We reconstruct the rotation curve of the Milky Way using the new trigono-metric parallax and proper motion data for masers in 43 high-mass star-forming re-gions obtained by VLBI, as well as the existing data from the literature, based on a new set of galactic constants （R0, -0） = （8.4 kpc, 254 km s^-1） measured by Reid et al. The revised rotation curve of the Milky Way is almost fiat or slightly rising in the region from about 6 to 15 kpc. The rotation velocities within 5 kpc of the Galactic center, as determined by VLBI, differ from those obtained by measurement of the HI-and CO-line tangent velocities. We fitted the revised rotation curve arising from three mass components： the bulge, disk and dark matter halo. The total mass of the Milky Way is found to be 2.3× 10^11 M⊙ （20 kpc）. This is about 10% larger than that from Sofue et al, and is comparable with the mass of M31, 3.4× 10^11 M⊙ （35 kpc）, given by Carignan et al. The limited accurate observational data, especially the VLBI data, do not permit a fully satisfactory fit to the rotation curve. The extensive par-allax and proper motion data that will be produced by the Bar and Spiral Structure Legacy Survey project in the next few years should lead to considerable progress in understanding the rotation curve and dark matter halo of the Milky Way.
As the second step of relativistic time transfer for a Mars lander,we investigate the transformation between Areocentric Coordinate Time（TCA）and Barycentric Coordinate Time（TCB）in the framework of IAU Resolutions.TCA is a local time scale for Mars,which is analogous to the Geocentric Coordinate Time（TCG）for Earth.This transformation has two parts:contributions associated with gravitational bodies and those depending on the position of the lander.After setting the instability of an onboard clock to 10;and considering that the uncertainty in time is about 3.2 microseconds after one Earth year,we find that the contributions of the Sun,Mars,Jupiter and Saturn in the leading term associated with these bodies can reach a level exceeding the threshold and must be taken into account.Other terms can be safely ignored in this transformation for a Mars lander.
New physics beyond the standard model of particles might cause a deviation from the inverse-square law of gravity. In some theories, it is parameterized by a power-law correction to the Newtonian gravitational force, which might originate from the simultaneous exchange of particles or modified and extended theories of gravity. Using the supplementary advances of the perihelia provided by INPOP 10a （IMCCE, France） and EPM2011 （IAA RAS, Russia） ephemerides, we obtain preliminary limits on this correction. In our estimation, we take the Lense-Thirring effect due to the Sun＇s angular momentum into account. The parameters of the power-law correction and the uncertainty of the Sun＇s quadrupole moment are simultaneously estimated with the method of minimizing X2. From INPOP10a, we find N - 0.605 for the exponent of the power-law correction. However, from EPM2011, we find that, although it yields N = 3.001, the estimated uncertainty in the Sun＇s quadrupole moment is much larger than the value given by current observations. This might be caused by the intrinsic nonlinearity in the power-law correction, which makes the estimation very sensitive to the supplementary advances of the perihelia.
The afterglow of GRB 081029 showed unusual behavior, with a signifi- cant rebrightening being observed at the optical wavelength at about 3000 s after the burst. One possible explanation is that the rebrightening resulted from an energy in- jection. Here we present a detailed numerical study of the energy injection process and interpret the X-ray and optical afterglow light curves of GRB 081029. In our model, we have assumed two periods of energy injection, each with a constant injec- tion power. One injection starts at 2.8 × 10^3 s and lasts for about 2500 s, with a power of 7.0 × 10^47 erg s-1. This energy injection mainly accounts for the rapid rebrighten- ing at about 3000 s. The other injection starts at 8.0 × 10^3 s and lasts for about 5000 s. The injection power is 3.5 × 10^47 erg s-1. This energy injection can help to explain the slight rebrightening at about 10 000 s. It is shown that the observed optical after- glow, especially the marked rebrightening at about 3000 s, can be reproduced well. In the X-ray band, the predicted amplitude of the rebrightening is much shallower, which is also consistent with the observed X-ray afterglow light curve. It is argued that the two periods of energy injection can be produced by clumpy materials falling onto the central compact object of the burster, which leads to an enhancement of accretion and gives rise to a strong temporary outflow.
Ground-based and space-borne observatories used for studying exoplanet transits now and in the future will considerably increase the number of exoplanets known from transit data and the precision of the measured times of transit minima.Variations in the transit times can not only be used to infer the presence of additional planets,but might also provide opportunities to test the general theory of relativity in these systems.To build a framework for these possible tests,we extend previous studies on the observability of the general relativistic precessions of periastron in transiting exoplanets to variations in secular transit timing under parametrized post-Newtonian formalism.We find that if one can measure the difference between observed and predicted variations of general relativistic secular transit timing to 1 s yr-1in a transiting exoplanet system with a Sun-like mass,a period of;day and a relatively small eccentricity of;.1,general relativity will be tested to the level of;%.
As the first step in relativistic time transfer for a Mars lander from its proper time to the time scale at the ground station, we investigate the transformation between proper time and Areocentric Coordinate Time （TCA） in the framework of IAU Resolutions. TCA is a local time scale for Mars, which is analogous to the Geocentric Coordinate Time （TCG） for Earth. This transformation contains two contributions： inter- hal and external. The internal contribution comes from the gravitational potential and the rotation of Mars. The external contribution is due to the gravitational fields of other bodies （except Mars） in the Solar System. When the （in）stability of an onboard clock is assumed to be at the level of 10-13, we find that the internal contribution is dominated by the gravitational potential of spherical Mars with necessary corrections asso- ciated with the height of the lander on the areoid, the dynamic form factor of Mars, the flattening of the areoid and the spin rate of Mars. For the external contribution, we find the gravitational effects from other bodies in the Solar System can be safely neglected in this case after calculating their maximum values.
