Orbital proportionality

[Enola Straight]

I read somewhere that there is a definite pattern to the average distance a planet orbits the sun.

Assume planet Mercury's orbit is one distance unit.

Mercury=1
Venus=2
Earth=4
Mars=8
Asteroid Belt=16
Jupiter=32
Saturn=64
Uranus=128
Neptune=256
(the odd orbit of Pluto...we don't count)

The Kuiper Belt and Oort Cloud also conform to this pattern, I
believe.

Is this pattern a valid observation?
If so, what are the mechanics involved in achieving such perfectly
mathematical proportions?

[David Simmons]

Originally posted by Enola Straight
I read somewhere that there is a definite pattern to the average distance a planet orbits the sun.

Assume planet Mercury's orbit is one distance unit.

Mercury=1
Venus=2
Earth=4
Mars=8
Asteroid Belt=16
Jupiter=32
Saturn=64
Uranus=128
Neptune=256
(the odd orbit of Pluto...we don't count)

The Kuiper Belt and Oort Cloud also conform to this pattern, I
believe.

Is this pattern a valid observation?
If so, what are the mechanics involved in achieving such perfectly
mathematical proportions?

No. The actual ratios based on the planet table in the Merriam-Webster Collegiate Dictionary are as follows:

Mercury=1
Venus=1.868
Earth=2.584
Mars=3.938
Asteroid Belt= not in table
Jupiter=13.444
Saturn=24.605
Uranus=49.615
Neptune=77.711

[Padeye]

That doesn't seem to be true at all. This page has orbical distances. If you adjust that so Mercury's orbit is "1" you get this.

Mercury 1
Venus 1.87
Earth 2.58
Mars 3.92
Jupiter 13.4
Saturn 24.6
Uranus 49.6
Neptune 77.5
Pluto 102

There doesn't seem to be any mechanics involved in a pattern that isn't really there.

[Padeye]

Rounding errors

[knock knock]

The proportionality thing is bs. What's really going on is that the six planets (mercury, venus, earth, mars, jupiter, saturn - the rest are just big asteroids) are arranged so as to have their orbits just fit between the five perfect Platonic solids arranged one inside the other- (from the inside out) octahedron, icosahedron, dodecahedron, tetrahedron, and cube. The orbits just work out so that each solid just fits around a sphere that encloses the next smaller solid. Johannes Kepler figured this out. He also came up with 3 laws of planetary motion that described how planets move in ellipses (not circles!), and how their speed, period, etc. are related.

[Chronos]

So Uranus and Neptune are asteroids, now? That's a new one by me. Somewhat surprising, considering that they're each bigger than the four inner planets combined.

The thing with the Platonic solids was one reason why it took Kepler so long to figure out his laws. You see, those distances aren't quite a match, and if you assume that they are, then Kepler's Laws don't work.

[MonkeyMensch]

Google on Bode's Law and I think you'll get what you were thinking of.

[CalMeacham]

This is the infamous Titius-Bode Law , made famous by Bode and called Bode's Law for years, until they found out that he lifted it from Titius without giving him credit.

It was because of the asteroid "gap" in the law that people started looking for objects there,. I'm told.


One thing you don't hear often is that the T-B law has been extended. Researchers named Blagg and Richardson, working independently, worked out a more general rule that holds for the satellites of the planets as well. There's a book about it -- The Titius-Bode Law and the Blagg-Richardson Formulation. The book came out at least 30 years ago, so I went back a few years ago to plug in the more recent data on satellites. I came to the conclusion that I wasn't impressed -- it was too easy to "fudge" in any orbit I wanted.

Is there any sort of physical reason for the law, or is it a coincidence? The judgment of the book above was that there wasn't any known law involved. Things may have changed since then, but I've never heard any sort of explanation for the spacing. It's not like orbital resonances or anything.

[RM Mentock]

Originally posted by CalMeacham
This is the infamous Titius-Bode Law , made famous by Bode and called Bode's Law for years

Not quite. Bode's law doesn't have a pure doubling relationship. In AU, I think it works out to be more like (3 x 2^n + 16)/40, with Mercury using zero, instead of a power of two in the formula. So, we'd get:

Mercury 1.0
Venus 1.75
Earth 2.5
Mars 4
Asteroid 7
Jupiter 13
Saturn 25
Uranus 49
Neptune 97
Pluto 193

Which compares pretty well to Padeye's figures, except for Neptune and Pluto--but Uranus hadn't been discovered at the time the law was formulated, right?

[CalMeacham]

Not quite. Bode's law doesn't have a pure doubling relationship. In AU, I think it works out to be more like (3 x 2^n + 16)/40, with Mercury using zero, instead of a power of two in the formula. So, we'd get:

I know that, but it's clearly what the original poster had in mind.

In the Blagg-Richardson formulation, the power they worked out wasn't a factor of 2, as in Titius-Bode (your form still has a squared factor in it), but 1.728, which they found independently. The virtues of log-log paper.

[RM Mentock]

Originally posted by CalMeacham
your form still has a squared factor in it

I'm not sure what you mean by this.

[CalMeacham]

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Originally posted by CalMeacham
your form still has a squared factor in it
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I'm not sure what you mean by this.

??????


n^2 means n squared. You have a second order equation. If I plotted it on log-log paper it'd almost be a straight line (despite the additive term), with a slope characteristic of a second order equation.

[CurtC]

I had never heard of this law, so I just did a little Googling. This law was formulated to fit the known planets at the time. You can always find an equation to fit any sequence of numbers, but this equation was simpler than what you might expect to be required to fit the six known planets' orbits. The fact that you could find such a simple equation to fit six data points (well, really five given that it's normalized to Mercury's orbit) was pretty remarkable.

Then when Uranus and the asteroid Ceres were discovered to be in positions predicted by the equation, that was even more remarkable. Seven data points described pretty well by a simple equation, d=0.4+0.3*N, where N=0,1,2,4... - the zero doesn't belong there, but hey, it's still remarkable.

I can understand why people 200 years ago were trying to figure out why it seemed to hold so well. Of course, Neptune sort of blew it. Then Pluto really missed, but Pluto's not really a planet anyway, right?

So has anyone done any work to figure out why the planets are where they are? They formed from a disk of material around the sun, drawn together by mutual gravity. It seems like you would expect that you would have a system with planets getting farther apart as you go out, because the higher rotational speeds of the inner dust clouds would allow closer-together planets, while the more slowly revolving outer stuff would pull material together from farther away. Is there a rule-of-thumb about this? Could we find that other stars also exhibit a Bode Law kind of relationship? I wouldn't be surprised, but I'm not an expert.

[CurtC]

Posted by CalMeacham:
n^2 means n squared.

Pssst... It's "2^n".

[CalMeacham]

quote:
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Posted by CalMeacham:
n^2 means n squared.
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Pssst... It's "2^n".

Ummmm .... yeah.


[Emily Litella] Never mind[/Emily Litella]




Doesn't invalidate my points or my references, though.