Dynamics and stability of the two body problem with Yukawa correction

Cavan, Eli; Haranas, Ioannis; Gkigkitzis, Ioannis; Cobbett, Kristin

doi:10.1007/s10509-020-3749-z

Cited by 9 publications

(14 citation statements)

References 13 publications

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“…In this letter, we build on work from [23], in which the dynamics and stability of the two body problem with a Newtonian potential corrected by a Yukawa term were explored. In particular, we reproduced their analytical results and applied them to the study of all the planets of our solar system.…”

Section: Introductionmentioning

confidence: 99%

“…where V Y k is the Yukawa correction to the Newtonian potential and α (λ) represents the strength (range) of the Yukawa correction. Previous studies [23,25] gave the nominal values (α = 10 −8 (λ = 10 3 AU = 10 15 m). However, our estimations gave a larger order of magnitude for the Yukawa strength: α ∼ 10 −4 − 10 −5 for terrestrial planets (Mercury, Venus, Earth, Mars and Pluto) and α ∼ 10 −3 for the remaining Giant planets (Jupiter, Saturn, Uranus and Neptune), which are in line with [13].…”

Section: Introductionmentioning

confidence: 99%

“…In section(2), we state the types of stability and determine the one corresponding to the system under study. We discuss, in section(3) and following [23], Bertrand's theorem and get the analytical solution to the equation of motion. Finally, we apply in section (4) the obtained approximative analytical results to the study of the solar system planets in order to estimate the Yukawa strength and re-determine the trajectory characteristics for both estimated and nominal values of α, as well as solve numerically the equations.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics and stability of the two-body problem with Yukawa correction to Newton's gravity, revisited and applied numerically to the solar system

Hasan¹,

Joudieh²,

Chamoun³

2023

Preprint

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In this manuscript, we review the motion of two-body celestial system (planet-sun) for a Yukawa-type correction on Newton's gravitational potential using Hamilton's formulation. We reexamine the stability using the corresponding linearization Jacobian matrix, and verify that the Bertrand's theorem conditions are met for radii 10 15 m, and so bound closed orbits are expected. Applied to the solar system, we present the equation of motion of the planet, then solve it both analytically and numerically. Making use of the analytical expression of the orbit, we estimate the Yukawa strength α, and find it larger than the nominal value (10 −8 ) adopted in previous studies, in that it is of order (α = 10 −4 − 10 −5 ) for terrestrial planets (Mercury, Venus, earth, Mars and Pluto) whereas it is even larger (α = 10 −3 ) for the Giant planets (Jupiter, Saturn, Uranus and Neptune). Taking as inputs (r min , v mas , e) observed by NASA, we analyse the orbits analytically and numerically for both the estimated and nominal values of α, and determine the corresponding trajectories. For each obtained orbit we recalculate the characterizing parameters (r min , r max , a, b, e) and compare their values according to the used potential (Newton with/without Yukawa correction) and to the method used (analytical and/or numerical). When compared to the observational data, we conclude that the correction on the path due to Yukawa correction is of order of and up to 80 million km (20 million km) as a maximum deviation occurring for Neptune (Pluto) for nominal (estimated) value of α.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics and stability of the two-body problem with Yukawa correction to Newton's gravity, revisited and applied numerically to the solar system

Hasan¹,

Joudieh²,

Chamoun³

2023

Preprint

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“…Haranas et al [23] have studied the circular and elliptical orbits of Earth under the consideration of Yukawa potential combined with Poynting-Robertson effect. Cavan et al [24] have studied the dynamics and stability of the two-body problem with Yukawa correction.…”

Section: Introductionmentioning

confidence: 99%

Triangular Equilibria in R3BP under the Consideration of Yukawa Correction to Newtonian Potential

Idrisi

Eshetie

Tilahun

et al. 2022

Journal of Applied Mathematics

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We study the triangular equilibrium points in the framework of Yukawa correction to Newtonian potential in the circular restricted three-body problem. The effects of α and λ on the mean-motion of the primaries and on the existence and stability of triangular equilibrium points are analyzed, where α ∈ − 1 , 1 is the coupling constant of Yukawa force to gravitational force, and λ ∈ 0 , ∞ is the range of Yukawa force. It is observed that as λ ⟶ ∞ , the mean-motion of the primaries n ⟶ 1 + α 1 / 2 and as λ ⟶ 0 , n ⟶ 1 . Further, it is observed that the mean-motion is unity, i.e., n = 1 for α = 0 , n > 1 if α > 0 and n < 1 when α < 0 . The triangular equilibria are not affected by α and λ and remain the same as in the classical case of restricted three-body problem. But, α and λ affect the stability of these triangular equilibria in linear sense. It is found that the triangular equilibria are stable for a critical mass parameter μ c = μ 0 + f α , λ , where μ 0 = 0.0385209 ⋯ is the value of critical mass parameter in the classical case of restricted three-body problem. It is also observed that μ c = μ 0 either for α = 0 or λ = 0.618034 , and the critical mass parameter μ c possesses maximum ( μ c max ) and minimum ( μ c min ) values in the intervals − 1 < α < 0 and 0 < α < 1 , respectively, for λ = 1 / 3 .

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“…Such a correction arises whenever the force is mediated by a scalar particle of mass m. Therefore testing gravity is equivalent to testing the existence of a fifth force of scalar nature. Analysis of Yukawa potential in two body problem is studies in different approaches [59][60][61][62][63][64][65][66]. In this letter we derive an analytical solution for the Yukawa potential using the equations of motion for compact binaries moving in eccentric orbits.…”

Section: Introductionmentioning

confidence: 99%

Testing modified gravity via Yukawa potential in two body problem: Analytical solution and observational constraints

Benisty¹

2022

Preprint

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Dynamics and stability of the two body problem with Yukawa correction

Cited by 9 publications

References 13 publications

Dynamics and stability of the two-body problem with Yukawa correction to Newton's gravity, revisited and applied numerically to the solar system

Dynamics and stability of the two-body problem with Yukawa correction to Newton's gravity, revisited and applied numerically to the solar system

Triangular Equilibria in R3BP under the Consideration of Yukawa Correction to Newtonian Potential

Testing modified gravity via Yukawa potential in two body problem: Analytical solution and observational constraints

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