Determination and survey of periodic trojan orbits in the restricted problem of three bodies
THREE-BODY COLLISION RATES IN ATOMIC RECOMBINATION REACTIONS
Three-body collision rates in atomic recombination reactions