Dimensional Analysis and Group Theory in Astrophysics

PrefacePart I Dimensional Analysis Chapter 1 The Technique of Dimensional Analysis § 1. Relativistic Phenomena § 2. Stellar Systems Chapter 2 Foundations of Dimensional Analysis § 3. Postulates of Dimensional Analysis § 4. The Pi Theorem Chapter 3 Applications of Dimensional Analysis to Problems of Stellar Radiation § 5. The Wien and Stefan-Boltzmann Laws § 6. Normal Forms of Spectral Densities § 7. Limb Darkening § 8. Two-Color Relations § 9. Interstellar Absorption § 10. Photometric Relations Chapter 4 Applications of Dimensional Analysis to Problems of Stellar Structure § 11. Mass-Luminosity Relations § 12. Asymptotic Photometric Relations § 13. Period-Luminosity Relations § 14. Proto-StarsPart II Applications of Group Theory Chapter 5 Group-Theoretical Reduction of Ordinary Differential Equations § 15. Local Lie Groups § 16. Group-Theoretical Reduction of Ordinary Differential Equations § 17. Autonomous Monomial Differential Equations § 18. Non-Autonomous Monomial Differential Equations Chapter 6 Reductions of the Differential Equations of Stellar Structure § 19. Polytropic Gas Balls § 20. Isothermal Gas Balls § 21. Stellar Envelopes § 22. Stellar Interiors § 23. Stellar Interiors With Convective CoresAppendices Appendix 1 The Law of Titius and Bode (cf. § 1) Appendix 2 Note on the Temperatures and Atmospheres of the Planets (cf. §5) 1-2: The Temperatures of the Planets 3-5: The Likelihood of the Existence of an Atmosphere 6-8: The Time of Escape Notes and References Appendix 3 The Mass-Radius Relation of the Major Planets (cf. § 11) Appendix 4 The Concept of a Group Notes and References Appendix 5 Methodological Reflections 1-3: Physical Theory 4-5: Physical Hypothesis 6-7: Induction and Analogy 8-9: Invariance and Regularity Hypotheses 10-11: Simplicity Postulates 12-13: Testing Hypotheses Notes and References Appendix 6 Some Data and DimensionsReferencesIndex