PROBLEME DER ASTRONOMIE FESTSCHRIFT FÜR HUGO v. SEELIGER DEM FORSCHER UND LEHRER ZUM FÜNFUNDSIEBZIGSTEN GEBURTSTAGE MIT 58 ABBILDUNGEN, I BILDNIS UND 3 TAFELN VERLAG VON JULIUS SPRINGER· BERLIN . 1924 MITARBEITER: OE. BE RGSTRAN D -UPSALA A. KOPFF-HEIDELBERG· W. E. BERNHEIMER-WIEN A. KUEHL-MÜNCHEN K. BOHLT N -STOCKHOLM L. LI C HTE N STE I N -LEIPZIG K. F. BOTTLINGER-BERLIN H. LUDENDORFF-POTSDAM BABELSBERG S. OPPENHEIM-WIEN M. BRENDEL-FRANKFURTA.M. J. S. PLASKETT·VICTORIA B. C. P. TEN BRUGGENCATE-GÖT K. POPOFF-SOFIA TINGEN P. J. VAN RHIJN-GRONINGEN G. EBERHARD-POTSDAl\i W. SAMETINGER-MÜNCHEN A.S. EDDINGTON-CAMBRIDGE F. SCHLESINGER-NEW HAVEN (ENGL.) G. SCHNA UDER t -POTSDAM R. EMDEN -MÜNCHEN K.SCHWARZSCHILD t-POTSDAM E. GROSSMANN-MÜNCHEN H. SHAPLEY-CAMBRIDGE P. G UTHNICK-BERLIN-BABELS- (MASS.) BERG J. STEBBINS-MADISON G. HER G LOTZ-LEIPZIG E. STROEMGREN-KOPENHAGEN R. HESS-MÜNCHEN A. WILKENS-BRESLAU J. H. JEANS-LONDON C. WI RTZ -KIEL H. KIENLE-GÖTTINGEN M. WOLF-HEIDELBERG A. KOHLSCHUETTER-POTS H. v. ZEIPEL-UPSALA DAM E. ZINNER-MÜNCHEN UNTER REDAKTION VON HA N SKI E N LE -GÖTTIN GEN ISBN 978-3-642-50455-6 ISBN 978-3-642-50764-9 (eBook) DOI 10.1007/978-3-642-50764-9 ALLE RECHTE, INSBESONDERE DAS DER ÜBERSETZUNG IN FREMDE SPRACHEN, VORBEHALTEN. COPYRIGHT 1924 BY JULIUS SPRINGER IN BERLIN. SOFTCOVER REPRINT OF THE HARDCOVER 1ST EDITION 1924 Inhaltsverzeichnis. Seite Jeans, J. H., London. The Origin of the Solar System Eddington, A. S., Cambridge (England). The Interior of a Star . . 25 Kienle, H., Göttingen. Die ruhenden Calciumlinien 38 Bruggencate; P. ten, Göttingen. Die Bedeutung von Farbenhelligkeitsdiagrammen für das Studium der Sternhaufen. . . . . . . . . . . . . . . . 50 Wirtz, C, Kiel. Kugelnebel, Spiralnebel und Flächenhelligkeit . . . . . . . . . . . 66 Ludendorff, H., Potsdam. Über die Beziehungen der verschiedenen Klassen der veränderlichen Sterne 80 Schwarzschild t, K., Potsdam. Stationäre Geschwindigkeitsverteilung im Sternsystem ...... . 94 Bohlin, K., Stockholm. Beziehungen zwischen den unter sich getrennten Bewegungsformen im Gebiete der Himmelsmechanik . . . . . . 106 Eberhard, G., Potsdam. Zur Bestimmung effektiver Wellenlängen der Sterne . . . . . . . . 115 Kohlschütter, A., Potsdam. Über die zwei Stern ströme . . . . . . . . . . . . . . . . 120 Oppenheim, S., Wien. Zur Statistik der Kometen und Planeten im Zusammenhang mit der Verteilung der Sterne 131 Zeipel, H. v., Upsala. Zum Strahlungsgleichgewicht der Sterne. . . . . . . . . . . . . . 144 Wilkens, A., Breslau. Über die Grenzkurven und ihre Einhüllende im asteroidischen Dreikörper problem bei elliptischer Bahn des störenden Körpers . . . . . . . . 153 Popoff, K., Sofia. Sur une propriHe geomHrique des trajectoires des bolides dans l'atmo sphere terrestre . . . . . . . . . . . . . . . . . . . . . . . . . 169 Brendel, M., Frankfurt a. Main. Probleme der rechnenden Himmelsmechanik 176 Herglotz, G., Leipzig. Bemerkungen zum dritten Keplerschen Gesetz 197 Lichtenstein, L., Leipzig. Untersuchungen über die Figur der Himmelskörper. . . . . . . . . 200 Strömgren, E., Kopenhagen. Zur Durchmusterung des Probleme restreint . . . . . . . . 228 Kopff, A., Heidelberg-Königstuhl. Zur \VeiterentwickIung der Weltgeometrie (Relativitätstheorie) 240 IV Inhaltsverzeichnis. Seite Rhijn, P. J. van, Groningen. Die Verteilung der Leuchtkräfte der Sterne, besonders des M-Typus 247 Hess, R., München. Die Verteilungsfunktion der absoluten Helligkeiten in ihrer Abhängig- keit vom Spektrum ....... . 265 Sametinger, W., München. Die Grenzen des typischen Sternsystems und die Verteilungsfunktion der absoluten Leuchtkräfte . . . . . . . . . . . . . . 276 0 0 0 0 0 0 Grossmann, E., München. Eigenbewegungen 300 Wolf, Mo, Heidelbergo Die Sternleeren bei S Monocerotis 312 Plaskett, J S., Victoria B.C. 0 Problems of the 0-Type Stars 328 Bottlinger, K. F., Berlin-Babelsberg. Die Durchmesser der Fixsterne 338 Emden, R., München. Über Strahlungsgleichgewicht und Helligkeitsverteilung der Sonnen- photosphäre 347 0 • 0 0 • • 0 • 0 • 0 0 0 0 • 0 0 0 0 0 • Zinner, E., München. Über das Reizempfindungsgesetz und die Farbengleichung 354 0 Kühl, A., München. Die Reduktion von Fernrohrbeobachtungen wegen Kontrastfehlers 372 Bergstrand, Ö., Upsala. Über die Abhängigkeit der photographisch effektiven Wellenlängen vom chromatischen Korrektionszustand des Objektivs 386 0 • 0 • 0 • 0 • • 0 Guthnick, P., Neubabelsberg. Zwölf Jahre lichtelektrischer Photometrie auf der Berliner Sternwarte 391 Schnauder t, G., Potsdam. Ionisation und Atomtheorie 403 Schlesinger, F., New Haven. Photographic Determinations of Stellar Parallaxes 422 0 0 0 0 • • • 0 0 Shapley, H., Cambridge. The Magellanic Clouds . . . 