Bode’s law is an observation that the distances of the planets from the Sun are in an offset geometric progression. It is not really a “law” of nature, in the same way we speak of the “law of gravitation”. But it is an intriguing idea. Some people call it “Bode’s rule”. I would even describe it as “Bode’s relationship” between planetary position and orbital radius. And, just to complexify the name further, the modern practice is to speak of the “Titius-Bode” law, rule, or relationship, because Bode took his inspiration from Titius (and cited Titius). My authority for this information is the excellent Wikipedia article https://en.wikipedia.org/wiki/Titius%E2%80%93Bode_law
Most scientific ideas have a similarly complicated origin, and names are flexible. In fact, sometimes the opinion is expressed that the person named as the author of some well-known property of nature, is usually not the originator. That’s glib. But, certainly, science is a collaborative endeavour. Anyway, I’m going to stick with “Bode’s law” for simplicity.
So, let’s state Bode’s law. At the time (1772) , the known planets were Mercury through Saturn. (Uranus was discovered in 1781, and the asteroid Ceres was discovered in 1801). Bode assigns Saturn a distance from the Sun of 100 units, and observes that, using that scale, Mercury is at a distance of 4 units, Venus at 7 (=4+3) units, Earth at 10 (=4+6) units, Mars at 16 (=4+12) units, an “empty” position (possible planet to be found) at 28 (=4+24) units, and Jupiter at 52 (=4+48) units. Moreover, Saturn’s distance at 100 units can be written as 100=4+96 units.
Thus Bode’s law is that, the planets which occupy positions N = 2,3,4,6,7,8 (with position 5 being skipped) are located at distances 4+3*2^(N-1) from the Sun. This really is an astonishing relationship.
Even more astonishing is that the later discovery of Uranus found it to be at position 9, and the later discovery of Ceres, the largest asteroid, found it to be at position 5. Neptune is not at position 10, but Pluto is found at that distance.
The Wikipedia article referenced above has quite a lot of further material, and I want to discuss some of that in future posts. Some questions which I hope to cover include
- What if we state Bode’s law with periods instead of distance?
- Is there a physical rationale for planets to be spaced per Bode’s law?
- Can Bode’s law be observed in exoplanet systems?
Best wishes, from Ken Roberts, 03-Jan-2023