We use a combination of spatial distribution and radial velocity to search for halo sub-structures in a sample of 412 RR Lyrae stars (RRLS) that covers a ∼ 525 square degrees region of the Virgo Overdensity (VOD) and spans distances from the Sun from 4 to 75 kpc. With a friends-of-friends algorithm we identified six high significance groups of RRLS in phase space, which we associate mainly with the VOD and with the Sagittarius stream. Four other groups were also flagged as less significant overdensities. Three high significance and 3 lower significance groups have distances between ∼ 10 and 20 kpc, which places them with the distance range attributed by others to the VOD. The largest of these is the Virgo Stellar Stream (VSS) at 19 kpc, which has 18 RRLS, a factor of 2 increase over the number known previously. While these VOD groups are distinct according to our selection cirteria, their overlap in position and distance, and, in a few cases, similarity in radial velocity are suggestive that they may not all stem separate accretion events. Even so, the VOD appears to be caused by more than one overdensity. The Sgr stream is a very obvious feature in the background of the VOD at a mean distance of 44 kpc. Two additional high significant groups were detected at distances > 40 kpc. Their radial velocities and locations differ from the expected path of the Sgr debris in this part of the sky, and they are likely to be remnants of other accretion events.

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The detection and study of the rotational motion of space debris, which is affected by environmental factors, is a popular topic. However, relevant research in extremely low-orbit regions cannot be conducted due to a lack of observational data. Here, we fill in the gaps to present the rotational evolution of Tiangong-1 in the 5 months prior to reentry. Derived from the changes in the relative distance of its two corner cube reflectors from satellite laser ranging data, the angular momentum of Tiangong-1, which is relatively stable during observation, deviates from its maximum principal axis of inertia and precesses around the normal direction of the orbital plane due to gravity gradient torque at an angle of 23.1 • ± 2.5 • . Requiring consistency with the relationship between the angular momentum and precession rate leads to a solution for the rotation rate, which is thus found to increase. This result cannot be explained by any previously developed torque models. Hence, an atmospheric density gradient torque (ADGT) model that considers the torque generated by the change in atmospheric density with orbital altitude at the satellite scale is proposed to explain the rotational acceleration mechanism of extremely low-orbit objects. The numerical results show that the ADGT model provides a non-negligible ability to explain, but cannot fully describe, the acceleration effect. The data on the rotational evolution of Tiangong-1 can provide an important basis for aerodynamic model improvement by addressing minor factors omitted in previous models. which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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