Titius-Bode Research Articles

UNLOCKING THE PLANTS’ DISTRIBUTION IN A FRACTAL SPACE

All known planets orbit the Sun so harmoniously that the entire Universe is believed to behave in a rhythmical and fractal way. Titius–Bode law is the main theoretical tool for planetary orbit description. Here we show that planetary sequence follows the Fibonacci-like prime sequence, and we introduce two gravitational spirals to predict orbits for solar members orbiting the Sun. Furthermore, we predict two hypothetical planets as far as 1500 AU and 2300 AU from the Sun, respectively, in our solar system, and some unknown planets in extrasolar planetary systems. Our planetary sequence demonstrates the possible frontier of our solar system, and the theory is also valid for other star systems and planetary systems, giving a simple way to finding the most possible adjacent unknown planets or moons near a known one. We anticipate our sequence can be more sophisticatedly used to search for unknown Universes and to depict the cosmos fully and exclusively, and we conclude that our whole Universe is of fractal property and all celestial bodies are distributed according to Fibonacci sequence.

Generalized Titius-Bode Law and How to Statistically Verify it

The Titius-Bode law has been historically successful in predicting the location of planets in the solar system. While the majority believes it is merely a coincidence, we too agree with that; however, we think there is some underlying universal truth hidden under the overfitting phenomena in the original Titius-Bode law; the generalized Titius-Bode, by removing the overfitting, can tell us about the mechanism of the formation of our early solar system, or more generally, all astronomical systems, as big as galaxies. Specifically, we analyzed the absolute error of the generalized Titius-Bode Law with the ground truth, and it suggested that the planets were formed iteratively, instead of each planet just magically finds its orbit where the centripetal force balances the centrifugal force.

Exoplanets prediction in multiplanetary systems

AbstractWe present the results of a search for additional exoplanets in all multiplanetary systems discovered to date, employing a logarithmic spacing between planets in our Solar System known as the Titius–Bode (TB) relation. We use the Markov Chain Monte Carlo method and separately analyse 229 multiplanetary systems that house at least three or more confirmed planets. We find that the planets in$\sim 53\%$of these systems adhere to a logarithmic spacing relation remarkably better than the Solar System planets. Using the TB relation, we predict the presence of 426 additional exoplanets in 229 multiplanetary systems, of which 197 candidates are discovered by interpolation and 229 by extrapolation. Altogether, 47 predicted planets are located within the habitable zone of their host stars, and 5 of the 47 planets have a maximum mass limit of 0.1–2${\rm M}_{\oplus}$and a maximum radius lower than 1.25${\rm R}_{\oplus}$. Our results and prediction of additional planets agree with previous studies’ predictions; however, we improve the uncertainties in the orbital period measurement for the predicted planets significantly.

HERSCHEL'S SPURIOUS MOONS OF URANUS: THEIR IMPACT ON SATELLITE ORBITAL THEORY, CELESTIAL CARTOGRAPHY AND LITERATURE

Positing unobserved satellites and attempting to establish a mathematical framework to explain the orbits of planetary satellites was inspired by the law of planetary distances made popular by Johann Bode, Director of Berlin Observatory, although applying orbital proportionality to posit the existence of more satellites predates Bode's Law by nearly a century. Whatever its merits, Bode's Law has played an important role in the history of astronomy but the application of a power-law approach to planetary satellite orbits has received scant attention. Several German-language papers of the late eighteenth century, never before printed in English, are used here to study this issue. This paper examines that topic in the context of Uranus, and goes further in offering the first comprehensive study of the four spurious satellites claimed by William Herschel and how they were represented—or misrepresented—in both literature (covering seven languages) and maps of the Solar System for a century after their 'discovery'.