438 0 • 0 • • 0 • • Stebbins, J., Madison. On the Reflection of Light in a Close Binary System. 442 0 0 0 • • • 0 Bernheimer, W. E., Wien. Das Problem der Veränderlichkeit der Sonnenstrahlung . . . . . . . 452 The Origin of the Solar System l). By J. H. Jeans, London. With 9 figures. The astronomer of to-day has at his disposal telescopes which range in aperture from his naked eye, of aperture ab out one-fifth of an inch, up to the giant Mount Wilson telescope of more than 100 inches. If we lived in the midst of a uniform infinite field of stars, or in a field which was uniform as far as our telescopes could reach, the numbers of stars visible in different telescopes would be proportional to the cubes of their apertures. In actual fact our naked eyes reveal about 5000 stars; with a one-inch telescope this number is increased to about 100,000, with a ten-inch to 5 million, and with the 100-inch telescope to perhaps 100 million. These numbers increase much less rapidly than the cubes of the apertures. We condude that we are not surrounded by an infinite uniform field of stars. We live in a finite universe, wbich thins out quite perceptibly witbin distances reached by telescopes of very moderate size. It is estimated that tbe whole universe consists of so me 1500 million stars, our sun being not very far from tbe centre of the system. Imagine tbe various celestial objects in this universe arranged according to tbeir distance from uso Disregarding altogether bodies which are mucb smaller tban our eartb, we must give first place to tbe planets Venus and Mars, which approacb to within 26 and 35 millions of miles respectively. Next comes Mercury with a dosest approach of 47 million miles, and tbe sun at 93 million miles. The remainder of the planets follow at distances ranging up to 2800 million miles, the radius of the orbit of Neptune. But now comes a great gap. The first objects beyond tbis gap are the iaint star Proxima Centauri at a distance oi 24 million million miles, or more than 8000 times the distance oi Neptune, and dose to it, <X Cen tauri at 25 million million miles. Next in order come the faint red star Munich 15,040 at 36 million million miles, and another faint star Lalande 21,185 at about 47 million million miles. Thus our nearest neighbours among the stars are at almost exactly a million tim es tbe distances of our nearest neighbours among tbe planets. After these comes Sirius, 1) Discourse delivered at the Royal Institution on February 15. See li g er -Festschrift. 2 J. H. JEANS: the brightest star in the sky, at 50 million million miles. From here on there is a steady succession of objects until we reach distances of more than 20,000 times that of Sirius; but long before these distances are reached other objects, spiral and spheroidal nebulae, and ultimately star-clusters, are found to be mingled with the stars. The furthest ob ject the distance of which is known with any accuracy is the star-cluster N.G.C. 7006, which Shapley estimates to be 25,000 times as distant as Sirius. This cluster is so remote that its light takes 200,000 years to reach us; even for light to cross the cluster takes hundreds of years. To all appearances the star~cloud N.G.C. 6822 is still more remote. According to Shapley its distance is about six million million million miles, a distance which light takes a million years to traverse. So far as is known at present, this brings us to the end of our universe, or perhaps I ought to say it brings us back to the beginning. It is no easy matter to get all these different distances clearly into focus simultaneously, but let us try. The earth speeds round the sun at about twenty miles a second; in a year it describes an orbit of nearly six hundred million miles circumference. If we represent the earth's orbit by a pin-head or a full-stot~f radius one-hundredth of an inch, the sun will be an invisible speck of dust, and the earth an ultra-micro scopic particle one-millionth of an inch in diameter. Neptune's orbit, which encloses the whole of the solar system, will be represented by a circle the size of a threepenny-piece, while the distance to the nearest star, Proxima Centauri, will be about 75 