Dimensional Analysis and Group Theory in Astrophysics

1st Edition - January 1, 1972
Author: Rudolf Kurth
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 8 0 2 0 - 2

Dimensional Analysis and Group Theory in Astrophysics describes how dimensional analysis, refined by mathematical regularity hypotheses, can be applied to purely qualitative… Read more

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Dimensional Analysis and Group Theory in Astrophysics describes how dimensional analysis, refined by mathematical regularity hypotheses, can be applied to purely qualitative physical assumptions. The book focuses on the continuous spectral of the stars and the mass-luminosity relationship. The text discusses the technique of dimensional analysis, covering both relativistic phenomena and the stellar systems. The book also explains the fundamental conclusion of dimensional analysis, wherein the unknown functions shall be given certain specified forms. The Wien and Stefan-Boltzmann Laws can be significant in the systematic application of dimensional analysis to the physics of a single star. The text also discusses group-theoretical reduction of ordinary differential equations and the reductions of the differential equations of stellar structure. The structure of a stellar envelope requires three hypotheses: (1) thermo-nuclear reactions as source of energy of stellar; (2) thermo-nuclear reactions occur at the star's core; and (3) that an envelope surrounding the core exists where no radiation is generated. To complete the model of a star, the investigator should have further assumptions such as the pressure is made-up of gas, radiation, or both. The book can prove helpful for astronomers, astro-physicists, cosmologists, and students of general physics.

Preface

Part 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-Stars

Part 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 Cores

Appendices

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 Dimensions

References

Index