The reliability of the Titius–Bode relation and its implications for the search for exoplanets

Abstract The major semiaxes of the planets in our solar system obey a simple geometric progression known as the Titius–Bode (TB) relation, whose physical origin remains disputed. It has been shown that the exoplanetary systems follow a similar (but not identical) progression of the form $a_n= a_0$ e$^{bn}$, where $a_0$ and b are constants to be determined for each system. Since its formulation, the TB relation has proved to be highly predictive in our solar system. Using data from 27 exoplanetary systems with five or more planets and applying a proposed method, we conclude that reliable TB-like fits can be obtained for systems with at least four planets and that the precision of the TB relation is $78\%$. By means of a statistical test we show that the periods of planets in real exoplanetary systems are not consistent with a random distribution. Rather, they show signs that their configuration is shaped by their mutual interactions.

The Secret of the Titius-Bode Law: A New Theory on How Our Planetary System Came Into Existence

Our planetary system still has several unsolved riddles. One of them is the Titius-Bode law. With the aid of this law, it is easy to find the distances of planets from the sun. For many astronomers, this is coincidence. They argue that there is no known physical mechanism that generates a particular sequence of planets’ distances. However, if one investigates the structure of the law, it quickly becomes clear that the Titius-Bode law is directly connected with the formation of planets. Our planets did not come into existence through so-called accretion. At the beginning of its existence, the sun was presumably a T-Tauri star. These are young stars in the process of their formation. They pulsate irregularly, thereby accelerating clouds of plasma in the surrounding dust disk. Each of these eruptions thus generated a planet. This of course goes much more quickly than if they had to be formed from the dust of planetary disks. This new theory not only describes how the planets and the distances of the planets came into existence. It also gives a new description of how the moon came into existence, the cause for large moon craters, the slow rotation of Venus, the formation of the asteroid belt, the high iron content of the planet Mercury, and the sun’s loss of rotational impulse, among other things.

An explanation of the titius-bode law resulted by a Kant-Laplace type model of the solar system’s forming

In the paper is shows that the Titius-Bode relation of the distances Sun-planet may be explained by a Kant-Laplace type model of planetary system forming, considering a linear decreasing of the lenticular protoplanetary nebula’s density and the constancy of its rotation speed. The resulted conclusions is that the protoplanetary material rings were formed by the successive halving of the nebular mass MN and thereafter- of the remained part and may be generalized for the star clusters, for the galaxies forming but also for the expansion of the galaxies super-clusters and of the Universe.

Diving into Exoplanets: Are Water Seas the Most Common?

One of the basic tenets of exobiology is the need for a liquid substratum in which life can arise, evolve, and develop. The most common version of this idea involves the necessity of water to act as such a substratum, both because that is the case on Earth and because it seems to be the most viable liquid for chemical reactions that lead to life. Other liquid media that could harbor life, however, have occasionally been put forth. In this work, we investigate the relative probability of finding superficial seas on rocky worlds that could be composed of nine different, potentially abundant, liquids, including water. We study the phase space size of habitable zones defined for those substances. The regions where there can be liquid around every type of star are calculated by using a simple model, excluding areas within a tidal locking distance. We combine the size of these regions with the stellar abundances in the Milky Way disk and modulate our result with the expected radial abundance of planets via a generalized Titius-Bode law, as statistics of exoplanet orbits seem to point to its adequateness. We conclude that seas of ethane may be up to nine times more frequent among exoplanets than seas of water, and that solvents other than water may play a significant role in the search for extrasolar seas.

The Formation of the Planets in the Solar System-A new theory derived from the Titius-Bode law

According to current teaching, the planets in our solar system originated from the dust in the protoplanetary disk clumping together, forming ever larger particles until gravitational pull took effect and formed the planets. The planets were thus produced by accretion. This seems logical at first, but it takes a very long time and also raises the question of where the planets actually got their angular momentum. It is thus more likely that the planets were formed from the vortexes of matter in the dust disk. These, in turn, were created by repeated eruptions of the unfinished sun, which was still in the throes of labour at that point. Magnetic force fields and gravitation then quickly turned the plasma and vortexes of matter into quickly rotating planets. The Titius-Bode law allows the distance between the planets and the sun to be easily calculated. If one then assumes that an emerging star like our sun did not gradually start fusing the gas masses that gravity pushed to the centre, but instead ignited repeatedly like a hydrogen bomb, this law is easy to understand. This is not a coincidence – the Titius-Bode law describes the temporal progression of the explosions of the sun from which the planets arose.

