Abstract
Objective: To find the periodic orbits using Fourier series expansions around the libration points L4 and L5 in the frame work of planar restricted threebody by considering the more massive primary a source of radiation.Methods/Statistical analysis: Period of the periodic orbits around the libration point L4 is found using the variational equations and function of the two finite masses. The period is independent on the size the orbit. When terms of higher order are retained in the analysis the period depends on the size of the orbit. Findings: The value of the critical mass is found in the photogravitational restricted three–body problem and is shown that the critical mass value corresponding to the small mass increases with the size of the orbit. It is shown that the classes of periodic orbits with infinitesimal limiting orbits L4 exist for values of the small mass greater than the critical mass value m0: A comparison between these orbits with and without radiation pressure is made. Applications: Periodic orbits can be used to explore small solar system bodies, including asteroids and comets. Perturbation due to solar radiation pressure has to be understood and should be taken care of during human exploration mission. Keywords: Photogravitational restricted problem; triangular liberation point; periodic orbits; solar radiation pressure; Fourier series expansions
Highlights
Brown (1) considered the long period orbits around the triangular libration points by supposing finite amplitudes of libration and discussed in some detail the dependence of period and orbit shape on amplitude
The study in (3) showed that the period of the periodic orbits around the libration points L4 and L5 appears as a function of the size of the orbits, when terms of second and third order are retained in the series expression, the investigation to the case that the masses have values in the neighbourhood of the critical values μ0 and 1- μ0
Restricted three-body problem (RTBP) describes the motion of a massless body which moves under the gravitational effect of two finite masses called primaries
Summary
Brown (1) considered the long period orbits around the triangular libration points by supposing finite amplitudes of libration and discussed in some detail the dependence of period and orbit shape on amplitude. The study in (3) showed that the period of the periodic orbits around the libration points L4 and L5 appears as a function of the size of the orbits, when terms of second and third order are retained in the series expression, the investigation to the case that the masses have values in the neighbourhood of the critical values μ0 and 1- μ0. Restricted three-body problem (RTBP) describes the motion of a massless body which moves under the gravitational effect of two finite masses called primaries. In(5) Radzievskii formulated the photo-gravitational restricted three-body problem (PRTBP) and studied the location of the equilibrium points. This arises from the classical problem when one of the masses is an intense emitter of radiation. If q < 0, radiation surpasses gravity and if 0 < q ≤ 1, gravitational force exceeds radiation
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