A Linear Operator Method to Compute the Normal Modes with Rotation of any Asymmetric 3D Planet with Pure Vector Spherical Harmonics

In order to compute the free core nutation of the terrestrial planets, such as Earth and Mars, the Moon and lower degree normal modes of the Jovian planets, we propose a linear operator method(LOM). Generalized surface spherical harmonics(GSSHs) are usually applied to the elliptical models with a stress tensor, which cannot be expressed in vector spherical harmonics explicitly. However, GSSHs involve complicated math. LOM is an alternative to GSSHs,whereas it only deals with the coupling fields of the same azimuthal order m, as is the case when a planet model is axially symmetric and rotates about that symmetry axis. We extend LOM to any asymmetric 3D model. The lower degree spheroidal modes of the Earth are computed to validate our method, and the results agree very well with what is observed. We also compute the normal modes of a two-layer Saturn model as a simple application.

A Spectral Element Method to Compute Earth’s Free Core Nutation

The Free Core Nutation(FCN)is a rotational mode caused by non-alignment of the rotation axis of the core and of the mantle.Its period observed by VLBI and superconducting gravimetry is around 430 sidereal days(Sd)with precision of better than 1 Sd,while its“theoretical”period calculated by traditional approaches and a given Earth model ranges from 450 to 470 Sd.Their gap of about 30 Sd is significant compared with its observation precision.We propose a spectral element method to compute the period of FCN and obtain a period of 434 Sd which is very close to the observed value.

Influence of Megaregolith on the Thermal Evolution of Mercury's Silicate Shell

A so-called megaregolith layer that is considered to be produced by continuous impacts in Mercury’s early stages is integrated into the thermal evolution models of Mercury to study its influence on the thermal evolution of Mercury’s silicate shell.This research first implements a one-dimensional parametric global thermal evolution model.Our results indicate that megaregolith directly affects the thermal evolution of Mercury’s silicate shell by virtue of its good insulation performance.The way megaregolith exerts its influence is by prolonging the process of partial melting and reducing the heat loss,resulting in a thicker crust and thinner stagnant lid.As for the deep parts of the silicate shell,it is suggested that more energy is taken away from the mantle due to the longer partial melting,leading to lower temperatures below the crust compared with the case in the absence of megaregolith,which further helps to advance the formation time of the inner core and promote its final size.In addition,we also carry out a simplified two-dimensional mantle convection simulation as a supplement to the one-dimensional model.The two-dimensional simulation depicts a typical mantle plume fractional melting scenario.Our calculations indicate that megaregolith may be key to the long-term volcanic activities on Mercury.As far as the megaregolith itself is concerned,the thermal structure of this particular layer is more sensitive to thermal conductivity,suggesting that for such a highly fragmented structure,the thermal conductivity coefficient plays a key role in its evolution.Our work emphasizes the importance of megaregolith to the evolution of Mercury.

Sensitivity study of high eccentricity orbits for Mars gravity recovery

By linear perturbation theory, a sensitivity study is presented to calculate the contribution of the Mars gravity field to the orbital perturbations in velocity for spacecrafts in both low eccentricity Mars orbits and high eccentricity orbits（HEOs）. In order to improve the solution of some low degree/order gravity coefficients, a method of choosing an appropriate semimajor axis is often used to calculate an expected orbital resonance, which will significantly amplify the magnitude of the position and velocity perturbations produced by certain gravity coefficients. We can then assess to what degree/order gravity coefficients can be recovered from the tracking data of the spacecraft. However, this existing method can only be applied to a low eccentricity orbit, and is not valid for an HEO. A new approach to choosing an appropriate semimajor axis is proposed here to analyze an orbital resonance. This approach can be applied to both low eccentricity orbits and HEOs. This small adjustment in the semimajor axis can improve the precision of gravity field coefficients and does not affect other scientific objectives.

A new telescope with three fields of view to measure the orientation parameters of the Moon and terrestrial planets

For lots of scientific questions about lunar physics deep inside the Moon,in-situ observation on lunar physical libration is one of the most potential ways.In this paper,we propose a brand new optical telescope functioned with simultaneously observing multiple(here there are three)fields of view(FOVs)for in-situ observation of lunar physical libration.The telescope can be placed at any place with any attitude on the Moon and do not require manned install,control or operation.It passively,continuously and simultaneously observe stars in three FOVs along with rotation of the Moon.Libration is to be measured and studied from celestial motion of the directions of three FOVs from image processing.The concept and design of this telescope are firstly introduced in this paper.The principle and feasibility of the method of insitu observation are also demonstrated.From simulation,precision of the determined lunar physical libration is expected to be several milliarcsecs,about two orders of magnitude better than the current precision of libration by lunar laser ranging observation.Libration data with milliarcsec precision level can play a valuable role in the study of the physics and dynamics of the interior of the Moon.This telescope can also be applied to observe the rotation of other terrestrial planets like Mars.

Weekly inter-technique combination of SLR,VLBI,GPS and DORIS at the solution level

Constructing and maintaining a stable terrestrial reference frame （TRF） is one of the key objectives of fundamental astronomy and geodesy. The datum realization for all the global TRF versions, such as ITRF2014 and its predecessor ITRF2008, assumes linear time evolution for transformation parameters and then imposes some conditions on these Helmert transformation parameters. In this paper, we investigate a new approach, which is based on weekly estimation of station positions and Helmert transformation parameters from a combination of the solutions of four space-geodetic techniques, i.e., Satellite Laser Ranging （SLR）, Very Long Baseline Interferometry （VLBI）, Global Positioning System （GPS） and Doppler Orbitography and Radiopositioning Integrated by Satellite （DORIS）. For this study, an interval of one week is chosen because the arc length of the SLR solutions is seven days. The major advantage of this weekly estimated reference frame is that both the non-linear station motions and the non-linear origin motion are implicitly taken into account. In order to study the non-linear behavior of station motions and physical parameters, ITRF2008 is used as a reference. As for datum definition of weekly reference frame, on one hand SLR is the unique technique to realize the origin and determine the scale together with VLBI, and on the other hand the orientation is realized via no net rotation with respect to ITRF2005 on a subset of core stations. Given the fact that without enough collocations an inter-technique combined TRF could not exist, the selection and relative weight of local ties surveyed at co-location sites are critical issues. To get stable results, we first assume that, if there were no events such as equipment changes between the measurement epoch of the local tie and that of the space- geodetic solution, the relative position between the two co-located stations should be invariant and this local tie could be used for computing the inter-technique combined reference flame in those weeks during the stable period of this tie. The resulting time series of both station positions and transformation parameters are studied in detail and are compared with ITRF2008. The residual station positions in the weekly combined reference frame are usually in the range of two millimeters without any periodic characteristic, but the residual station positions, when subtracting the regularized station position in ITRF2008, may reach a magnitude of a few centimeters and seem to have a significant annual signal. The physical parameter series between the weekly reference frame and ITRF2008 also show the obvious existence of an annual signal and reach a magnitude of one centimeter for origin motion and two parts per billion （ppb） for scale.