Linear Stability of Equilibrium Points in the Generalized Photogravitational Chermnykh's Problem

The equilibrium points and their linear stability has been discussed in the generalized photogravitational Chermnykh's problem. The bigger primary is being considered as a source of radiation and small primary as an oblate spheroid. The effect of radiation pressure has been discussed numerically. The collinear points are linearly unstable and triangular points are stable in the sense of Lyapunov stability provided $\mu< \mu_{Routh}=0.0385201$. The effect of gravitational potential from the belt is also examined. The mathematical properties of this system are different from the classical restricted three body problem

Nonlinear Stability in the Generalised Photogravitational Restricted Three Body Problem with Poynting-Robertson Drag

The Nonlinear stability of triangular equilibrium points has been discussed in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. The problem is generalised in the sense that smaller primary is supposed to be an oblate spheroid. The bigger primary is considered as radiating. We have performed first and second order normalization of the Hamiltonian of the problem. We have applied KAM theorem to examine the condition of non-linear stability. We have found three critical mass ratios. Finally we conclude that triangular points are stable in the nonlinear sense except three critical mass ratios at which KAM theorem fails.Comment: Including Poynting-Robertson Drag the triangular equilibrium points are stable in the nonlinear sense except three critical mass ratios at which KAM theorem fail

The Effect of Radiation Pressure on the Equilibrium Points in the Generalised Photogravitational Restricted Three Body Problem

The existence of equilibrium points and the effect of radiation pressure have been discussed numerically. The problem is generalized by considering bigger primary as a source of radiation and small primary as an oblate spheroid. We have also discussed the Poynting-Robertson(P-R) effect which is caused due to radiation pressure. It is found that the collinear points $L_1,L_2,L_3$ deviate from the axis joining the two primaries, while the triangular points $L_4,L_5$ are not symmetrical due to radiation pressure. We have seen that $L_1,L_2,L_3$ are linearly unstable while $L_4,L_5$ are conditionally stable in the sense of Lyapunov when P-R effect is not considered. We have found that the effect of radiation pressure reduces the linear stability zones while P-R effect induces an instability in the sense of Lyapunov

On the a and g families of symmetric periodic orbits in the photo-gravitational hill problem and their application to asteroids

This paper focuses on the exploration of families of planar symmetric periodic orbits around minor bodies under the effect of solar radiation pressure. For very small asteroids and comets, an extension of the Hill problem with Solar Radiation Pressure (SRP) perturbation is a particularly well-suited dynamical model. The evolution of the a and g families of symmetric periodic orbits has been studied in this model when SRP is increased from the classical problem with no SRP to levels corresponding to current and future planned missions to minor bodies, as well as one extreme case with very large SRP. In addition, the feasibility an applicability of these orbits for the case of asteroids was analysed, and the effect of SRP in their stability is presented