Relationships of parameters of planetary orbits in solar-type systems

RNDr. Pavel PINTR

Doctoral thesis

Abstract:

We deal with regularities of the distances in the solar system in chapter 2. On starting with the Titius--Bode law, these prescriptions include, as ''hidden parameters", also the numbering of planets or moons. We reproduce views of mathematicians and physicists of the controversy between the opinions that the distances obey a law and that they are of a random origin. Hence, we pass to theories of the origin of the solar system and demonstrations of the chaotic dynamics and planetary migration, which at present lead to new theories of the origin of the solar system and exoplanets. We provide a review of the quantization on a cosmic scale and its application to derivations of some Bode-like rules. We have utilized the fact in chapter 3 that the areal velocity of a planet is directly proportional to the appropriate number of the planet, while its distance is directly proportional to the square of this number. We have confirmed a previous proposal of the quantization of the planetary orbits, but with the first possible orbit of a planet in the solar system identical only to an order of magnitude. Using this method, we have treated moons of two planets and one extrasolar system. We have investigated a successive numbering and suggested a Schmidtlike formula in the planets and the Jovian moons. We have introduced some new functions (called ''normalized parameters") of usual parameters of extrasolar systems in chapter 4. One pair of these parameters exhibits areas, where the density of exoplanets is higher. One of these parameters along with the specific angular momentum indicate two groups of exoplanets with the Gaussian distributions. We have found that for five multi-planet extrasolar systems, the power function leads to the best determination of the product of the exoplanet distance and the stellar surface temperature by the specific angular momentum. We have revealed the role of the Schmidt law. We have also considered the spectral classes of the stars. We have also explored the data of 2321 exoplanet candidates from the Kepler mission. We have determined the theoretical number of exoplanets using the statistical analysis of extrasolar systems for the spectral classes F, G, K and M in chapter 5. We have predicted many possible habitable exoplanets for the stellar spectral class G. The stellar spectral class F should have by 52% less possible habitable exoplanets than the class G, the stellar spectral class K should have by 67% less possible habitable exoplanets than the class G and the stellar spectral class M should have by 90 % less possible habitable exoplanets than the class G, i. e., the least possible habitable exoplanets. We have also found the dependence of effective temperature of exoplanets on the orbital parameters of exoplanets. Using the model of planetary atmospheres, we have predicted habitable zones for the stellar spectral classes F, G, K and M. In chapter 6 some brief conclusions are presented, concerning a comparison of the results from the chapter 2, chapter 3, chapter 4 and chapter 5.

Abstract:

We deal with regularities of the distances in the solar system in chapter 2. On starting with the Titius--Bode law, these prescriptions include, as ''hidden parameters", also the numbering of planets or moons. We reproduce views of mathematicians and physicists of the controversy between the opinions that the distances obey a law and that they are of a random origin. Hence, we pass to theories of the origin of the solar system and demonstrations of the chaotic dynamics and planetary migration, which at present lead to new theories of the origin of the solar system and exoplanets. We provide a review of the quantization on a cosmic scale and its application to derivations of some Bode-like rules. We have utilized the fact in chapter 3 that the areal velocity of a planet is directly proportional to the appropriate number of the planet, while its distance is directly proportional to the square of this number. We have confirmed a previous proposal of the quantization of the planetary orbits, but with the first possible orbit of a planet in the solar system identical only to an order of magnitude. Using this method, we have treated moons of two planets and one extrasolar system. We have investigated a successive numbering and suggested a Schmidtlike formula in the planets and the Jovian moons. We have introduced some new functions (called ''normalized parameters") of usual parameters of extrasolar systems in chapter 4. One pair of these parameters exhibits areas, where the density of exoplanets is higher. One of these parameters along with the specific angular momentum indicate two groups of exoplanets with the Gaussian distributions. We have found that for five multi-planet extrasolar systems, the power function leads to the best determination of the product of the exoplanet distance and the stellar surface temperature by the specific angular momentum. We have revealed the role of the Schmidt law. We have also considered the spectral classes of the stars. We have also explored the data of 2321 exoplanet candidates from the Kepler mission. We have determined the theoretical number of exoplanets using the statistical analysis of extrasolar systems for the spectral classes F, G, K and M in chapter 5. We have predicted many possible habitable exoplanets for the stellar spectral class G. The stellar spectral class F should have by 52% less possible habitable exoplanets than the class G, the stellar spectral class K should have by 67% less possible habitable exoplanets than the class G and the stellar spectral class M should have by 90 % less possible habitable exoplanets than the class G, i. e., the least possible habitable exoplanets. We have also found the dependence of effective temperature of exoplanets on the orbital parameters of exoplanets. Using the model of planetary atmospheres, we have predicted habitable zones for the stellar spectral classes F, G, K and M. In chapter 6 some brief conclusions are presented, concerning a comparison of the results from the chapter 2, chapter 3, chapter 4 and chapter 5.

Keywords

areal velocities, statistical analyses, extrasolar systems, habitable zones, Kepler candidates, effective temperature, stellar spectral classes

Language used: English

Date on which the thesis was submitted / produced: 28. 3. 2013

Accessible from:: 28. 3. 2013

Thesis defence

• Date of defence: 4. 6. 2013

PALACKÝ UNIVERSITY IN OLOMOUC

Faculty of Science

Doctoral programme / field:
Physics / Applied Physics