Mathematical Modelling of Meteoroid Streams

Modern computer power and high-precision observational data have greatly improved the reliability of meteoroid stream models. At present, scientific research calls for two kinds of models: precise ones for individual streams, and statistically averaged ones for Solar System dust distribution models. Thus, there is a wide field of study open to stream modellers.

This brief describes step-by-step computer simulations of meteoroid stream formation and evolution. Detailed derivations of relevant formulae are given, along with plenty of helpful, digestible figures explaining the subtleties of the method. Each theoretical section ends with examples aimed to help readers practice and master the material.

Most of the examples are based on the Geminid meteoroid stream model, which has been developed by the author in the last 30 years. The book is intended for researchers interested in meteor astronomy and mathematical modelling, and it is also accessible to physics andastrophysics students.

Auteur
Galina Ryabova is a Principal Researcher and Professor at Tomsk State University. Her scientific interests are mathematical modelling of meteoroid streams and interrelations in asteroid-comet-meteoroid complex. She developed a mathematical model of the Geminid meteoroid stream one of the three existing stream models. She has served on the Organizing Committee of the International Astronomical Union's "Meteors, Meteorites and Interplanetary Dust" Commission (IAU C.F1). She was also a Council member of the International Meteor Organization. She is editor-in-chief of the reference book Meteoroids: Sources of Meteors on the Earth and Beyond (Cambridge University Press, 2019).

Contenu
Preface1. Introduction1.1 Mathematical modelling in general1.2 On history of meteoroid stream modelling2. Initial stage: the model stream generation2.1 Choice of the ejection point on the reference orbit2.1.1 Ejection in one point2.1.2 Ejection along the orbit2.2 Ejection velocity vector2.2.1 Coordinate system2.2.2 Isotropic ejection2.2.3 Ejection in a cone2.2.4 Subsolar point and the cosine ejection2.2.5 Ejection speed2.3 Calculation of the model meteoroid orbit2.4 A simple model: the nonperturbed stream3. The model stream evolution3.1 Numerical integration3.2 Analytical solution3.3 How to take into account the radiation pressure force3.4 How to take into account the PoyntingRobertson drag force4. The end stage: the model stream now4.1 Meteoroids registration on the Earth4.2 The activity profile of the model meteor shower4.3 Model radiants4.4 Mass distribution in the model shower5. Visualization of the results5.1 Crosssection in the ecliptic plane5.2 Crosssection perpendicular to the velocity vector6. Application to real streams, analysis6.1 Physical model of a meteoroid stream6.2 Age of a meteoroid stream6.3 Observations the base for modellingNotation conventionsGlossaryReferencesAPPENDICESA1. Transition from the rectangular coordinates to the orbital elements and backA2. Transition between the coordinate systemsA3. Random number generation