Comparison and analysis on lunar rotation with lunar gravity field models

Liu

Xiao

et al. 2020

A&A

Self Cite

Context. Chinese lunar missions have grown in number over the last ten years, with an increasing focus on radio science investigations. In previous work, we estimated two lunar gravity field models, CEGM01 and CEGM02. The recently lunar mission, Chang’e 5T1, which had an orbital inclination between 18 and 68 degrees, and collected orbital tracking data continually for two years, made an improved gravity field model possible. Aims. Our aim was to estimate a new lunar gravity field model up to degree and order 100, CEGM03, and a new tidal Love number based on the Chang’e 5T1 tracking data combined with the historical tracking data used in the solution of CEGM02. The new model makes use of tracking data with this particular inclination, which has not been used in previous gravity field modeling. Methods. The solution for this new model was based on our in-house software, LUGREAS. The gravity spectrum power, post-fit residuals after precision orbit determination (POD), lunar surface gravity anomalies, correlations between parameters, admittance and coherence with topography model, and accuracy of POD were analyzed to validate the new CEGM03 model. Results. We analyzed the tracking data of the Chang’e 5T1 mission and estimated the CEGM03 lunar gravity field model. We found that the two-way Doppler measurement accuracy reached 0.2 mm s−1 with 10 s integration time. The error spectrum shows that the formal error for CEGM03 was at least reduced by about 2 times below the harmonic degree of 20, when compared to the CEGM02 model. The admittance and correlation of gravity and topography was also improved when compared to the correlations for the CEGM02 model. The lunar potential Love number k2 was estimated to be 0.02430±0.0001 (ten times the formal error). Conclusions. From the model analysis and comparison of the various models, we identified improvements in the CEGM03 model after introducing Chang’e 5T1 tracking data. Moreover, this study illustrates how the low and middle inclination orbits could contribute better accuracy for a low degree of lunar gravity field.

Section: Introductionmentioning

confidence: 99%

A degree-100 lunar gravity model from the Chang’e 5T1 mission

Liu

Xiao

et al. 2020

A&A

Self Cite

“…In this state of motion, any deviation from uniform orbital motion affects the rotational motion immediately, and vice versa. For this reason, the orbital motion and rotational motion of the Moon is usually integrated simultaneously (Folkner et al 2008(Folkner et al , 2014Viswanathan et al 2017;Yang et al 2018). However, due to a lack of observational data of Phobos, the orbital perturbations have only been deliberated in Chapront-Touzé (1990), and Phobos' rotation rate is set to match the orbit's mean longitude rate (synchronous rotation) in generating Phobos's numerical ephemerides (Lainey et al 2007(Lainey et al , 2016Jacobson 2010).…”

Section: Model Of Phobos' Orbitmentioning

confidence: 99%

“…To investigate the librations of Phobos numerically, we integrated the numerical equations via single-step Runge-Kutta-Fehlberg (RKF) and multi-steps Adams-Bashforth-Moulton (ABM) (Yang et al 2018), the integration step is set at 1/24 day (1 h). The initial values of Phobos' rotation are quoted from Archinal & Acton (2018).…”

Section: Forced Librationsmentioning

confidence: 99%

An elastic model of Phobos’ libration

Yang

Guo

et al. 2020

A&A

Self Cite

Context. Study the rotation of a celestial body is an efficient way to infer its interior structure, and then may give information of its origin and evolution. In this study, based on the latest shape model of Phobos from Mars Express (MEX) mission, the polyhedron approximation approach was used to simulate the gravity field of Phobos. Then, the gravity information was combined with the newest geophysical parameters such as GM and k2 to construct the numerical model of Phobos’ rotation. And with an appropriate angles transformation, we got the librational series respect to Martian mean equator of date. Aims. The purpose of this paper is to develop a numerical model of Phobos’ rotational motion that includes the elastic properties of Phobos. The frequencies analysis of the librational angles calculated from the numerical integration results emphasize the relationship between geophysical properties and dynamics of Phobos. This work will also be useful for a future space mission dedicated to Phobos. Methods. Based on the latest shape model of Phobos from MEX mission, we firstly modeled the gravity field of Phobos, then the gravity coefficients were combined with some of the newest geophysical parameters to simulate the rotational motion of Phobos. To investigate how the elastic properties of Phobos affect its librational motion, we adopted various k2 into our numerical integration. Then the analysis was performed by iterating a frequency analysis and linear least-squares fit of Phobos’ physical librations. From this analysis, we identified the influence of k2 on the largest librational amplitude and its phase. Results. We showed the first ten periods of the librational angles and found that they agree well with the previous numerical results which Phobos was treated as a perfectly rigid body. We also found that the maximum amplitudes of the three parameters of libration are also close to the results from a rigid model, which is mainly due to the inclination of Phobos and moments of inertia. The other amplitudes are slightly different, since the physics contained in our model is different to that of a previous study, specifically, the different low-degree gravity coefficients and ephemeris. The libration in longitude τ has the same quadratic term with previous numerical study, which is consistent with the secular acceleration of Phobos falling onto Mars. We investigated the influence of the tidal Love number k2 on Phobos’ rotation and found a detectable amplitude changes (0.0005°) expected in the future space mission on τ, which provided a potential possibility to constrain the k2 of Phobos by observing its rotation. We also studied the influence of Phobos’ orbit accuracy on its libration and suggested a simultaneous integration of orbit and rotation in future work.

“…As the Moon is a not perfectly rigid body, we consider three coordinate axes to be along the axes of principal moments of inertia of the mantle and the instantaneous angular velocity ω utilized to describe it in an inertial refer-ence system. We refer to Yang et al (2018Yang et al ( , 2017 for full descriptions. As displayed in Figure 2, OX i (i = 1, 2, 3) is defined, where OX 1 is along the minimum moment of inertia axis and OX 3 is the maximum moment of inertia axis.…”

Section: Numerical Model and Integrationmentioning

confidence: 99%

“…In this paper, the rotational equations of the Euler angles are applied to describe the Moon's orientation with respect to (w.r.t.) the inertial coordinate system (Yang et al 2018;Viswanathan et al 2017;Pavlov et al 2016;Folkner et al 2014;Cappallo et al 1981). Based on the integration approach implemented independently, the difference between a one-layer and two-layer lunar model and precise position of Earth's pole in calculating the figure interaction between Earth and Moon is analyzed.…”

Section: Introductionmentioning

confidence: 99%

Influence of the layered Moon and Earth’s orientation on lunar rotation

Yang

Ping

Res. Astron. Astrophys.

et al. 2020

One of the most efficient ways to probe the lunar inner structure at present is through the study of its rotation. Range and range rate (Doppler) data between the Chang’E-3 lander and station on the Earth were collected from the beginning of the Chang’E-3 lunar mission in 2013. These observation data, taken together with the existing lunar laser ranging data, provide a new approach to extend research on the Earth-Moon system. The high precision of current observation data imposes exacting demands, making it necessary to include previously neglected factors. In this paper, motivated by progress of the Chinese lunar exploration project and to use its data in the near future, two lunar models: a one-layer model and a two-layer model with a fluid core, were applied to the rotational equations based on our implemented algorithm of the Moon’s motion. There was a difference of about 0.5″ in ϕ and ψ, but 0.2″ in θ between the two models. This result confirms that stratification of the inner structure of the Moon can be inferred from rotation data. We also added precise Earth rotation parameters in our model; the results show that this factor is negligible at present, due to the limited precision of the existing data. These results will help us understand the rotational process clearly and build a more realistic Earth-Moon model when we combine Lunar Laser Ranging data with high precision radio data to fit lunar motion in the near future.