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Motion about equilibrium points in the Jupiter-Europa system with oblateness

Saleem Yousuf

Saleem Yousuf

Department of Mathematics, Central University of RajasthanIndia
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Yousuf, Saleem
, 
Ram Kishor

Ram Kishor

Department of Mathematics, Central University of RajasthanIndia
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Kishor, Ram
 e 
Manoj Kumar

Manoj Kumar

Department of Mathematics, Central University of RajasthanIndia
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Kumar, Manoj
  
15 apr 2022
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Pubblicato online: 15 apr 2022
Pagine: 2075 - 2090
Ricevuto: 14 set 2020
Accettato: 01 giu 2021
DOI: https://doi.org/10.2478/amns.2021.2.00124
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© 2023 Saleem Yousuf et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Configuration of the restricted three body problem.
Configuration of the restricted three body problem.

Fig. 2

Characteristic roots at A21 = 0.000285, A22 = 0.007198 in Jupiter-Europa system. Dashed lines represents imaginary roots and bold lines represents real roots.
Characteristic roots at A21 = 0.000285, A22 = 0.007198 in Jupiter-Europa system. Dashed lines represents imaginary roots and bold lines represents real roots.

Fig. 3

Characteristic roots for μ = 0.01 in Jupiter-Europa system at (a) A21 = 0.18436 and (b) A22 = 0.05459. Dashed lines represents imaginary roots and bold lines represents real roots.
Characteristic roots for μ = 0.01 in Jupiter-Europa system at (a) A21 = 0.18436 and (b) A22 = 0.05459. Dashed lines represents imaginary roots and bold lines represents real roots.

Fig. 4

The perturbed solution α(t), β (t) about the L4 point at A21 = 0.000285 and A22 = 0.007198 for time period T ≈ 57.12.
The perturbed solution α(t), β (t) about the L4 point at A21 = 0.000285 and A22 = 0.007198 for time period T ≈ 57.12.

Fig. 5

Tadpole orbit in Jupiter (J) - Europa (E) system for k = 0.0001 at (a) A21 = 0 = A22 (b) A21 = 0.0285, A22 = 0 (c) A21 = 0, A22 = 0.0007189 and (d) A21 = 0.0285, A22 = 0.0007189.
Tadpole orbit in Jupiter (J) - Europa (E) system for k = 0.0001 at (a) A21 = 0 = A22 (b) A21 = 0.0285, A22 = 0 (c) A21 = 0, A22 = 0.0007189 and (d) A21 = 0.0285, A22 = 0.0007189.

Fig. 6

Horseshoe orbit in Jupiter (J) - Europa (E) system for k = 0.005 at (a) A21 = 0 = A22 (b) A21 = 0.00285, A22 = 0 (c) A21 = 0, A22 = 0.0007189 and (d) A21 = 0.00285, A22 = 0.0007189.
Horseshoe orbit in Jupiter (J) - Europa (E) system for k = 0.005 at (a) A21 = 0 = A22 (b) A21 = 0.00285, A22 = 0 (c) A21 = 0, A22 = 0.0007189 and (d) A21 = 0.00285, A22 = 0.0007189.

Fig. 7

Poincaré surfaces of section at different mass ratio μ.
Poincaré surfaces of section at different mass ratio μ.

Fig. 8

Variation in Poincaré surfaces of section for μ = 0.001 at different values of Cj.
Variation in Poincaré surfaces of section for μ = 0.001 at different values of Cj.

Fig. 9

Poincaré surfaces of section for μ = 0.001, Cj = 2.85 with the variation in the oblateness A21.
Poincaré surfaces of section for μ = 0.001, Cj = 2.85 with the variation in the oblateness A21.

Fig. 10

Effect of oblateness A22 on Poincaré surfaces of section with μ = 0.001, Cj = 2.85.
Effect of oblateness A22 on Poincaré surfaces of section with μ = 0.001, Cj = 2.85.
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