Unveiling Perturbing Effects of P-R Drag on Motion around Triangular Lagrangian Points of the Photogravitational Restricted Problem of Three Oblate Bodies

The perturbing effects of the Poynting-Robertson drag on motion of an infinitesimal mass around triangular Lagrangian points of the circular restricted three-body problem under small perturbations in the Coriolis and centrifugal forces when the three bodies are oblate spheroids and the primaries are emitters of radiation pressure, is the focus of this paper. The equations governing the dynamical system have been derived and locations of triangular Lagrangian points are determined. It is seen that the locations are influenced by the perturbing forces of centrifugal perturbation and the oblateness, radiation pressure and, P-R drag of the primaries. Using the software Mathematica, numerical analysis are carried out to demonstrate how the dynamical elements: mass ratio, oblateness, radiation pressure, P-R drag and centrifugal perturbation influence the positions of triangular equilibrium points, zero velocity surfaces and the stability. Our investigation reveals that, though the radiation pressure, oblateness and centrifugal perturbation decrease region of stability when motion is stable, however, they are not the influential forces of instability but the P-R drag. In the region when motion around the triangular points are stable an inclusion of the P-R drag of the bigger primary even by an almost negligible value of 1.04548*10-9 overrides other effect and changes stability to instability. Hence, we conclude that the P-R drag is a strong perturbing force which changes stability to instability and motion around triangular Lagrangian points remain unstable in the presence of the P-R drag.

SEARCH FOR STABLE ORBITS AROUND THE BINARY ASTEROID SYSTEMS 1999 KW4 AND DIDYMOS

This work includes analytical and numerical studies of spacecrafts orbiting two binary asteroid systems: 1999 KW4 and Didymos. The binary systems are modeled as full irregular bodies, such that the whole evolution of the results will show the impact of the irregular gravity field in the lifetime and dynamics of the spacecraft’s orbit. The equations of motion of the binary system and the spacecraft are derived from Lagrange Equations. The solar radiation pressure is consired in the dynamics of the spacecraft.Two distinct methods are used to search for stable orbits around the binary systems. One is called the grid search method, which defines the main body as a point mass to estimate the initial state of the spacecraft based on a circular Keplerian orbit. The second method is the search for periodic orbits based on zero-velocity surfaces.

Numerical Study of the Zero Velocity Surface and Transfer Trajectory of a Circular Restricted Five-Body Problem

We focus on a type of circular restricted five-body problem in which four primaries with equal masses form a regular tetrahedron configuration and circulate uniformly around the center of mass of the system. The fifth particle, which can be regarded as a small celestial body or probe, obeys the law of gravity determined by the four primaries. The geometric configuration of zero-velocity surfaces of the fifth particle in the three-dimensional space is numerically simulated and addressed. Furthermore, a transfer trajectory of the fifth particle skimming over four primaries then is designed.

BIFURCATIONS FROM PLANAR TO THREE-DIMENSIONAL PERIODIC ORBITS IN THE RING PROBLEM OF N BODIES WITH RADIATING CENTRAL PRIMARY

We consider the three-dimensional motion of a massless particle in a regular polygon formation of N primary bodies, one of which is located at the system's center of mass. Assuming that the central primary is a radiation source, we apply the simplified theory suggested by Radzievskii, in order to study the effect of radiation pressure in the three-dimensional dynamics of the system. We particularly study the evolution of the zero-velocity surfaces for various values of the radiation coefficient b0 and investigate also the cases with b0 > 1 (that is, radiation surpasses gravity) since for these cases, significant changes in the dynamics occur. We then locate numerically the onset of three-dimensional periodic motion from planar periodic motion by calculating the orbits' vertical critical stability. Many families of three-dimensional periodic motions are presented and the regions of the three-dimensional space where these motions take place, are determined. We subsequently investigate how the bifurcations from planar to three-dimensional periodic orbits are affected by the increase of the primary's radiation coefficient and how the overall dynamics of the system is affected by the value of the primaries' number N.

BIFURCATIONS IN THE TOPOLOGY OF ZERO-VELOCITY SURFACES IN THE PHOTO-GRAVITATIONAL COPENHAGEN PROBLEM

We study the evolution of the regions where three-dimensional motions of a small body are allowed in the Copenhagen case of the restricted three-body problem where one or both primaries, are radiation sources. We discuss the bifurcations in the topology of the zero-velocity surfaces, as well as in the trapping regions of the particle motion for various cases.