Predicting The Orbit of TRAPPIST-1i

The TRAPPIST-1 system provides an exquisite laboratory for advancing our understanding exoplanetary atmospheres, compositions, dynamics and architectures. A remarkable aspect of TRAPPIST-1 is that it represents the longest known resonance chain, where all seven planets share near mean motion resonances with their neighbors. Prior to the measurement of 1h's period, Luger et al. (2017) showed that six possible and highly precise periods for 1h were expected, assuming it also participated in the resonant chain. We show here that combining this argument with a Titius-Bode law fit of the inner six worlds narrows the choices down to a single precise postdiction for 1h's period, which is ultimately the correct period. But a successful postdiction is never as convincing as a successful prediction, and so we take the next step and apply this argument to a hypothetical TRAPPIST-1i. We find two possible periods predicted by this argument, either 25.345 or 28.699 days. If successful, this may provide the basis for planet prediction in compact resonant chain systems. If falsified, this would indicate that the argument lacks true predictive power and may not be worthwhile pursuing further in our efforts to build predictive models for planetary systems.

Self-organizing systems in planetary physics: Harmonic resonances of planet and moon orbits

The geometric arrangement of planet and moon orbits into a regularly spaced pattern of distances is the result of a self-organizing system. The positive feedback mechanism that operates a self-organizing system is accomplished by harmonic orbit resonances, leading to long-term stable planet and moon orbits in solar or stellar systems. The distance pattern of planets was originally described by the empirical Titius–Bode law, and by a generalized version with a constant geometric progression factor (corresponding to logarithmic spacing). We find that the orbital periods Ti and planet distances Ri from the Sun are not consistent with logarithmic spacing, but rather follow the quantized scaling (Ri+1/Ri)=(Ti+1/Ti)2/3=(Hi+1/Hi)2/3, where the harmonic ratios are given by five dominant resonances, namely (Hi+1:Hi)=(3:2),(5:3),(2:1),(5:2),(3:1). We find that the orbital period ratios tend to follow the quantized harmonic ratios in increasing order. We apply this harmonic orbit resonance model to the planets and moons in our solar system, and to the exo-planets of 55 Cnc and HD 10180 planetary systems. The model allows us a prediction of missing planets in each planetary system, based on the quasi-regular self-organizing pattern of harmonic orbit resonance zones. We predict 7 (and 4) missing exo-planets around the star 55 Cnc (and HD 10180). The accuracy of the predicted planet and moon distances amounts to a few percents. All analyzed systems are found to have ≈ 10 resonant zones that can be occupied with planets (or moons) in long-term stable orbits.

Titius–Bode law applied to satellite systems: A historical sketch

The aim of this paper is to examine the attempts made by some astronomers (Wurm, Challis, Carlini, and Gaussin), in the Nineteenth Century, for extending the Titius–Bode law to satellite systems and also for finding other formulae for planetary distances. Many flaws and naiveties that make vain these researches will be shown.

Geo-cosmic Universal X-structure of Solar System Planets and Satellites in Applying to Exoplanet Systems

