6 July 2007

Observing Location	VP
Observational Period	1000-1015 EDT
Atmospheric Conditions	Cloud Cover Clear very light haze Temperature 77°F Wind Calm Humidity Moderate Feels Like Warm It feels warm and a little close so I suspect that there is more than a little haze up there. Transparency Good Seeing II
Instruments	Brunton 8x21 compact binocular w/Welco gold shade 14 welder's filter - Charlie
Observing Party	Charlie Ridgway

Target Sunspots Constellation Gem Category Solar Time yyyymmdd.hhmm 20070706 EDT Comments Distance Light Time 1.016673 AU 8ms Angular Size 31'30.8" Altitude 48.3° Heliographic Latitude (B0) 3.43° Heliographic Longitude (L0) 156.08° Position Angle (P) -0.35° Carrington rotation number (CR) 2058 I only have the small binoculars with me again today and did not see 961 although Space Weather says it is still there. I suspect that it is shrinking and checked Active Region Explorer which shows that it could be either growing or shrinking.   Groups Spots R North 0 0 0 South 0 0 0 Total 0 0 0 R = (Groups * 10) + Spots)

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I was straightening up a pile of books last night when I came across the essential atlas of astronomy which was initially published in Spanish as Atlas de Astronomia and translated into English by Barron’s. I bought it at one of those stores that caters to K-12 learners.

Looking through it I came across Bode’s Law, which I have always wondered about but never analyzed. How accurate is it?

I created a spreadsheet to answer that question and did some light research on the law.

It turns out that the law wasn’t developed by J. E. Boode (1717-1826) at all, he is just the one who made it popular and his name was applied to it. Johann Daniel Titius (1729-1796) actually came up with the idea that there was a relationship in the distances of the planets from the Sun and devised a “law” to explain that relationship and to predict an object at 2.8 au from the Sun, which is where Ceres was later found on 1Jan1801 by Giuseppe Piazzi.

Titius made a list of 4s down a page and next to them, starting with the second 4 made a list beginning with 3 and doubling that value on each subsequent line. He added the two adjacent values together and divided them by 10 giving a distance factor for where an object should be. The distance factor for the Earth was 1 or 1 au. At that time only the planets Mercury through Saturn were known and the “law” is close to the distance for those planets. But there was no known planet at distance 2.8 au, where the law said there should be one. The law predicted the location of Uranus, but placed Pluto where Neptune is.

Bode wrote a book in 1772 that referenced the “law” and used the law to show that Uranus was right where it should be when it was discovered by William Herschel in 1781. But there was still no planet between Mars and Jupiter. A society was formed to find the missing planet. Piazzi subsequently found the object but it was lost before anyone else could validate his claim. Carl Friedrich Gauss used a new technique to predict the position where the object would be found and it was recovered. (The new technique was able to predict the path using only a few prior sightings and didn’t care what shape the orbit was.)

Ceres was called a planet. Subsequently Pallas (1802), Juno (1804) and Vesta (1807) were discovered at roughly the same distance and they were termed asteroids so Ceres was demoted. Now with the IAU’s definition of a planet Ceres has been elevated to a position between that of an asteroid and a planet. It is now a dwarf planet, at least until the definition of a planet is revised in a few years.

The law became known as Bode’s law after it appeared in his book but is more properly called the Titius-Bode Law.

For my chart I have added the Asteroid Belt and Ceres to see how they fit in, and extended the chart out through Eris and the next, still unknown object. Objects in light yellow were unknown in Titius’ time and the one in pink is still unknown.

Object			Distance Factor	Predicted Distance kilometers	Acutual Mean Distance kilometers	Prediction Error
Mercury	4	0	0.4	59,840,000	57,900,000	3.24%
Venus	4	3	0.7	104,720,000	108,000,000	-3.13%
Eathr	4	6	1.0	149,600,000	149,600,000	0.00%
Mars	4	12	1.6	239,360,000	228,000,000	4.75%
Asteroid Belt	4	24	2.8	418,880,000	448,800,000	-7.14%
Ceres	4	24	2.8	418,880,000	413,900,000	1.19%
Jupiter	4	48	5.2	777,920,000	778,000,000	-0.01%
Saturn	4	96	10.0	1,496,000,000	1,430,000,000	4.41%
Uranus	4	192	19.6	2,932,160,000	2,870,000,000	2.12%
Neptune	4	384	38.8	5,804,480,000	4,500,000,000	22.47%
Pluto	4	768	77.2	11,549,120,000	5,900,000,000	48.91%
Eris	4	1536	154	23,038,400,000	10,200,000,000	55.73%
?	4	3072	307.6	46,016,960,000