More correctly
called the Titius-Bode relationship, the *ad hoc* scheme to
account
for the mean distances of the planets from the Sun known as "Bode's
Law"
was originally conceived by Johann Titius in 1766 and then relegated by
the latter (perhaps because of its deficiencies) to the status of a
page-note.
Subsequently revived and popularized by Johannes Bode in 1772, the
"Law"
correlated well enough with the mean distance of the newly discovered
major
planet Uranus (1781) and also that of the largest asteroid Ceres
(discovered
in 1801), but it later failed completely when applied to the mean
distances
of Neptune and Pluto. Nevertheless, apart from latter-day variants^{1-7} of
Bode's Law it would seem that the underlying structure of the Solar
System
still remains essentially undetermined. Yet there are obvious
objections
to Bode's Law over and above its *ad hoc* nature and the fact
that
it is no law all. In reality, the scheme was a dubious combination of *two*
separate *ad hoc* relationships that was flawed from the outset,
as
Titius himself was perhaps aware. In particular, with reference to *unity*
and the *ad hoc* constants:
*A = 4*, *B = 3*,
**C
= 10**, the first part of the "Law" applies only to the mean
heliocentric
distance of Mercury, the first planet from the Sun, i.e.,

whereas the rest of the
mean distances are obtained from the application
of a second *ad hoc *relationship expressed in terms of
exponents
as follows:

Relation [**2**] either
begins with the mean distance of ** Venus
**for

More specifically, the ratio
of the increase in distance between Mercury and Venus is* 1 : 1.75
,* but instead of being

Thus there is not only a definite
kink in the "law," there is also a major question mark concerning the
position
of Earth itself. In fact, it appears that the ratios and the resulting
distances for Earth and Mars are ** both atypical**, those
pertaining
to Earth especially so. The "law" implies that planet-to-planet
distances
increase exponentially towards a ratio of

**Figure
1. The Kink in
Bode's Law**

But what are the norms for
planetary systems in any case, and where might the Solar System fit in
the general scheme of things? We now know that this planetary system
embodies
a number of anomalies, including major variations in planetary
composition
and size, exceptions in both orbital and rotational inclination, marked
differences in eccentricity, an asteroid belt of debatable origin,
as-yet
unexplained periodic changes in solar output, planetary resonances, and
that the System is also subject to chaotic orbital behaviour. Moreover,
although it is generally accepted that the Sun and planets owe their
origins
to the process of accretion, there still remains an apparent lack of
primordial
residue, an unusual mass/momentum distribution between the Sun and
planets,
and a slower than expected solar rotational speed to be factored into
the
equation. Because of these anomalies it would seem unlikely that the
Solar
System is perfect, unchanging, and readily represented by ordinal
numbers
and simple expansions, etc. In fact, recent chaos theory-related
investigations
carried out by Sussman,** ^{8}**
Wisdom,

Thus the situation is not only as described by Ivars Petersen

How then should we proceed? And what are the viable alternatives? These questions and partial answers provide the subject matter for Part Two.

- Caswell, A.E., "A Relation Between the Mean Distances of the
Planets
from
the Sun,"
(1929):384.*Science 69* - Malisoff, William M, "Some New Laws for the Solar System,"
(1929):328-329. The latter is included here mainly because of his response to Caswell above and also his initial treatment of integers in the present context.The remaining parts of his paper, however, concern neither Bode nor variants of the "Law", but concepts that include logarithmic spirals in the same context; see Part III for further details.*Science 70* - Richardson, D.E., "Distances of Planets from the Sun,"
, (1945) 14-26.*Popular Astronomy 53* - Ovenden, M. W., "Bode's Law and the Missing Planet,"
(1972) 508-509.*Nature 239* - Nieto, M.M., "The Titius-Bode Law and the Evolution of the Solar
System,"
(1974) 171-174.*Icarus 25* - Bass, R. "The Titius-Bode Law from 1766 to 1996," (Kronia Communications).
- Blagg, M.A., "On a Suggested Substitute for Bode's Law,"
, Vol. LXXIII 6, April 1913:414:422. Noteworthy here are M.A. Blagg's early and valid criticisms of the "law" itself, and also the application of logarithmic ratios in the analysis.*Monthly Notices of the Royal Astronomical Society* - Sussman, G. and Wisdom, J. "Chaotic Evolution of the Solar
System,"
3 Jul 1992: 56-62.*Science*257, - Wisdom, Jack. "Chaotic Dynamics in the Solar System,
(Nov 1987)*Icarus*72**:**241-275. - Kerr, Richard, A. "From Mercury to Pluto, chaos
pervades the Solar System,"
(Jul 1992):33.**Science**257 - _________ "Does Chaos permeate the Solar System?"
(14 Apr 1989).**Science**244 - Milani, A. "Emerging stability and chaos."
(16 March 1989):207-208.**Nature**338 - Laskar, J. "A numerical experiment on the chaotic behavior of the
Solar
System"
(16 Mar 1989):237-238.**Nature**, 338 - _________ "The chaotic motion of the Solar System: a
numerical estimate of the size
of the chaotic zones."
(Dec 1990):266-291.**Icarus**88 - _________ Laskar, J., Joutel, F. and Robutel, P. "The
chaotic obliquity of the
planets"
(18 Feb 1993):608-612.**Nature**361 - _________ Laskar, J.
Thomas Quinn, and Scott Tremaine. "Confirmation of resonant structure
in
the Solar System".
(Jan 1992):148-152.**Icarus**95 - Petersen, I.
, W.H. Freeman, New York, 1993.*Newton's Clock: Chaos in the Solar System*

II The Alternative

http://www.spirasolaris.ca/sbb4b_07.html

Describes an alternative approach to the structure of the Solar System that employs logarithmic data, orbital velocity, synodic motion, and mean planetary periods in contrast to

III The Exponential
Order

http://www.spirasolaris.ca/sbb4c_07.html

The constant of linearity for the resulting planetary framework
is the
ubiquitous constant *Phi* known since antiquity. Major departures
from the theoretical norm are the ASTEROID BELT, NEPTUNE, and EARTH in
a resonant *synodic* position between VENUS and MARS.
Fibonacci/Golden Section Resonances in the Solar System.