Given a new unique method of calculating satellite systems approved at all, without exception, 185 satellites of the Solar system. The base of the Geo-cosmic Universal X-structure of Solar system planets and satellites represents a discrete-continuous distribution of satellite and longest rings in axes the density/orbital radius (semi-major axis of the orbit), converted to the scale of the central body. Previously, it was found that in all cases, the maximum radius of the rings is the same as the triple radius of the central body for the border zones of destructive tidal actions with 12% spread. For Pluto's radius 1184 km radius of rings on X-structure may range from 4000 to 7000 km. It was far enough away from 12000 km radius of passage of spacecraft "New horizons". The success of the application of the method of the X-structure is shown here. For some exoplanets within 50 light-years (15pc) of the Earth by a method of the Geo-cosmic universal X-structure it is studied questions of the definition of the exoplanets parameters: density-diameter etc. Given also the Universal Geo-cosmic X-structure theoretical Levels of the similarity of natural satellites of the Solar system planets. Comparative characteristics between the method of the X-structure on the one hand and the modification of the Lunar systems Titius-Bode law оn the other hand given in Appendix A. From the theory, in particularly, follows the mystery similarity between the Mercury and the Earth’s Moon. Study of this layer of the undoubted new reality held in Appendix B. On pictures of the surface of Pluto and Charon the crust thickness was determined. Crust of Pluto from pole 21 km. The ice crust Charon thickness at pole is 18 km.

Stellar wind–magnetosphere interaction at exoplanets: computations of auroral radio powers

We present calculations of the auroral radio powers expected from exoplanets with magnetospheres driven by an Earth-like magnetospheric interaction with the solar wind. Specifically, we compute the twin cell-vortical ionospheric flows, currents, and resulting radio powers resulting from a Dungey cycle process driven by dayside and nightside magnetic reconnection, as a function of planetary orbital distance and magnetic field strength. We include saturation of the magnetospheric convection, as observed at the terrestrial magnetosphere, and we present power law approximations for the convection potentials, radio powers and spectral flux densities. We specifically consider a solar-age system and a young (1 Gyr) system. We show that the radio power increases with magnetic field strength for magnetospheres with saturated convection potential, and broadly decreases with increasing orbital distance. We show that the magnetospheric convection at hot Jupiters will be saturated, and thus unable to dissipate the full available incident Poynting flux, such that the magnetic Radiometric Bode's Law (RBL) presents a substantial overestimation of the radio powers for hot Jupiters. Our radio powers for hot Jupiters are $\sim$5-1300 TW for hot Jupiters with field strengths of 0.1-10 $B_J$ orbiting a Sun-like star, while we find that competing effects yield essentially identical powers for hot Jupiters orbiting a young Sun-like star. However, in particular for planets with weaker magnetic fields our powers are higher at larger orbital distances than given by the RBL, and there are many configurations of planet that are expected to be detectable using SKA.

The Solar System: A New Geometric Classification and Prediction of a New Asteroid

One of the most popular theories of measuring planetary distances in the solar system is Bode's law, but this law has some deviations when compared to the real distances. In this paper a new classification (Hazaymeh-Hawarey Classification) is presented. This classification aims to explain the inability of Bode's law to identify the two orbital dimensions of Neptune and Pluto, and it provides a new geometric image for the orbital distribution of the solar system, including Neptune and Pluto. This new classification shows that orbits of the solar system are divided into four equal groups, where the (10/3 = 4) is true. It also discovers that the two dimensions of Neptune and Pluto are much more systematic in the solar system, compared to Bode's law. The new classification includes the adjustment of the distances of Sedna and Eris, and enables the mathematical identification of a new asteroid located after Iris, even before the astronomical verification. The new classification reveals the symmetry and the anomaly of the solar system orbits and that the diameters of the first and fourth groups follow a geometric sequence. According to this, the diameter of the new asteroid can be determined.

Four Poission-Laplace Theory of Gravitation (I)

The Poisson-Laplace equation is a working and acceptable equation of gravitation which is mostly used or applied in its differential form in Magneto-Hydro-Dynamic (MHD) modelling of e.g. molecular clouds. From a general relativistic standpoint, it describes gravitational fields in the region of low spacetime curvature as it emerges in the weak field limit. For non-static gravitational fields, this equation is not generally covariant. On the requirements of general covariance, this equation can be extended to include a time-dependent component, in which case one is led to the Four Poisson-Laplace equation. We solve the Four Poisson-Laplace equation for radial solutions, and apart from the Newtonian gravitational component, we obtain four new solutions leading to four new gravitational components capable (in-principle) of explaining e.g. the Pioneer anomaly, the Titius-Bode Law and the formation of planetary rings. In this letter, we focus only on writing down these solutions. The task showing that these new solutions might explain the aforesaid gravitational anomalies has been left for separate future readings.

