Understanding of Jeans Rule
Chong Gao · Acta Astronomica Sinica · 2002
Jeans empirical rule has always been used in planetary physics. From the static equation of atmosphere, the equation of state for ideal gases, the law of gravitation and the law of Maxwell distribution, Jeans empirical rule can be derived. Therefore, it seems that Jeans empirical rule should be called Jeans rule. It can be formulated in three forms: in terms of velocity, height, or energy. These three formulations are completely equivalent. According to concrete situation, any one of these forms can be taken freely and used as a criterion, which define whether the atmospheric composition of a given species of particles at the planet surface will exist forever or not. The factor in the energy formulation will be neither too large nor too small. According to statistical theory, taking the viewpoint of energy, Jeans rule can be explained more easily. The condition satisfying Jeans rule is only the necessary condition for a given species of particles to be major atmospheric composition of the planets which have dense atmosphere. Jeans rule is not only applicable for the planets and satellites in the solar system, but also suitable for the asteroids, meteoroids and outer solar system objects, such as Centaurs and Kuiper belt objects. The application scope of Jeans rule can be expressed with nomogram as well as denned by equations or by figures. Having been widely used for a long time, it still has a general practical significance in detecting age of planets in the solar system nowadays, especially for the research of outer solar system objects.