The effect of solar radiation pressure on the Lagrangian points in the elliptic restricted three-body problem

Abstract

In this paper the effect of solar radiation pressure on the location and stability of the five Lagrangian points is studied, within the frame of elliptic restricted three-body problem, where the primaries are the Sun and Jupiter acting on a particle of negligible mass. We found that the radiation pressure plays the rule of slightly reducing the effective mass of the Sun and changes the location of the Lagrangian points. New formulas for the location of the collinear libration points were derived. For large values of the force ratio β, we found that at β = 0.12, the collinear point L 3 is stable and some families of periodic orbits can be drawn around it.

Effects of radiation on stability of triangular equilibrium points in elliptic restricted three body problem

“…In case of complex roots, there must be roots with positive real parts leading to instability of the equilibrium points in the first approximation.   "Ammar [11]" found that the triangular equilibrium points are stable for For values of the eccentricity close to 0 e , both 1  and 2  are small quantities .For small eccentricities, when one of the quantities 1  is small, the others differ a little from unity. The schematic behavior of the system can be investigated when the infinitesimal move around the triangular equilibriums points under the radiating bigger primaries by plotting the transition curves for different values of 'e' and parameters 'β' using MATLAB 7.1 version of software.…”

“…The equations of motion of the infinitesimal mass in the elliptic restricted three body problem in rotating pulsating coordinate system are presented below "following Ammar [11]" by…”

“…The total action from the Sun on the particle can be expressed by the acceleration "as given by Ammar [11]".…”

“…In spite of the large amount of analytical and numerical work in CR3BP, there are relatively a few analytical results in ER3BP. The stability of the infinitesimal around the triangular equilibrium points in the elliptical restricted three body is "described in considerable details by Grebenikov [1], Danby [3], Bennet [4], Rabe [5], [6], Meire [7], Markeellos [8], Roberts [9], Zimvoschikov and Thakai [10], Ammar [11]". The linear stability of elliptic Lagrange orbits in ER3BP by numerical integration technique has been "studied by Danby [3]".…”

“…The librational solutions to the photogravitational restricted three body problems by considering both primaries as radiating have been "studied by Khasan [12], [13]". The effect of solar radiation pressure on the location and stability of lagrangian points in ER3BP has been "studied by Ammar [11]" and was seen that radiation pressure plays the role of reducing the effective mass and slightly changes the location of the Lagrangian points. It was found that the triangular equilibrium points are stable for 0.5…”