An elastic model of Phobos’ libration

Yang, Yongzhang; Yan, Jianguo; Guo, Xunhua; He, Qingbao; Barriot, Jean‐Pierre

doi:10.1051/0004-6361/202037446

Cited by 3 publications

(1 citation statement)

References 34 publications

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“…The main difference between the full model and the simple model lies in the consideration of the complete rotation of Deimos in inertial space in the full model. There have been some research efforts on the rotation of Phobos [27,28]. In this section, we will establish the rotation model of Deimos based on the theory of rigid body rotation.…”

Section: Full Modelmentioning

confidence: 99%

Dynamical Model of Rotation and Orbital Coupling for Deimos

Huang,

Zhang,

Yang

et al. 2024

Remote Sensing

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This paper introduces a novel dynamical model, building upon the existing dynamical model for Deimos in the current numerical ephemerides, which only encompasses the simple libration effects of Deimos. The study comprehensively incorporates the rotational dynamics of Deimos influenced by the torque exerted by the major celestial bodies (Mars, the Sun) in the solar system within the inertial space. Consequently, a full dynamical model is formulated to account for the complete coupling between the rotation and orbit of Deimos. Simultaneously, employing precision orbit determination methods used for artificial satellites, we develop an adjustment model for fitting data to the complete model. The 12-order Adams–Bashforth–Moulton (ABM) integration algorithm is employed to synchronously integrate the 12 state variables of the full model to obtain the orbit of Deimos.The difference in the orbits obtained by integrating the full model over a period of 10 years and those obtained by the simplified model is at the order of 10 km. After precise orbit determination, this difference decreases to below 100 m, so numerical simulation results indicate that the full dynamical model and adjustment model are stable and reliable. Simultaneously, the integration of the Deimos third-order gravity field in the full model over a 10-year period induces only meter-level positional changes. This suggests that when constructing the complete model, the utilization of a second-order gravity field alone is sufficient. Compared to the simple model, the polar axis of Deimos in the inertial space exhibits a more complex oscillation in the full model. Additionally, the full model calculates that the minimum moment of inertia principal axis of Phobos has an amplitude of approximately 0.5 degrees in the longitude direction and does not exceed 2 degrees in the latitude direction. This work further advances the current dynamical model for Deimos and establishes the foundational model for the generation of a new set of precise numerical ephemerides for Deimos.

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Section: Full Modelmentioning

confidence: 99%

Dynamical Model of Rotation and Orbital Coupling for Deimos

Huang,

Zhang,

Yang

et al. 2024

Remote Sensing

Self Cite

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Numerical model of Phobos’ motion incorporating the effects of free rotation

Yang,

Yan,

Jian

et al. 2024

A&A

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Context. High-precision ephemerides are not only useful in supporting space missions, but also in investigating the physical nature of celestial bodies. This paper reports an update to the orbit and rotation model of the Martian moon Phobos. In contrast to earlier numerical models, this paper details a dynamical model that fully considers the rotation of Phobos. Here, Phobos’ rotation is first described by Euler’s rotational equations and integrated simultaneously with the orbital motion equations. We discuss this dynamical model, along with the differences with respect to the model now in use. Aims. This work is aimed at updating the physical model embedded in the ephemerides of Martian moons, considering improvements offered by exploiting high-precision observations expected from future missions (e.g., Japanese Martian Moons exploration, MMX), which fully supports future studies of the Martian moons. Methods. The rotational motion of Phobos can be expressed by Euler’s rotational equations and integrated in parallel with the equations of the orbital motion of Phobos around Mars. In order to investigate the differences between the two models, we first reproduced and simulated the dynamical model that is now used in the ephemerides, but based on our own parameters. We then fit the model to the newest Phobos ephemeris published by Institut de Mécanique Céleste et de Calcul des Éphémérides (IMCCE). Based on our derived variational equations, the influence of the gravity field, the Love number, k2, and the rotation behavior were studied by fitting the full model to the simulated simple model. Our revised dynamic model for Phobos was constructed as a general method that can be extended with appropriate corrections (mainly rotation) to systems other than Phobos, such as the Saturn and Jupiter systems. Results. We present the variational equation for Phobos’ rotation employing the symbolic Maple computation software. The adjustment test simulations confirm the latitude libration of Phobos, suggesting gravity field coefficients obtained using a shape model and homogeneous density hypothesis should be re-examined in the future in the context of dynamics. Furthermore, the simulations with different k2 values indicate that it is difficult to determine k2 efficiently using the current data.

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A Novel Ephemeris Model for Martian Moons Incorporating Their Free Rotation

Yang,

Huang,

Yan

et al. 2024

Res. Astron. Astrophys.

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High-precision ephemerides not only support space missions, but can also be used to study the origin and future of celestial bodies. In this paper, a coupled orbit-rotation dynamics model that fully takes into account the rotation of the Martian moons is developed. Phobos and Deimos' rotation are firstly described by Eulerian rotational equations, and integrated simultaneously with the orbital motion equations. Orbital and orientational parameters of Mars satellites were simultaneously obtained by numerical integration for the first time. In order to compare the differences between our newly developed model and the one now used in the ephemerides, we first reproduced and simulated the current model using our own parameters, and then fit it to the IMCCE ephemerides using least-square procedures. The adjustment test simulations show Phobos and Deimos‘ orbital differences between the refined model and the current model is no more than 300~$m$ and 125~$m$, respectively. The orientation parameters are confirmed and the results are in good agreement with the IAU results. Moreover, we simulated two perturbations (main asteroids and mutual torques) which were not included in our refined model, and find that their effects on the orbits are completely negligible. As for the effect on rotation, we propose to take care of the role of mutual attraction in future models.

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An elastic model of Phobos’ libration

Cited by 3 publications

References 34 publications

Dynamical Model of Rotation and Orbital Coupling for Deimos

Dynamical Model of Rotation and Orbital Coupling for Deimos

Numerical model of Phobos’ motion incorporating the effects of free rotation

A Novel Ephemeris Model for Martian Moons Incorporating Their Free Rotation

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