(Solar system / Double stars / Galaxies)
In this section, the three interesting points discussed are the applicability of Newton’s law of gravitation to the solar system, double stars, and galaxies.
1. Solar system:
“This discovery shows that Newton’s laws are absolutely right in the solar system; but do they extend beyond the relatively small distances of the nearest planets (Feynman et al., 1963, section 7.5 Universal gravitation).”
Feynman mentions that there were attempts to analyze the “elliptical” motions of Jupiter, Saturn, and Uranus on the basis of Newton’s law of gravitation. Importantly, the motion of Uranus could not be understood even if allowance were made for the attractions of Jupiter and Saturn. Thus, it could not be ruled out that the law of gravitation was not exactly true. On the other hand, the location of Neptune predicted by Le Verrier and Adams were based on some guesswork, for example, the mass of Neptune as well as the orbital distance of Neptune from the Sun. Furthermore, they were both fortunate because Uranus and Neptune were relatively close together in the period from 1800-1850. In a sense, the prediction of Neptune is the first idea related to the dark matter in which its existence was deduced from the gravitational effects.
In one of his Messenger Lectures, Feynman humorously adds that “‘How absurd,’ said one of the observatories, ‘some guy sitting with pieces of paper and pencils can tell us where to look to find some new planet.’ The other observatory was more ... well, the administration was different, and they found Neptune! (p. 24).” This humor is rather misleading. Firstly, Le Verrier was arrogant and thus, many astronomers did not check his prediction (Lequeux, 2013). Next, when John Couch Adams shared a predicted location of Neptune with George Airy, Airy’s own calculations suggested that the gravitational force of a new planet would not explain the motion of Uranus completely (Lequeux, 2013). The motion of Uranus is a complex problem that is complicated by many possibilities: the law of gravitation needs refinement, the existence of a resisting medium, hit by a comet, or the presence of a massive satellite (Smart, 1946).
Note that there is no mention of Mercury’s motion in The Feynman Lectures on Physics. Curiously, in his Messenger Lecture for the public, he elaborates that “in the beginning of the twentieth century, it became apparent that the motion of the planet Mercury was not exactly right. This caused a lot of trouble and was not explained until it was shown by Einstein that Newton’s Laws were slightly off and that they had to be modified (Feynman, 1965, p. 24).” Similarly, in a paper presented to the Academy of Sciences on 12 September 1859, Le Verrier predicted an undiscovered planet, Vulcan, that was closer to the Sun than Mercury as to be invisible. This prediction of the planet fails and the need for “dark matter” in this case is now explained by Einstein’s general theory of relativity instead of Newton’s law of gravitation.
Note: According to Drake and Kowal (1980), Neptune was first observed by Galileo on the night of Jan. 28, 1613.
2. Double stars:
“Thus we can analyze double stars, moving about each other, according to the requirements of the gravitational law (Feynman et al., 1963, section 7.5 Universal gravitation).”
Feynman explains that Newton’s law of gravitation is applicable to double stars that are relatively close together. Based on careful measurements of the relative positions of Sirius A and Sirius B (the nearest binary star system), their motions are almost elliptical. Furthermore, Feynman elaborates that Sirius A is not at the focus because the plane of the ellipse is not in the “plane of the sky.” In other words, we are not looking at the motions of Sirius B that is at right angles to the orbit plane. Essentially, this ellipse is viewed at a tilt, and thus, the focus is not at the same place.
In his first Messenger lecture, Feynman (1965) says that “God has not presented us with this orbit face-on; it is tilted at a funny angle. If you take an ellipse and mark its focus and hold the paper at an odd angle and look at it in projection, you will find that the focus does not have to be at the focus of the projected image. It is because the orbit is tilted in space that it looks that way (pp. 24-25).” This explanation is more interesting and concrete in the sense that he uses the paper to illustrate the concept of a tilted plane.
Bessel (1844) deduces from the motion of Sirius A (the brightness star in night’s sky) that it has a weak companion. This companion star was later observed by Alvan Graham Clark in 1862 and it is named Sirius B, or “the Pup.” Strictly speaking, the orbital motion of Sirius B with respect to Sirius A is not perfectly elliptical. From an orbital analysis of the binary Sirius A-B, Benest and Duvent (1995) suggest the existence of a Brown Dwarf star in the system. However, there is still no detection of a third body or the suspected Sirius C.
3. Galaxies:
“…Thus galaxies attract each other at such distances that they too are agglomerated into clusters (Feynman et al., 1963, section 7.5 Universal gravitation).”
According to Feynman, the law of gravitation is still correct even for longer distances such as a globular star cluster. Firstly, there are significantly more stars in a center of the cluster toward the center and there are fewer and fewer stars as we move outward. That is, the shape of a galaxy indicates an obvious tendency for its matter to form a cluster. Importantly, Feynman clarifies that we cannot prove that the gravitation law here is precisely inverse square, but we can conclude that there is still an attraction, at this enormous dimension, that holds a large group of stars together. Furthermore, the shape (or spatial distribution) of the galaxy is due to its spinning as well as its angular momentum which remains constant.
The concept of a cluster in a galaxy is not clarified in The Feynman Lectures on Physics. However, in Feynman’s (1965) own words in his first Messenger lecture, “[t]hat cluster was just a little pin-point inside the big galaxy in plate 3, which shows a typical galaxy, and it is clear that again this thing is held together by some force, and the only candidate that is reasonable is gravitation (p. 26).”
In general, the gas and dust swirling at the outer edges of a galaxy are rotating just as fast as the gas and dust near the center of the galaxy. By studying the way in which galaxies rotate, Vera Rubin suggests an existence of dark matter that helps to understand the galaxies. Alternatively, Rubin opines that the solution to the mystery would be a refinement of the gravitational law if the dark matter cannot be detected. However, the shape of the galaxy can be approximately explained by the gravitational law even though the complexities of its structure are not completely understood. Interestingly, Astronomer Edwin Hubble (1926) has classified galaxies into four major types: spiral, elliptical, lenticular, and irregular.
Questions for discussion:
1. How do we know that Newton’s law of gravitation is absolutely right in the solar system?
2. How do we know that Newton’s law of gravitation is applicable to double stars (or binary stars system)?
3. Does the shape of a galaxy indicate that the gravitation law is precisely inverse square?
The moral of the lesson: Newton’s law of gravitation is applicable to the solar system, binary star systems, and galaxies.
References:
1. Benest, D. & Duvent, J. L. (1995). Is Sirius a triple star? Astronomy and Astrophysics, 299, 621-628.
2. Drake S., & Kowal, C. T. (1980). Galileo’s Sighting of Neptune. Scientific American, 243(6), 74-81.
3. Feynman, R. P. (1965). The character of physical law. Cambridge: MIT Press.
4. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.
5. Lequeux J. (2013). The Discovery of Neptune (1845–1846). In: Le Verrier —Magnificent and Detestable Astronomer. Astrophysics and Space Science Library, vol 397. Springer, New York, NY.
6. Smart, W. M. (1946). John Couch Adams and the Discovery of Neptune. Nature, 158, 648-652.