对地球大气密度随高度分布规律的讨论

Studies of Altitude Distribution of Earth's Atmosphere Density

以NASA大气模式MSISE-1990为依据,用实例验证的方式证明了关心大气成分的数密度时,玻耳兹曼能量分布律仅适用于几公里至几十公里高度以内的分子态气体。考虑重力加速度随高度变化时,用该分布律得到的无限高处大气数密度在数学形式上不为零,但从物理角度分析其值与零没有差别。忽略重力加速度随高度变化时,用该分布律得到的无限高处大气数密度在数学形式上似乎为零,但无限高处重力加速度应为零,因而不能解决无限高处大气数密度在数学形式上不为零的问题。计算大气分子总数时,积分上限只需数十公里。考虑重力加速度随高度变化时,用该分布律计算大气分子总数的积分发散,因此上限不应超过数百倍地球半径;忽略重力加速度随高度变化时无此限制。达道安等人(宇航学报,2006,27(06): 1306-1313)对该分布律导出的大气密度随高度分布所作的修正,不仅在数学形式上解决了无限高处大气数密度不为零的问题和计算大气分子总数的积分发散的问题,而且在有实际意义的范围内与该分布律精密吻合。

The influence of various factors,including the number density of the atmospheric components and the altitude dependence of the gravity acceleration on the Altitude Distribution Rule of the atmosphere density was analytically and experimentally studied,based on the exteneded version of the Mass Spectrometer Incoherent Scatter model(MSISE-1990) and the experimental data available.Our conclusions are as follows:(i)The experimental results on the basis of MSISE-1990 show that Boltzmann energy distribution is valid only at the altitude ranging from several to tens of kilometers, when the number density of the atmospheric gas phase molecules is considered.(ii)When the variation of the gravity acceleration with altitude is considered,since the integral of the total gas molecule number diverges,its upper radial limit should be within hundreds of times of the radius of the Earth;however,omission of the altitude variations of the gravity acceleration removes the upper limits of the integral.(iii)When variation in the gravity acceleration is considered, there is a discrepancy between the physical and mathematical values of the atmosphere number densities at the infinite height.(iv) The modification made by Da Daoan et.al.succeeded in eliminating the integral divergence and the discrepancy between the physical and mathematical resuts.In addition,their modified model provides good results in the range of realistic interest.