yards and that to Sirius about 160 yards. On this same sc ale the distance to the remote star cluster N.G.C. 7006 is 2400 miles and that to the star-cloud N.G.C. 6822 <).bout 12,000 miles, so that roughly speaking the whole universe may be represented by our earth. I t thus appears that we are on this occasion to discuss the origin and past history of a system which bears the same relation to the uni verse as a whole as does a threepenny-piece to our earth. Why are we so interested in this particular threepenny-piece? Primarily because, although a poor thing, it is our own, or at least one particle of it, one millionth of an inch in diameter, is our own. Eut there is a historical reason of a less sentimental kind. We have already noticed the immensity of the gap between our system and its nearest neighbciurs. As regards astronomical knowledge this gap has taken a great deal of crossing. Well on into last century, human knowledge of the further side of this gap was infinitesimal; the stars were scarcely more than points of light, described as "fixed stars". In those days the problem of cosmogony reduced perforce to the problem of the origin of our own system. Recent research has changed all this, and the modern astronomer has a very extensive knowledge of the nature, structure and movements of the various bodies outside our system. The cosmogonist of a century The Origin of the Solar System. 3 ago could assert thai the solar system had evolved in such and such a way,and need have no fear of his theories being upset by comparison with other systems. Eut if I put before you now a theüry of the origin of our system, you will at once inquire as to the behaviour of the 1500 million or so of systems beyond the great gap. Are they following the same evolutionary course as our own system, and, if not, why not? It may be weIl to consider these other systems first. Among these 1500 million ür so of objects there are certain com paratively small c1asses the nature and interpretation of which are still enigmatical-the planetary nebulae, the Cepheid variables, the long period variables such as Mira Ceti, and a few others. Apart from these, practically all known bodies can be arranged in one single continuous sequence. The sequence is approximately one of increasing density: it begins with nebulae of almost incredible tenuity and ends with solid stars as dense as iron. There is but little doubt that the sequence is an evolutionary one, für the laws of physics require that as a body radiates he at its density should increase, at least until it can increase no further. Let us begin our survey at the furthest point back to which we can attain on this evolutionary chain-the nebulae. After the enigmatical "planetary" nebulae have been excluded, the remaining nebulae fall into two fairly sharply defined classes, which may be briefly described as regularly and irregularly shaped nebulae. The irregularly shaped nebulae comprise such objects as the great nebula in Orion, and the nebulosity surrounding the Pleiades. Until quite recently these irregular nebulae were supposed to be of great evolutionary importance. It was noticed that they were usually asso ciated with the very hottest stars: whence arose a beautifully simple cosmogony, asserting that these very hot stars were the immediate products of condensation of the nebulae, and that their after-lite con sisted merely of a gradual cooling until they got quite cold. This cos mogony was too simple to live für long-it was buried so me ten years ago by the researches of RUSSELL, HERTZSPRUNG, and others. Thi'mks to these researches, we now know that the very hot stars associated with irregular nebulae, so far from being newly born, are standing at the summit of their lives awaiting their decline into old age. A mass oi hot gas isolated in space radiates heat, and this causes it to contract. If the mass radiated without contracting, it would, oi course, get cooler; on the other hand, if it contracted without radiating, it would get hotter. But when radiation and contraction are proceeding together it is not obvious without mathematical investigation which of the two tendencies will take command. In 1870, HOMER LANE showed that a mass of gas of density low enough für the ordinary gas laws to be approximately obeyed, will in actual fact get hotter as it radiates heat away. Cooling does not set in until a density is reached at which 1* J. H. JEANS: