Warren Platts

2007-Nov-13, 04:56 PM

That Bode's Law is an ATM concept is evidenced by the fact that the main planetary science journal Icarus does not accept manuscripts that discuss Bode's Law.

I take it that the essence of Bode's Law is that planetary spacing is approximately logarithmic in scale.

One problem is that there's not a lot of data sets to test it on. However, five exoplanets have been discovered around 55 Cancri A. Amazingly, the semimajor axes are well predicted by the following simple relation:

a = 0.039en-1

where a is the semimajor axis, e is the natural logarithm constant (2.7 ...), n is the number of the planet starting from it's sun, and the 0.039 is the semimajor axis of the closest planet in AU's.

The tables show the data for 55 Cancri and the Sol system (1st column = observed value; 2nd column = predicted value; 3rd column = the square of the difference between the first two columns; data from the Wikipedia):

55 Cancri

0.038 --- 0.039 --- 0.0000010

0.115 --- 0.106 --- 0.0000808

0.240 --- 0.288 --- 0.0023207

0.781 --- 0.783 --- 0.0000055

????? --- 2.129 --- ??????????

5.770 --- 5.788 --- 0.0003281

????? --- 15.73 --- ??????????

Solar system (planet #5 is Ceres)

00.400 --- 0.390 --- 0.0001

00.700 --- 0.720 --- 0.0004

01.000 --- 1.000 --- 0.0000

01.600 --- 1.520 --- 0.0064

02.800 --- 2.770 --- 0.0009

05.200 --- 5.200 --- 0.0000

10.000 --- 9.540 --- 0.2116

19.600 --- 19.20 --- 0.1600

Thus the average for the squared differences for 55 Cancri is 0.0005472, whereas that for the Sol system is 0.0474250. Even if we just take the average of the squared differences from Mercury through Jupiter, the average is 0.00130--still higher than that predicted for 55 Cancri.

It is striking that the very first extrasolar test of Bode's Law-like relations agrees with the predictions better than our own solar system does.

If Bode's Law like spacings are ubiquitous, that suggests that logarithmic spacings are not in fact merely coincidental, but result from a deep, underlying physical explanation.

The best reference so far I've found is Graner and Dubulle (1994). (http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1994A%26A...282..262G&data_type=PDF _HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf)

Edit: this thread is a continuation of a discussion started in the Is there a pattern to how our solar system is laid out? (http://www.bautforum.com/astronomy/66784-there-pattern-how-our-solar-system-laid-out.html) thread in the Astronomy section.

I take it that the essence of Bode's Law is that planetary spacing is approximately logarithmic in scale.

One problem is that there's not a lot of data sets to test it on. However, five exoplanets have been discovered around 55 Cancri A. Amazingly, the semimajor axes are well predicted by the following simple relation:

a = 0.039en-1

where a is the semimajor axis, e is the natural logarithm constant (2.7 ...), n is the number of the planet starting from it's sun, and the 0.039 is the semimajor axis of the closest planet in AU's.

The tables show the data for 55 Cancri and the Sol system (1st column = observed value; 2nd column = predicted value; 3rd column = the square of the difference between the first two columns; data from the Wikipedia):

55 Cancri

0.038 --- 0.039 --- 0.0000010

0.115 --- 0.106 --- 0.0000808

0.240 --- 0.288 --- 0.0023207

0.781 --- 0.783 --- 0.0000055

????? --- 2.129 --- ??????????

5.770 --- 5.788 --- 0.0003281

????? --- 15.73 --- ??????????

Solar system (planet #5 is Ceres)

00.400 --- 0.390 --- 0.0001

00.700 --- 0.720 --- 0.0004

01.000 --- 1.000 --- 0.0000

01.600 --- 1.520 --- 0.0064

02.800 --- 2.770 --- 0.0009

05.200 --- 5.200 --- 0.0000

10.000 --- 9.540 --- 0.2116

19.600 --- 19.20 --- 0.1600

Thus the average for the squared differences for 55 Cancri is 0.0005472, whereas that for the Sol system is 0.0474250. Even if we just take the average of the squared differences from Mercury through Jupiter, the average is 0.00130--still higher than that predicted for 55 Cancri.

It is striking that the very first extrasolar test of Bode's Law-like relations agrees with the predictions better than our own solar system does.

If Bode's Law like spacings are ubiquitous, that suggests that logarithmic spacings are not in fact merely coincidental, but result from a deep, underlying physical explanation.

The best reference so far I've found is Graner and Dubulle (1994). (http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1994A%26A...282..262G&data_type=PDF _HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf)

Edit: this thread is a continuation of a discussion started in the Is there a pattern to how our solar system is laid out? (http://www.bautforum.com/astronomy/66784-there-pattern-how-our-solar-system-laid-out.html) thread in the Astronomy section.