A Mathematical Model for Simulating Meteor Showers

ABSTRACT This paper presents a mathematical model to simulate the trajectory of a meteor as seen by a single observer located anywhere on Earth. Our strategy is to define a new coordinate system, called Radiant Coordinate System, which is centered on the observer and has its z-axis aligned with the radiant. This new coordinate system allows us to describe the meteors’ path by applying a reduced number of equations in a simple solution. We also present a computational implementation of this model, which is developed as a new plug-in of Stellarium, a free and open-source planetarium software. Moreover, we show that our model can be used to simulate both meteor showers and sporadic meteors. In particular, meteor showers are simulated using data provided by real catalogs.

摘要 本文提出一种数学模型，用于模拟地球上任意位置的单个观测者所观测到的流星轨迹。本研究的核心思路是定义一种全新的坐标系——辐射点坐标系（Radiant Coordinate System），该坐标系以观测者为原点，其z轴与流星辐射点对齐。借助该新坐标系，我们仅需通过少量方程即可以简洁的求解方式描述流星的运行路径。本文同时给出了该模型的计算机实现方案，该方案被开发为免费开源天文馆软件Stellarium的全新插件。此外，本文证实该模型可同时用于模拟流星雨与偶发流星；具体而言，流星雨的模拟采用了真实星表提供的观测数据。