Everything about The Titius-bode Law totally explained
The
Titius-Bode law (sometimes termed just
Bode's law) is a hypothesis that the
semi-major axes of
planets in the
solar system follow a simple rule. It was discredited with the discovery of
Neptune in 1846.
Formulation
The law relates the semi-major axis, a, of each planet outward from the sun in units such that the Earth's semi-major axis = 10, with
»
where
n = 0, 3, 6, 12, 24, 48 ..., with each value of
twice the previous value. The resulting values can be divided by 10 to convert them into
astronomical units (AU), which would result in the expression
» = 0.4 + 0.3 · 2
m
for
m =
, 0, 1, 2,...
For the outer planets, each planet is 'predicted' to be roughly twice as far away from the Sun as the next inner object.
History
The first mention of a series approximating Bode's Law is found in
David Gregory's
The Elements of Astronomy, published in 1715. In it, he says, "...supposing the distance of the Earth from the Sun to be divided into ten equal Parts, of these the distance of Mercury will be about four, of Venus seven, of Mars fifteen, of Jupiter fifty two, and that of Saturn ninety five." A similar sentence, likely paraphrased from Gregory,
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 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 length scales), the latter being a feature of many phenomena considered to play a role in planetary formation, such as turbulence.
There are a decidedly limited number of systems on which Bode's law can be tested. Two of the solar planets have a number of large moons that appear possibly to have been created by a process similar to that which created the planets themselves. The four large satellites of
Jupiter plus the largest inner satellite —
Amalthea — adhere 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 large moons of Uranus have a regular, but non-Bode, spacing.
Recent discoveries of extrasolar planetary systems don't yet provide enough data to test whether similar rules apply to other solar systems, although an attempt has been made with the
55 Cancri system.
Further Information
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