planet in the 55 Cancri system have been greatly revised (from 2.817 days to 0.737 days and from 0.038 to 0.016 , respectively) since the publication of these studies. Recent astronomical research suggests that planetary systems around some other stars may follow Titius–Bode-like laws. Bovaird and Lineweaver applied a generalized Titius–Bode relation to 68 exoplanet systems that contain four or more planets. They showed that 96% of these exoplanet systems adhere to a generalized Titius–Bode relation to a similar or greater extent than the Solar System does. The locations of potentially undetected exoplanets are predicted in each system. Subsequent research detected five planet candidates from the 97 planets predicted for the 68 planetary systems. The study showed that the actual number of planets could be larger. The occurrence rates of Mars- and Mercury-sized planets are currently unknown, so many planets could be missed due to their small size. Other possible reasons that may account for apparent discrepancies include planets that do not transit the star or circumstances in which the predicted space is occupied by circumstellar disks. Despite these types of allowances, the number of planets found with Titius–Bode law predictions was lower than expected. In a 2018 paper, the idea of a hypothetical eighth planet around TRAPPIST-1 named "TRAPPIST-1i", was proposed by using the Titius–Bode law. TRAPPIST-1i had a prediction based exclusively on the Titius–Bode law with an orbital period of . Finally, raw statistics from exoplanetary orbits strongly point to a general fulfillment of Titius–Bode-like laws (with exponential increase of semi-major axes as a function of planetary index) in all the exoplanetary systems; when making a blind histogram of orbital semi-major axes for all the known exoplanets for which this magnitude is known, and comparing it with what should be expected if planets distribute according to Titius–Bode-like laws, a significant degree of agreement (i.e., 78%) is obtained. See also Dermott's law Phaeton (hypothetical planet) Logarithmic spiral Lennard-Jones potential Mysterium Cosmographicum Footnotes References Further reading The ghostly hand that spaced the planets New Scientist 9 April 1994, p13 Plants and Planets: The Law of Titius–Bode explained by H.J.R. Perdijk Distancias planetarias y ley de Titius-Bode (Spanish) by Dr. Ramon Parés Discoveries by Johann Elert Bode Obsolete theories in physics Planets Ceres (dwarf planet) Uranus Astronomical hypotheses