提丢斯-波得定则(Titius-Bode law),简称“波得定律”,是关于太阳系中行星轨道的一个简单的几何学规则。它是在 1766 年德国的一位中学教师戴维·提丢斯(Johann Daniel Titius,1729~1796)发现的。后来被柏林天文台的台长波得(JohannElert Bode)归纳成了一个经验公式来表示。
Bode's law is a hypothesis that the bodiesin some orbital systems, including the Sun's, orbit at semi-major axes in afunction of planetary sequence. The hypothesis correctly predicted the orbitsof Ceres and Uranus, but failed as a predictor of Neptune's orbit.
When originally published, the law wasapproximately satisfied by all the known planets —MercurythroughSaturn— with agap between the fourth and fifth planets. It was regarded as interesting, butof no great importance until the discovery of Uranus in 1781 which happens tofit neatly into the series. Based on this discovery, Bode urged a search for afifth planet. Ceres, the largest object in the asteroid belt, was found atBode's predicted position in 1801. Bode's law was then widely accepted untilNeptune was discovered in 1846 and found not to satisfy Bode's law.Simultaneously, the large number of known asteroids in
the belt resulted in Ceres no longer beingconsidered a planet at that time. Bode's law was discussed as an example offallacious reasoning by the astronomer and logician Charles Sanders Peirce in1898.
The discovery of Pluto in 1930 confoundedthe issue still further. While nowhere near its position as predicted by Bode'slaw, it was roughly at the position the law had predicted for Neptune. However,the subsequent discovery of the Kuiper belt, and in particular of the objectEris, which is larger than Pluto yet does not fit Bode's law, have furtherdiscredited the formula.
2. 最初发布的时候,波德定律满足当时所知道的几乎所有行星。直到 1781 年天王星的发现,它的运行轨迹完全契合了波德定律,引起了人们对波德定律的强烈重视。
3. 1930 年冥王星的发现使得人们对波德定律更加疑惑。随即柯伊伯带和阋神星的发现也不符合波德定律的预测,使得这一定律的可信性大大降低。
Test Point – TPO26L2
Right. In astronomical units—not perfect,but tantalizingly close. The value for Mars is off by . . . 6 or 7 percent orso. It’s . . . but it’s within 10 percent of the average distance to Mars fromthe Sun. But I kind of have to skip the one after Mars for now. Then Jupiter’sright there at 5-point something, and then Saturn is about 10 astronomicalunits from the Sun. Um, well, this pattern is known as Bode’s Law.
Um, it isn’t really a scientific law, notin the sense of predicting gravitation mathematically or something, but it’sattempting a pattern in the spacing of the planets, and it was noticed by Bode hundredsof years ago. Well, you can imagine that there was some interest in why the 2.8spot in the pattern was skipped, and um . . . but there wasn’t anything obviousthere, in the early telescopes. Then what happened in the late 1700s? Thediscovery of . . . ?
The next planet out, Uranus—after Saturn.And look, Uranus fits in the next spot in the pattern pretty nicely, um, notperfectly, but close. And so then people got really excited about the validityof this thing and finding the missing object between Mars and Jupiter. Andtelescopes, remember, were getting better. So people went to work on findingobjects that would be at that missing distance from the Sun, and then in 1801,the object Ceres was discovered.
And Ceres was in the right place—themissing spot. Uh, but it was way too faint to be a planet. It looked like alittle star. Uh, and because of its starlike appearance, um, it was calledan“asteroid.” OK? “Aster” is Greek for “star,” as in “astronomy.” Um, and so,Ceres was the first and is the largest of what became many objects discoveredat that same distance. Not just one thing, but all the objects found at thatdistance from the asteroid belt. So the asteroid belt is the most famoussuccess of this Bode’s Law. That’s how the asteroid belt was discovered.