Polemical Titius Bode Law By G G Nyambuya 16 November 2016 Presentation made at the Copper Belt University Kitwe Zambia During the SAROAD Astronomical Observations and Data Analysis Workshop ID: 1021428
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1. On the Theoretical Foundations of the Polemical Titius-Bode LawBy,G. G. Nyambuya(16 November 2016)Presentation made at the Copper Belt University, Kitwe – Zambia. During the SAROAD Astronomical Observations and Data Analysis WorkshopNational University of Science and Technology, Bulawayo – Zimbabwe.
2. Talk OutlineHistoric AnecdoteTheoretical JustificationDerivationApplication to the Solar systemApplication to Exoplanets
3. 1.0 Historic AnecdotenObjectDistance(AU)1Mercury0.402Venus0.703Earth1.004Mars1.405Asteroids2.806Jupiter5.207Saturn9.608Neptune30.109Pluto40.00
4. 1.0 Historic Anecdote …. Titius and Bode) AU; Johann Elert Bode (1747-1826)Johann Daniel Titius (1729 -1796)Predicts objects must exist at 2.80 AU.
5. 1.1: Historic Anecdote …. European Celestial PolicenObjectDistance(AU)n(TBL)T-B Law(AU)% Deviation1Mercury0.400.4002Venus0.7000.70+33Earth1.0011.0004Mars1.4021.60-55Asteroids2.8032.80-16Jupiter5.2045.2007Saturn9.60510.00-58Uranus19.20619.60-29Neptune30.10738.80-2810Pluto40.007(8)38.80(77.20)+2(+95)nObjectDistance(AU)n(TBL)T-B Law(AU)% Deviation1Mercury0.400.4002Venus0.7000.70+33Earth1.0011.0004Mars1.4021.60-55Asteroids2.8032.80-16Jupiter5.2045.2007Saturn9.60510.00-58Uranus19.20619.60-29Neptune30.10738.80-2810Pluto40.007(8)38.80(77.20)+2(+95)
6. 1.1: Historic Anecdote …. Ceres, Pallas, Juno and VestaCeresPallasJunoCeresVestaKarl Ludwig Harding (1765-1834)Karl Ludwig Harding (1765-1834)Giuseppe Piazzi (1746-1826)Heinrich Wilhelm Olbers
7. 1.1: Historic Anecdote …. Discovery of Uranus and NeptuneNeptuneUranusFrederick William Herschel (1738-1822)Urbain Jean Joseph Le Verrier (1811-1877)William Herschel
8. 2.0: Theoretical JustificationPoisson-Laplace EquationUsually …. Leading to Newtonian PotentialAzimuthally Symmetric Solution
9. 2.1: Theoretical JustificationPerihelion shift of Solar PlanetsSecular drift of Earth-Moon systemFlyby anomalyReduces to Newtonian gravitation for small spin.
10. 2.2: Theoretical Justification …. Continued Paul Adrian Maurice Dirac (1902-1984)Father of Mathematical Beauty“It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress.”“A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data.”``God used beautiful mathematics in creating the World.”``Was an English theoretical physicist who made fundamental contributions to the early development of both Quantum Mechanics and Quantum Electrodynamics.”
11. 2.3: Theoretical Justification …. Continued [Nordstrom (1913) Equation]Assume separable solutions:Beautiful equation. Lorentz Invariant!with …..Gunnar Nordström (1881-1923)``Was a Finnish theoretical physicist best remembered for his theory of gravitation, which was an early competitor of general relativity.”
12. 2.4: Theoretical Justification …. Continued SolutionCondition1.2.3.Component(Newtonian-Component)(Yukawa-Term)(Planetary Ring Component)
13. 2.5: Theoretical Justification …. Continued DarkmatterTitius-Bode Law
14. 2.6: Theoretical Justification …. Continued
15. 2.7: Theoretical Justification …. Continued
16. 2.8: Theoretical Justification …. Continued
17. Application to the Solar system= MercuryVacant Planet PositionsMarsEarthVenus
18. Application to Exoplanets
19. Application to Exoplanets ….. continued
20. Application to Exoplanets ….. continued
21. Final Result