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We report the application of Titius-Bode's law on 43 exoplanetary systems containing four or more planets. Due to the fact that most of these systems have their planets located within compact regions extending for less than the semi-major axis of Mercury we found the necessity to scale down the Titius-Bode law in each case. In this short article we present sample calculations for three systems out of the whole set. Results show that all systems studied are verifying the applicability of the law with high accuracy. Consequently our investigation verifies practically the scale invariance of Titius-Bode law.
With the recent surge in exoplanet discoveries in recent years, some new and unproven techniques have appeared. One such technique is fitting a model to a system with 3 or more known planets to predict new planets within the system. A 2015 paper by Bovaird, et al. predicted 228 planets in 151 Kepler systems. These predictions were made by using a generalized Titius-Bode relation and have an expected 15% detection rate among candidates with a > .55 probability of transiting their host star. The purpose of this project will be to test the validity and predicting power of this technique.
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 < 2.5R⊕) 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.