The photogravitational restricted three-body problem

Todoran, I.

doi:10.1007/bf00660081

Cited by 9 publications

(4 citation statements)

References 5 publications

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“…In the previous years several authors have made studies on Lagrangian points in the restricted three-body problem by considering the more massive primary or both primaries as source of radiation. Some of the important contributions are by Kunitsyn & Perezhogin (1985); Bhatnagar & Chawla (1979); Kunitsyn & Tureshbaev (1985); Lukyanov (1988); Todoran (1994); Ragos & Zagouras (1988a,b); Xue-tang et al (1994); Kalantonis et al (2006); Papadakis (2006). Sharma (1982) and Sharma & Ishwar (1995) investigated the linear stability of the triangular points in the planar case by considering the more massive primary as source of radiation and the smaller primary as oblate spheroid and found that the critical mass value decreases with the increase in radiation pressure.…”

Section: Introductionmentioning

confidence: 99%

Unveiling the influence of the radiation pressure in nature of orbits in the photogravitational restricted three-body problem

Zotos

2015

Astrophys Space Sci

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The case of the planar circular photogravitational restricted three-body problem where the more massive primary is an emitter of radiation is numerically investigated. A thorough numerical analysis takes place in the configuration (x, y) and the (x, C) space in which we classify initial conditions of orbits into three main categories: (i) bounded, (ii) escaping and (iii) collisional. Our results reveal that the radiation pressure factor has a huge impact on the character of orbits. Interpreting the collisional motion as leaking in the phase space we related our results to both chaotic scattering and the theory of leaking Hamiltonian systems. We successfully located the escape as well as the collisional basins and we managed to correlate them with the corresponding escape and collision times. We hope our contribution to be useful for a further understanding of the escape and collision properties of motion in this interesting version of the restricted three-body problem.

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Section: Introductionmentioning

confidence: 99%

Unveiling the influence of the radiation pressure in nature of orbits in the photogravitational restricted three-body problem

Zotos

2015

Astrophys Space Sci

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“…Some of the important contributions are by Radzievsky (1950Radzievsky ( , 1953, Chernikov (1970), Perezhogin (1976), Kunitsyn and Perezhogin (1978), Bhatnagar and Chawla (1979), Schuerman (1980), Simmons et al (1985), Kunitsyn and Tureshbaev (1985), Lukyanov (1988), Todoran (1994), Zagouras (1988a, 1988b), Xue-tang et al (1994), Kalantonis et al (2006) and Papadakis (2006). Some of the significant studies carried out related to the Lagrangian points by considering the oblateness of one or both the primaries with their equatorial planes coincident with the plane of motion, are by Vidyakin (1974), Sharma (1975), Sharma and Subba Rao (1975.…”

Section: Introductionmentioning

confidence: 98%

Effect of oblateness and radiation pressure on angular frequencies at collinear points

Namboodiri

Reddy

Sharma

2008

Astrophys Space Sci

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In the three-dimensional restricted three-body problem, by considering the more massive primary as an oblate spheroid with its equatorial plane coincident with the plane of motion as well as source of radiation, it is found that the collinear point L 1 comes nearer to the primaries with the increase in oblateness and radiation pressure, while L 2 and L 3 move away from the more massive primary with the increase in oblateness and come nearer to it with the increase in radiation pressure. It is noted that the angular frequency s 1 at L 1 increases with oblateness as well as with radiation pressure. s 2 increases with oblateness and decreases with radiation pressure and s 3 decreases with oblateness and increases with radiation pressure. A study on the norms of the characteristic roots λ and s at L 1 , L 2 and L 3 is carried out.It is established that for certain oblateness and radiation pressure parameters there is a one-to-one commensurability at the collinear points L 2 , L 3 between the planar angular frequencies (s 2,3 ) and the corresponding angular frequency (s z ) in the z-direction, and that at L 1 no such commensurability exists. At L 2 and L 3 , the value of oblateness parameter providing the commensurability decreases with the increase in the radiation pressure. However, the commensurable angular frequencies and eccentricity of the periodic orbits decrease at L 2 and increase at L 3 , with the increase in the radiation pressure.

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“…With the effect of radiation pressure, apart from these five coplanar ones, other equilibrium points than L 1 ∼ L 5 are found and analyzed in literatures, e.g. Simmons, McDonald & Brown (1985); Ragos & Zagouras (1988); Todoran (1994); Roman (2001); Ansari (2017). When the oblateness of primaries (one or both) is taken into account, the existence of out-of-plane equilibrium points, locating out of the orbital plane of primaries, is also declared (Douskos & Markellos 2006), and the dynamics of orbits around these new equilibrium points have been discussed in some other literatures.…”

Section: Introductionmentioning

confidence: 99%

On existence of out-of-plane equilibrium points in restricted three-body problem with oblateness

Wang,

Wu,

Zhou

et al. 2018

Preprint

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We analyze in this paper the existence of the "out-of-plane" equilibrium points in the restricted three-body problem with oblateness. From the series expansion of the potential function of an oblate asteroid, we show analytically all equilibrium points locate on the orbital plane of primaries and how artificial equilibrium points may arise due to an inappropriate application of the potential function. Using the closed form of the potential of a triaxial ellipsoid, we analytically demonstrate that the gravitational acceleration in z-direction is always pointing toward the equatorial plane, thus it could not be balanced out at any value of z = 0 and the out-of-plane equilibrium points cannot exist. The out-of-plane equilibrium points appear only when additional acceleration other than the gravitation from primaries is taken into account. We suggest that special attention must be paid to the application of the spherical harmonics expansion of potential to find the equilibrium points, especially when these points may be very close to the celestial body.

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The photogravitational restricted three-body problem

Cited by 9 publications

References 5 publications

Unveiling the influence of the radiation pressure in nature of orbits in the photogravitational restricted three-body problem

Unveiling the influence of the radiation pressure in nature of orbits in the photogravitational restricted three-body problem

Effect of oblateness and radiation pressure on angular frequencies at collinear points

On existence of out-of-plane equilibrium points in restricted three-body problem with oblateness

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