Determination of the free lunar libration modes from ephemeris DE430

Res. Astron. Astrophys.

et al. 2021

Self Cite

Observations of the sky irradiation intensity in the visible wavelengths during a solar eclipse permit to model the Sun diameter, a key number to constrain the internal structure of our star. In this paper, we present an algorithm that takes advantage of the precise Moon topography from Lunar Reconnaissance Orbiter to compute, with a high resolution in time, the geometrical part (i.e. top-of-atmosphere, and for a given wavelength) of the sky irradiation at any given location on the Earth during these events. The algorithm is also able to model the Baily’s beads. We give as an application the theoretical computation of the light curve corresponding to the solar eclipse observed at Lakeland (Queensland, North Australia) on 2012 November 13. The application to real data, with the introduction of atmospheric and instrumental passbands, will be considered in a forthcoming paper.

Section: Example Of Limb Computationmentioning

confidence: 90%

Computation of the atmosphere-less light intensity curve during a total solar eclipse by using Lunar Reconnaissance Orbiter topography data and the DE430 astronomical ephemeris

Wang

Res. Astron. Astrophys.

et al. 2021

Self Cite

“…To estimate the components of the libration parameters P 1 , P 2 , and τ, a frequency analysis algorithm and fitting model are needed. We employ the method used in Yang et al (2017Yang et al ( , 2019b and assume that the solutions of the three quantities have a (1 + µ j t) C j cos(ω j t) + S j sin(ω j t) ,…”

Section: The Fitting Methodsmentioning

confidence: 99%

“…which make the integration of the theoretical equations of motion easier and are often described in the analytical theories (Petrova 1996;Pesek 1991;Chapront-Touzé 1990). In this paper, based on the previous studies (Eckhardt 1981;Petrova 1996;Rambaux & Williams 2011;Rambaux et al 2012;Yang et al 2017), we used P 1 , P 2 , and τ to describe the librational motion of Phobos.…”

Section: Introductionmentioning

confidence: 99%

An elastic model of Phobos’ libration

Yang

Guo

et al. 2020

A&A

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%

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

Yang

Ping

Res. Astron. Astrophys.

et al. 2020

Self Cite

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.