the gas laws are already beginning to fail-that is to say when lique faction and solidification are already within measurable distance. Thus we see that maximum temperature is associated withmiddleage in astar, the age at which the star may no longer be regarded as a perfect gas. At this period of middle age the surface temperature of the star may be anything up to ab out 25,000° C., while the temperature at its centre will amount to millions of degrees. Its average density will probably be something like one-tenth of that of water. It is still not known why stars at this special maximum temperature are so commonly associated Fig. 1. Regular shaped nebula (N.G.C. 3115). with irregular nebulae. Possibly it may be that only stars at the very highest temperatures are capable of lighting up surrounding nebulosity which would otherwise remain invisible. Be this as it may, it is fairly dear that these irregular nebular masses are not an essential part of the evolutionary chain. They are probably mere by-products, and as such may be dismissed from further consideration. We turn to the nebulae of regular shape. A great number of these appear as cirdes or ellipses, some as ellipses drawn out at the ends of their major-axes, sometimes almost to sharp points. An example of this last type of figure is shown in Fig. 1 (Nebula N.G.C. 3115). A number of these regular-shaped nebulae have been examined spectroscopically, and in every case have been found to be rotating with high velocities ab out an axis which appears in the sky as the shortest diameter of the nebula. The mathematician can caIclllate what configurations will be assumed by masses of tenuous gas in rotation. If rotation were entirely absent the mass would, of course, assurne a spherical shape. With slow rotation its shape would be an oblate spheroid of low ellipticity-an orange-shaped figure like our earth. At higher rotations the spheroidal shape is departed from, the eqllator blllging out more and more until finally, for quite rapid rotation, the shape is approxi mately that of a double convex lens having a sharp circular edge for its equator, the shape, in fact, exhibited by the nebula shown in Fig. 1. The whole succession of figures, if looked at along all possible lines of sight, will exhibit precisely the series of shapes which are found to be The Origin of the Solar System. 5 exhibited by the regular nebulae under diseussion. There are, then, good grounds for eonjeeturing that these nebulae are rotating masses of gas; but we ean test this eonjecture further before finally aeeep tingit. As a mass of gas radiates its energy away it must shrink. If it is in rotation, its angular momentum will remain eonstant, and the shrunken Fig. 2. Regular shaped nebula (N.G.C. 5866) with band of dark matter on equator. mass ean only earry its original dose of angular momentum by rotating more rapidly than before. This eoneeption, whieh formed the eorner stone of the eosmogonies of KANT and LAPLACE, is still oi fundamental import anc e to the cosmogonist oi to-day. Thus every nebula, as it grows older, will rotate ever more and more rapidly and, barring aecidents, will in due course reaeh the configuration shown in Fig. 1. This con figuration marks a veritable landmark in the evolutionary path oi a nebula. Until this eonfiguration is reached the effect of shrinkage can be adjusted, and is adjusted, by a mere change oi shape; the mass earries the same angular momentum as before, in spite of its redueed size, by the simple expedient oi rotating more rapidly, and res tores equilibrium by bulging out its equator. But mathematical analysis shows that this is no longer possible when onee this landmark has been passed. Further shrinkage now involves an actual break-up oi the nebula, the exeess of the angular moment um beyond that which can be carried by the shrunken mass being thrown off into space by the ejection oi matter from the equator oi the nebula. We have so far spoken of the nebular equator as being of eircular shape, as it undoubtedly would be if the nebula were alone by itself in space. But an aetual nebula must have neighbours, and these neighbours will raise tides on its surfaee, just as the sun and mo on raise tides on the surface of the rotating earth. Whatever the neighbours are, there will always be two points oi high tide antipodally opposite to one an other, and two points of low tide intermediate between the two points