对金斯定则的几点认识

用物理学基本定律可导出金斯经验定则,它似应称为金斯定则.该定则的速度、高度或能量等表述完全等效,可随意选用.用能量观点更容易解释此定则.满足金斯定则只是给定的粒子成为具有稠密大气的行星或卫星的主要大气成分的必要条件.该定则的适用范围可用方程或其图像表示,也能用诺模图确定;它适用于太阳系内的行星、卫星、小行星、流星体和像柯伊伯带天体与半人马族星这样的外太阳系天体.此定则现在仍有普遍的现实意义.

Research career of an astronomer who has studied celestial mechanics

Celestial mechanics has been a classical field of astronomy. Only a few astronomers were in this field and not so many papers on this subject had been published during the first half of the 20th century. However, as the beauty of classical dynamics and celestial mechanics attracted me very much, I decided to take celestial mechanics as my research subject and entered university, where a very famous professor of celestial mechanics was a member of the faculty. Then as artificial satellites were launched starting from October 1958, new topics were investigated in the field of celestial mechanics. Moreover, planetary rings, asteroids with moderate values of eccentricity, inclination and so on have become new fields of celestial mechanics. In fact I have tried to solve such problems in an analytical way. Finally, to understand what gravitation is I joined the TAMA300 gravitational wave detector group.

Studying the Equilibrium Points of the Modified Circular Restricted Three-body Problem: The Case of Sun–Haumea System

We intend to study a modified version of the planar Circular Restricted Three-Body Problem(CRTBP) by incorporating several perturbing parameters. We consider the bigger primary as an oblate spheroid and emitting radiation while the small primary has an elongated body. We also consider the perturbation from a disk-like structure encompassing this three-body system. First, we develop a mathematical model of this modified CRTBP.We have found there exist five equilibrium points in this modified CRTBP model, where three of them are collinear and the other two are non-collinear. Second, we apply our modified CRTBP model to the Sun–Haumea system by considering several values of each perturbing parameter. Through our numerical investigation, we have discovered that the incorporation of perturbing parameters has resulted in a shift in the equilibrium point positions of the Sun–Haumea system compared to their positions in the classical CRTBP. The stability of equilibrium points is investigated. We have shown that the collinear equilibrium points are unstable and the stability of non-collinear equilibrium points depends on the mass parameter μ of the system. Unlike the classical case, non-collinear equilibrium points have both a maximum and minimum limit of μ for achieving stability. We remark that the stability range of μ in non-collinear equilibrium points depends on the perturbing parameters. In the context of the Sun–Haumea system, we have found that the non-collinear equilibrium points are stable.

Determining proportions of lunar crater populations by fitting crater size distribution

We determine the proportions of two mixed crater populations distinguishable by size distributions on the Moon. A ＂multiple power-law＂ model is built to formulate crater size distribution N（D） ∝ D-αwhose slope α varies with crater diameter D. This model is then used to fit size distributions of lunar highland craters and Class 1 craters. The former is characterized by α = 1.17 ± 0.04, 1.88 ± 0.07,3.17 ± 0.10 and 1.40 ± 0.15 for D ranges ~ 10- 49, 49- 120, 120- 251 and ~ 251- 2500 km, while the latter has a single slope α = 1.96 ± 0.14 for about 10- 100 km. They are considered as Population 1 and2 crater size distributions, whose sum is then fitted to the global size distribution of lunar craters with D between 10 and 100 km. Estimated crater densities of Population 1 and 2 are 44 × 10-5and 5 × 10-5km-2respectively, leading to the proportion of the latter being 10%. This result underlines the need for more thoroughly investigating Population 1 craters and their related impactors, the primordial main-belt asteroids, which dominated the late heavy bombardment.