Gravitational interactions — mergers and y-by encounters — between galaxies play a key role as the drivers of their evolution. Here we perform a cosmological N-body simulation using the tree-particle-mesh code GOTPM, and attempt to separate out the effects of mergers and y-bys between dark matter halos. Once close pair halos are identified by the halo finding algorithm PSB, they are classified into mergers (E12 < 0) and y-by encounters (E12 > 0) based on the total energy (E12) between two halos. The y-by and merger fractions as functions of redshift, halo masses, and ambient environments are calculated and the result shows the following: (1) Among Milky-way sized halos (0:33-2:0 X 1012h-1M⊙), 5:37±0:03% have experienced major y-bys and 7.98±0.04% have undergone major mergers since z ~ 1; (2) Among dwarf halos (0:1 - 0.33 X 1012h-1M⊙), 6.42 ± 0.02% went through major y-bys and 9.51 ± 0.03% experienced major mergers since z ~ 1; (3) Milky-way sized halos in the cluster environment experienced fly-bys (mergers) 4-11(1.5 - 1.7) times more frequently than those in the field since z ~ 1; and (4) Approaching z = 0, the y-by fraction decreases sharply with the merger fraction remaining constant, implying that the empirical pair/merger fractions (that decrease from z ~ 1) are in fact driven by the fly-bys, not by the mergers themselves.

Being a torque free motion of the rotating Earth, Chandler wobble is the major component in the Earth’s polar motion with amplitude about 0.05-0.2 arcsec and period about 430-435 days. Free core nutation, also called nearly diurnal free wobble, exists due to the elliptical core-mantle boundary in the Earth and takes almost the whole part of un-modelled variation of the Earth’s pole in the celestial sphere beside precession and nutation. We hereby present a brief summary of their theories and report their recent features acquired from updated datasets (EOP C04 and ECMWF) by using Fourier transform, modelling, and wavelet analysis. Our new findings include (1) period-instability of free core nutation between 420 and 450 days as well as its large amplitude-variation, (2) re-determined Chandler period and its quality factor, (3) fast decrease in Chandler amplitude after 2010.

The atmosphere strongly affects the Earth’s spin rotation in wide range of timescale from daily to annual. Its dominant role in the seasonal perturbations of both the pole position and spinning rate of the Earth is once again confirmed by a comparison of two recent data sets; i) the Earth orientation parameter and ii) the global atmospheric state. The atmospheric semi-diurnal tide has been known to be a source of the Earth’s spin acceleration, and its magnitude is re-estimated by using an enhanced formulation and an up-dated empirical atmospheric S2 tide model. During the last twenty years, an unusual eastward drift of the Earth’s pole has been observed. The change in the Earth’s inertia tensor due to glacier mass redistribution is directly assessed, and the recent eastward movement of the pole is ascribed to this change. Furthermore, the associated changes in the length of day and UT1 are estimated.