scholarly journals Optimal Two-Impulse Trajectories with Moderate Flight Time for Earth-Moon Missions

2012 ◽  
Vol 2012 ◽  
pp. 1-34 ◽  
Author(s):  
Sandro da Silva Fernandes ◽  
Cleverson Maranhão Porto Marinho
Keyword(s):  
Phase Angle ◽  
Initial Phase ◽  
Space Vehicle ◽  
Optimization Criterion ◽  
Flight Time ◽  
Three Body Problem ◽  
Dynamical Models ◽  
Velocity Impulse ◽  
Three Body ◽  
Raphson Method

A study of optimal two-impulse trajectories with moderate flight time for Earth-Moon missions is presented. The optimization criterion is the total characteristic velocity. Three dynamical models are used to describe the motion of the space vehicle: the well-known patched-conic approximation and two versions of the planar circular restricted three-body problem (PCR3BP). In the patched-conic approximation model, the parameters to be optimized are two: initial phase angle of space vehicle and the first velocity impulse. In the PCR3BP models, the parameters to be optimized are four: initial phase angle of space vehicle, flight time, and the first and the second velocity impulses. In all cases, the optimization problem has one degree of freedom and can be solved by means of an algorithm based on gradient method in conjunction with Newton-Raphson method.

scholarly journals Pluto's Lyapunov numbers in different dynamical models

1996 ◽  
Vol 172 ◽  
pp. 71-74 ◽  
Author(s):  
R. Dvorak ◽  
E. Lohinger
Keyword(s):  
Body Problem ◽  
Stable Region ◽  
Three Body Problem ◽  
Orbital Elements ◽  
Dynamical Models ◽  
Characteristic Numbers ◽  
Numerical Integrations ◽  
Lyapunov Numbers ◽  
Three Body ◽  
Lyapunov Characteristic Numbers

We present the results of numerical integrations of Pluto and some fictitious Plutos in three different models (the circular and the elliptic restricted three body problem and the outer solar system). We determined the “extension” of the stable region in these models by means of the Lyapunov Characteristic Numbers and by an analysis of the orbital elements.

scholarly journals Alternative paths to Earth-Moon transfer

2006 ◽  
Vol 2006 ◽  
pp. 1-20 ◽  
Author(s):  
Cristiano Fiorilo de Melo ◽  
Othon Cabo Winter
Keyword(s):  
Body Problem ◽  
Low Cost ◽  
Flight Time ◽  
The Moon ◽  
Three Body Problem ◽  
The Earth ◽  
Probe System ◽  
Four Body Problem ◽  
Low Altitude ◽  
Three Body

The planar, circular, restricted three-body problem predicts the existence of periodic orbits around the Lagrangian equilibrium point L1. Considering the Earth-lunar-probe system, some of these orbits pass very close to the surfaces of the Earth and the Moon. These characteristics make it possible for these orbits, in spite of their instability, to be used in transfer maneuvers between Earth and lunar parking orbits. The main goal of this paper is to explore this scenario, adopting a more complex and realistic dynamical system, the four-body problem Sun-Earth-Moon-probe. We defined and investigated a set of paths, derived from the orbits around L1, which are capable of achieving transfer between low-altitude Earth (LEO) and lunar orbits, including high-inclination lunar orbits, at a low cost and with flight time between 13 and 15 days.

The Tangled Tale of Phase Space

2018 ◽  
Author(s):  
David D. Nolte
Keyword(s):  
Phase Space ◽  
Chaotic Behavior ◽  
Three Body Problem ◽  
Henri Poincaré ◽  
History Of ◽  
The Stability ◽  
Three Body ◽  
Space Phase ◽  
Central Paradigm ◽  
System Phase

This chapter presents the history of the development of the concept of phase space. Phase space is the central visualization tool used today to study complex systems. The chapter describes the origins of phase space with the work of Joseph Liouville and Carl Jacobi that was later refined by Ludwig Boltzmann and Rudolf Clausius in their attempts to define and explain the subtle concept of entropy. The turning point in the history of phase space was when Henri Poincaré used phase space to solve the three-body problem, uncovering chaotic behavior in his quest to answer questions on the stability of the solar system. Phase space was established as the central paradigm of statistical mechanics by JW Gibbs and Paul Ehrenfest.

Rigid-Rotator and Fixed-Shape Solutions to the Coulomb Three-Body Problem

1997 ◽  
Vol 22 (1) ◽  
pp. 37-60 ◽  
Author(s):  
A. Santander ◽  
J. Mahecha ◽  
F. Pérez
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
Rigid Rotator ◽  
Three Body

On the modified circular restricted three-body problem with variable mass

New Astronomy ◽  
2021 ◽  
Vol 84 ◽  
pp. 101510
Author(s):  
Md Sanam Suraj ◽  
Rajiv Aggarwal ◽  
Md Chand Asique ◽  
Amit Mittal
Keyword(s):  
Body Problem ◽  
Variable Mass ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

Triple close approach in the three-body problem: A limit for the bounded orbits

1984 ◽  
Vol 32 (1) ◽  
pp. 15-28 ◽  
Author(s):  
Jacques Laskar ◽  
Christian Marchal
Keyword(s):  
Body Problem ◽  
Close Approach ◽  
Three Body Problem ◽  
Three Body
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