There is no solid theoretical explanation of the Titius–Bode law, but if there is one it is possibly a combination of orbital resonance and shortage of degrees of freedom: any stable planetary system has a high probability of satisfying a Titius–Bode-type relationship. Since it may simply be a mathematical coincidence rather than a "law of nature", it is sometimes referred to as a rule instead of "law".[5] However, astrophysicist Alan Boss states that it is just a coincidence, and the planetary science journal Icarus no longer accepts papers attempting to provide improved versions of the law.[4]

Orbital resonance from major orbiting bodies creates regions around the Sun that are free of long-term stable orbits. Results from simulations of planetary formation support the idea that a randomly chosen stable planetary system will likely satisfy a Titius–Bode law.

Dubrulle and Graner[6][7] have shown that power-law distance rules can be a consequence of collapsing-cloud models of planetary systems possessing two symmetries: rotational invariance (the cloud and its contents are axially symmetric) and scale invariance (the cloud and its contents look the same on all scales), the latter being a feature of many phenomena considered to play a role in planetary formation, such as turbulence.

Lunar systems and other planetary systems

There is a decidedly limited number of systems on which Bode's law can presently be tested. Two of the solar planets have a number of big moons that appear possibly to have been created by a process similar to that which created the planets themselves. The four big satellites of Jupiter and the biggest inner satellite, Amalthea, cling to a regular, but non-Bode, spacing with the four innermost locked into orbital periods that are each twice that of the next inner satellite. The big moons of Uranus have a regular, but non-Bode, spacing.[8] However, according to Martin Harwit, "a slight new phrasing of this law permits us to include not only planetary orbits around the Sun, but also the orbits of moons around their parent planets."[9] The new phrasing is known as Dermott's law.

Of the recent discoveries of extrasolar planetary systems, few have enough known planets to test whether similar rules apply to other planetary systems. An attempt with 55 Cancri suggested the equation a = 0.0142 e 0.9975 n, and predicts for n = 5 an undiscovered planet or asteroid field at 2 AU.[10] This is controversial.[11] Furthermore the orbital period and semimajor axis of the innermost planet in the 55 Cancri system have been significantly revised (from 2.817 days to 0.737 days and from 0.038 AU to 0.016 AU respectively) since the publication of these studies.[12]

Recent astronomical research suggests that planetary systems around some other stars may fit Titius–Bode-like laws.[13][14] Bovaird and Lineweaver[15] applied a generalized Titius-Bode relation to 68 exoplanet systems which 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 managed to detect five planet candidates from predicted 97 planets from the 68 planetary systems. The study showed that the actual number of planets could be larger. The occurrence rate of Mars and Mercury sized planets are currently unknown so many planets could be missed due to their small size. Other reasons were accounted to planet not transiting the star or the predicted space being occupied by circumstellar disks. Despite this, the number of planets found with Titius-Bode law predictions were still lower than expected.[16]