Relative equilibria of four identical satellites

We consider the Newtonian 5-body problem in the plane, where 4 bodies have the same mass m, which is small compared to the mass M of the remaining body. We consider the (normalized) relative equilibria in this system, and follow them to the limit when m/M -> 0. In some cases two small bodies will coalesce at the limit. We call the other equilibria the relative equilibria of four separate identical satellites. We prove rigorously that there are only three such equilibria, all already known after the numerical researches in [SaY]. Our main contribution is to prove that any equilibrium configuration possesses a symmetry, a statement indicated in [CLO2] as the missing key to proving that there is no other equilibrium.Comment: 16 pages, 2 figure

Some remarks about Descartes' rule of signs

What can we deduce about the roots of a real polynomial in one variable by simply considering the signs of its coefficients? On one hand, we give a complete answer concerning the positive roots, by proposing a statement of Descartes' rule of signs which strengthens the available ones while remaining as elementary and concise as the original. On the other hand, we provide new kinds of restrictions on the combined numbers of positive and negative roots.Comment: 10 page

Symmetry of Planar Four-Body Convex Central Configurations

International audienceWe study the relationship between the masses and the geometric properties of central configurations. We prove that in the planar four-body problem, a convex central configuration is symmetric with respect to one diagonal if and only if the masses of the two particles on the other diagonal are equal. If these two masses are unequal, then the less massive one is closer to the former diagonal. Finally, we extend these results to the case of non-planar central configurations of five particles

Laser-generated surface acoustic wave-based study and detection of surface cracks

Monitoring cracks to check the integrity of engineering materials by Non- Destructive Testing (NDT) in industry is significant in industry. And within the NDT techniques, Laser-Generated Surface Acoustic Wave technique (LSAW) has shown to be a promising technique. To further develop non-contact and accurate testing strengths of this method, models for analyzing the generation, propagation and tracking of surface acoustic waves (SAW’s) changes in S45C steel samples with distributed cracks are developed by using Finite Element Method (FEM). Time and frequency domain analyses are used to process the acoustic wave signals after the interaction with cracks. The simulation results and preliminary analyses reveal the good potential LSAW’s have to monitor cracks. First results in developing an experimental setup for crack detection are also provided

Simulation study of asteroid mass determination using CSST asteroid observations

The objective of this study is to explore the potential of the Chinese Space Station Telescope (CSST) in asteroid mass determination with asteroid-asteroid close encounters. The CSST is expected to observe some asteroids with an accuracy of several milliarcseconds and has a limiting magnitude of 26 (AB mag) or higher in the g and r bands. By combining CSST observations with existing ground-based observations, significant improvements in asteroid mass precision can be achieved. To quantify the CSST’s capability in asteroid mass determination, three types of simulations are conducted. In Type A simulation, 58 close encounters with available Gaia DR2 observations were considered, assuming CSST observes asteroids at a frequency similar to Gaia’s. After using the simulated CSST observations, asteroid mass precision is improved substantially. In seven events, the determined precision are better than 5%. Type B simulation is performed based on a tentative optical survey plan of CSST, but the limited opportunities to observe asteroids involved in a close encounter with strong perturbation from to-be-determined masses. As a result, the precision of mass determination is low, though the improvement brought by CSST data is obvious. This implies that the dedicated observations are necessary for CSST to contribute masses with high precision. Type C simulation is performed with a small amount of CSST observing time, to be specific for a strong encounter, 144 observations spanning 3 years centered at the encounter time, totaling about 7.2 observation hours. In this case, CSST can determine a number of asteroid masses, of which 10 asteroid’s precision are expected to be better than 10%

Reconciling results of 2019 and 2020 stellar occultations on Pluto's atmosphere. New constraints from both the 5 September 2019 event and consistency analysis

A stellar occultation by Pluto on 5 September 2019 yielded positive detections at two separate stations. Using an approach consistent with comparable studies, we derived a surface pressure of $11.478 \pm 0.55~\mathrm{\mu bar}$ for Pluto's atmosphere from the observations of this event. In addition, to avoid potential method inconsistancies highlighted by Sicardy et al. when comparing with historical pressure measurements, we reanalyzed the data by 15 August 2018 and 17 July 2019 events, respectively. All the new measurements provide a bridge between the two different perspectives on the pressure variation since 2015: a rapid pressure drop from previous studies of the 15 August 2018 and 17 July 2019 events and a plateau phase from that of the 6 June 2020 event. The pressure measurement from the 5 September 2019 event aligns with those from 2016, 2018, and 2020, supporting the latter perspective. While the measurements from the 4 June 2011 and 17 July 2019 events suggest probable V-shaped pressure variations unaccounted for by the volatile transport model (VTM) from Meza et al., the VTM remains applicable on average. And, the validity of the V-shaped variations is debatable due to the stellar faintness of the 4 June 2011 event and the grazing single-chord geometry of the 17 July 2019 event. To reveal and understand all significant pressure variations of Pluto's atmosphere, it is essential to provide constraints on both short-term and long-term evolutions of the interacting atmosphere and surface by continuous pressure monitoring through occultation observations, whenever possible, complemented by frequent spectroscopy and photometry of the surface.Comment: Accepted for publication in Astronomy & Astrophysics. 10 pages, 6 figure

The Empirical Mass-Luminosity Relation for Low Mass Stars

This work is devoted to improving empirical mass-luminosity relations and mass-metallicity-luminosity relation for low mass stars. For these stars, observational data in the mass-luminosity plane or the mass-metallicity-luminosity space subject to non-negligible errors in all coordinates with different dimensions. Thus a reasonable weight assigning scheme is needed for obtaining more reliable results. Such a scheme is developed, with which each data point can have its own due contribution. Previous studies have shown that there exists a plateau feature in the mass-luminosity relation. Taking into account the constraints from the observational luminosity function, we find by fitting the observational data using our weight assigning scheme that the plateau spans from 0.28 to 0.50 solar mass. Three-piecewise continuous improved mass-luminosity relations in K, J, H and V bands, respectively, are obtained. The visual mass-metallicity-luminosity relation is also improved based on our K band mass-luminosity relation and the available observational metallicity data.Comment: 8 pages, 2 figures. Accepted for publication in Astrophysics & Space Scienc