Second-order matching in the restricted three-body problem (small?)

1974 ◽  
Vol 9 (4) ◽  
pp. 437-450 ◽  
Author(s):  
J. V. Breakwell ◽  
L. M. Perko
Keyword(s):  
Body Problem ◽  
Second Order ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

scholarly journals A Study of Single- and Double-Averaged Second-Order Models to Evaluate Third-Body Perturbation Considering Elliptic Orbits for the Perturbing Body

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
R. C. Domingos ◽  
A. F. Bertachini de Almeida Prado ◽  
R. Vilhena de Moraes
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Second Order ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Body ◽  
Elliptic Orbits ◽  
Three Body ◽  
The Impact ◽  
Third Body Perturbation

The equations for the variations of the Keplerian elements of the orbit of a spacecraft perturbed by a third body are developed using a single average over the motion of the spacecraft, considering an elliptic orbit for the disturbing body. A comparison is made between this approach and the more used double averaged technique, as well as with the full elliptic restricted three-body problem. The disturbing function is expanded in Legendre polynomials up to the second order in both cases. The equations of motion are obtained from the planetary equations, and several numerical simulations are made to show the evolution of the orbit of the spacecraft. Some characteristics known from the circular perturbing body are studied: circular, elliptic equatorial, and frozen orbits. Different initial eccentricities for the perturbed body are considered, since the effect of this variable is one of the goals of the present study. The results show the impact of this parameter as well as the differences between both models compared to the full elliptic restricted three-body problem. Regions below, near, and above the critical angle of the third-body perturbation are considered, as well as different altitudes for the orbit of the spacecraft.

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

scholarly journals GEOMETRY OF HOMOCLINIC CONNECTIONS IN A PLANAR CIRCULAR RESTRICTED THREE-BODY PROBLEM

2007 ◽  
Vol 17 (04) ◽  
pp. 1151-1169 ◽  
Author(s):  
MARIAN GIDEA ◽  
JOSEP J. MASDEMONT
Keyword(s):  
Symbolic Dynamics ◽  
Body Problem ◽  
Invariant Manifolds ◽  
Libration Point ◽  
Homoclinic Orbits ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Lyapunov Orbits ◽  
Homoclinic Connections ◽  
Three Body

The stable and unstable invariant manifolds associated with Lyapunov orbits about the libration point L1between the primaries in the planar circular restricted three-body problem with equal masses are considered. The behavior of the intersections of these invariant manifolds for values of the energy between that of L1and the other collinear libration points L2, L3is studied using symbolic dynamics. Homoclinic orbits are classified according to the number of turns about the primaries.

Sign in / Sign up

Export Citation Format

Share Document