Physicochemical Stages of Evolution: Ring-Like Structures in the Universe

This short digest is devoted to the mechanism of ring formation during the origination and evolution of planetary and satellite systems in the Universe. The appearance of these structures can be traced back to the phenomenon of spatially periodic condensation which can be observed on the Earth. The author actually posited the existence of exoplanetary systems and the cosmic scale of this phenomenon. It was accurately predicted that Uranus, Neptune and other heavenly bodies have rings. The suggested general mechanism rationalized the Titius-Bode law which, while not being a precise law, often accurately describes the tendency towards varying distances between planets (and their moons) and central bodies. The possibility of this law manifestation in exoplanetary systems had been predicted by the author long before their discovery. Many exoplanetary systems have been discovered by now and there is some evidence corroborating the mechanism of spatially periodic condensation involved in the formation of ring-like structures in these systems. The author’s hypothesis is now becoming a theory or a fact. It appears that we are now witnessing the dawn of a new extensive cosmology, taking into account general physicochemical mechanisms of space object formation.

Testing the Titius–Bode law predictions for Kepler multiplanet systems

We use three and half years of Kepler Long Cadence data to search for the 97 predicted planets of Bovaird & Lineweaver (2013) in 56 of the multi-planet systems, based on a general Titius-Bode relation. Our search yields null results in the majority of systems. We detect five planetary candidates around their predicted periods. We also find an additional transit signal beyond those predicted in these systems. We discuss the possibility that the remaining predicted planets are not detected in the Kepler data due to their non-coplanarity or small sizes. We find that the detection rate is beyond the lower boundary of the expected number of detections, which indicates that the prediction power of the TB relation in general extra solar planetary systems is questionable. Our analysis of the distribution of the adjacent period ratios of the systems suggests that the general Titius-Bode relation may over-predict the presence of planet pairs near the 3:2 resonance.

A probabilistic model for the Solar System planetary distribution

The discovery of several extrasolar systems, each one characterized by its own planetary distribution around a central star, made the scientific interest addressed to the analysis of models permitting to predict, or at least estimate, the orbital features of the extrasolar planets. The main purpose of this work is to describe a mathematical model, inspired by quantum mechanics, able to provide a probability distribution of planets placing in a star system, mainly driven by the central star mass. More in detail, for any given eigenvalue of the model discrete spectrum, a distinct probability distribution with respect to the central star distance can be built. As per the Solar System, it has been possible to prove that both inner and outer planets belongs to two different spectral sequences, each one originated by the minimum angular momentum owned by silicate/carbonate and icy planetesimals respectively. In both sequences, the peak of the probability distributions almost precisely coincided with the average planets distance from Sun; furthermore, the eigenvalue spectrum of the inner planets thickens in an accumulation point corresponding to the asteroids belt, thus showing a striking similarity to the real matter distribution in the Solar System. From this point of view, the Titius–Bode law for the Solar System planets distribution is nothing but an exponential interpolation of the eigenvalues of both inner and outer sequences.

Exoplanet predictions based on the generalized Titius–Bode relation

We evaluate the extent to which newly detected exoplanetary systems containing at least four planets adhere to a generalized Titius-Bode (TB) relation. We find that the majority of exoplanet systems in our sample adhere to the TB relation to a greater extent than the Solar System does, particularly those detected by the Kepler mission. We use a generalized TB relation to make a list of predictions for the existence of 141 additional exoplanets in 68 multiple-exoplanet systems: 73 candidates from interpolation, 68 candidates from extrapolation. We predict the existence of a low-radius (R < 2.5 Earth Radii) exoplanet within the habitable zone of KOI-812 and that the average number of planets in the habitable zone of a star is 1-2. The usefulness of the TB relation and its validation as a tool for predicting planets will be partially tested by upcoming Kepler data releases.