No abstract

This work is devoted to improving empirical mass-luminosity relations (MLR) and mass-metallicity-luminosity relation (MMLR) for low mass stars. For these stars, observational data in the mass-luminosity plane or the mass-metallicityluminosity 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 MLR. 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 M⊙to 0.50 M⊙. Three-piecewise continuous improved MLRs in K, J, H and V bands, respectively, are obtained. The visual MMLR is also improved based on our K band MLR and the available observational metallicity data.

The Hill stability of the low mass binary system in the presence of a massive third body moving on a wider inclined orbit is investigated analytically. It is found that, in the case of the third body being on a nearly circular orbit, the region of Hill stability expands as the binary/third body mass ratio increases and the inclination (i) decreases. This i-dependence decreases very quickly with increasing eccentricity (e 2 ) of the third body relative to the binary barycentre. In fact, if e 2 is not extremely small, the Hill stable region can be approximately expressed in a closed form by setting i = 90 • , and it contracts with increasing e 2 as e 2 2 for sufficiently low mass binary. Our analytic results are then applied to the observed triple star systems and the Kuiper belt binaries.

Context. For a general N-body system, Marchal constructed an analytical test of escape, which uses only a one-dimensional projected motion state of the system at any given instant. This test is well adapted to identifying real, disintegrating small stellar systems, of which the full motion states are generally unavailable. However, to our knowledge, there has been no practical application of this test until the present-day. Aims. In this paper, we aim at adapting the above test to visual triple stars with estimable component masses and known kinematic data on the plane perpendicular to the line-of-sight. As illustrating examples, our goal is to identify disintegrating Hipparcos linear triple systems. Methods. The fundamental techniques of analytical geometry were used to adapt the test of escape to practical applications, and the Monte Carlo method used to cope with the unavoidable observational errors, so that the confidence probability of a real triple star disintegrating could be obtained. Results. A practical algorithm was designed to make full use of the two-dimensional kinematic data in testing usual visual triple stars. This algorithm is then applied to 24 Hipparcos linear triple systems with estimable component masses and the disintegration probability given. Conclusions.

We show that there exists a new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem. In such a solution, the infinitesimal body is confined to the vicinity of a primary and moves on a nearly circular orbit. This orbit is almost perpendicular to the orbital plane of the primaries, where the line of symmetry of the orbit lies. The existence is shown by applying a corollary of Arenstorf's fixed point theorem to a periodicity equation system of the problem. And this existence doesn't require any restriction on the mass ratio of the primaries, nor on the eccentricity of their relative elliptic orbit. Potential relevance of this new class of periodic solutions to real celestial body systems and the follow-up studies in this respect are also discussed.periodic orbits, spatial restricted three-body problem, symmetric orbits, averaging Poincaré believed that any (bounded) particular solution of a nearly integrable Hamiltonian system can be approximated by a periodic one for any finite time interval with any precision [1] . This belief established the importance of periodic solutions, and now is known as Poincaré conjecture on periodic solutions. In ref.[2], this conjecture reads "the periodic orbits are dense in the set of bounded orbits" and is listed as the first unsolved conjecture on 3 or N-body problem. For various aspects of the study of periodic solutions of the N-body problem with or without restrictions, the reader can refer to, e.g. Siegel & Moser [3] , Hénon [4] , Meyer [5] , Chenciner [6] , Terracini [7] , Hadjidemetriou [8] .In such kind of study, the model of restricted three-body problem (Szebehely) [9] is useful because it can be served not only as a relatively simple example of non-integrable dynamical systems, but also as a successful model in understanding many almost periodic phenomena in astronomy. To prove the existence of a periodic solution of the restricted three-body problem, the analytical continuation method of Poincaré, which is based on the implicit function theorem for regular functions, is often used. However, there are cases to which this classical theorem does not apply. In some such cases, one may resort to Arenstorf's fixed point theorem [10] . Recent successful applications of this latter theorem to the restricted three-body problem are given by Howison and Meyer [11,12] , Cors, Pinyol and Soler [13,14] , and Brandão and Vidal [15] .Brandão and Vidal [15] considered the periodic solutions of the elliptic collision isosceles restricted threebody problem, where the two primaries with equal mass move, respectively, along collision elliptic orbits lying on the same line, and the infinitesimal body is strictly confined to the plane passing through the mass center of the system and perpendicular to the orbital line of the primaries.In the case when the infinitesimal body moves in the 3-dimensional space, Howison and Meyer [11] proved the existence of two classes of doubly symmetric periodic orbits of circular restricted 3-body problem. One class is