PART ONE
OUTLINE OF A SYSTEMATIC ARRANGEMENT OF THE FIXED STARS AND OF THE VAST NUMBER OF SUCH SYSTEMS OF FIXED STARS
Is the great chain, that draws all to agree,
And drawn supports, upheld by God, or thee?
(Pope)10*
SHORT OUTLINE OF THE NECESSARY FUNDAMENTAL PRINCIPLES OF NEWTONIAN PHILOSOPHY REQUIRED FOR AN UNDERSTANDING OF THE FOLLOWING THEORY11*
Six planets, including three with accompanying satellites, Mercury, Venus, Earth with its moon, Mars, Jupiter with four satellites, and Saturn with five, describe orbits around the sun as the mid-point and, together with the comets, which do the same thing from all sides in very long orbits, make up a system which we call the Solar System or the planetary world structure. The fact that the movement of all these bodies takes the form of a circle and returns back on itself presupposes two forces which are equally necessary for any sort of theory, namely, a projectile force, by which at every point of their curved linear movement the bodies would continue on a straight line and disappear into the infinite distance, unless another force, whatever it may be, constantly required them to leave this path and move on a curved track around the mid-point of the sun. This second force, as geometry itself has established with certainty, always aims at the sun and is therefore called the sinking force, the centripetal force, or gravity.
If the orbits of the celestial bodies were exact circles, then the very simplest breakdown of the compounded curved movements would reveal that a continuous impulse towards the central point would be required for the arrangement. However, although the movements of all planets and comets are ellipses in which the sun is located at a common focal point, higher geometry with the help of Keplerās model (according to which the radius vector or the line drawn from the planet to the sun always cuts out on its elliptical path areas proportional to the times) similarly establishes with unequivocal certainty that a force must constantly draw the planet throughout its entire orbital path towards the midpoint of the sun.12* This sinking force, which governs throughout the whole space of the planetary system and directs itself to the sun, is thus an accepted natural phenomenon. Equally clearly demonstrated is the law according to which this force extends from the mid-point of the sun into the far distances. It always decreases inversely as the square roots of the distances from the centre increase. This rule is derived in an equally infallible way from the time which the planets need at different distances to complete their orbits. These times are always in a ratio to the square root of the cubes of their average distance from the sun. From this we deduce that the force which pulls these cosmic bodies to the mid-point of their orbits must decrease inversely as the square of the distance.
This very same law which governs among the planets in their movements around the sun occurs also in connection with small systems, namely, with those which are made up of moons moving about their main planet. Their orbital times are in exactly the same way proportional to the distances and establish a relationship of the force which causes sinking towards the planet, which is exactly the same as the one by which the planet is pulled towards the sun. All this, derived from the most infallible geometry and uncontested observations, has been placed forever beyond contradiction. From this arises now the idea that this sinking force may be exactly the same impetus which is called heaviness on the surface of the planet and which gradually diminishes with the distances from the surface according to the above-mentioned law. We see this from the comparison of the quantity of heaviness on the surface of the earth with the force which pulls the moon to the mid-point of its orbit. These stand in relation to each other just as the force of attraction in the entire planetary system, namely, in inverse proportion to the square of the distances. Hence people also call this frequently reported central force gravity.
Moreover, because there is the highest degree of probability that if an effect occurs only in the presence of and in proportion to the distance to a certain body and if the direction of this effect is related as precisely as possible to this body, then it is credible that this body is the cause of the effect, however it occurs. Therefore, we have sufficient reason to think that this universal downward movement of the planets towards the sun can be attributed to the power of attraction of the sun and to ascribe the capacity for the power of attraction in general to all the celestial bodies.
Hence, if a body is left free to the influence of this impulse which drives it to sink toward the sun or some other planet, then it will fall towards it with a constantly accelerating motion and soon will be united with that same mass. However, if it gets a push directing it to the side, then, if that push is not powerful enough to achieve an exact equilibrium with the sinking force, the body will sink down to the central mass with a curved movement. And if, before the sinking body touches the outer surface of the central mass, the impulse impressed on it has grown at least strong enough to shift it from the vertical line about half the thickness of the body at the mid-point, then it will not touch this surface but, after it has swung closely around it, will, thanks to the velocity achieved in its fall, be raised up high again just as far as it fell, so as to continue its path in a constant circular movement.
Thus, the difference between the orbital paths of the comets and the planets consists in the sideways deviation in opposition to the force which drives them to fall. The more these two forces approach an equilibrium, the more the orbit will become circular in shape; the more unequal they are, the weaker the projectile force in relation to the force pulling to the centre, then the longer the orbit, or, as we say, the more eccentric the orbit is, because the celestial body in one part of its path comes far closer to the sun than in another.
Because nothing in all nature is exactly balanced, no planet has an entirely circular motion. However, the comets deviate the most from a circular orbit, because at their first distance from the sun the impetus which was impressed on them towards the side was the least proportional to the force pulling them to the centre.
In this treatise I will very often use the expression a systematic arrangement of the cosmic structure. So that people will have no difficulty clearly imagining what this term is to mean, I will explain it briefly. Strictly speaking, all the planets and comets which belong to our cosmic structure already form a system by the fact that they rotate around a common central body. However, I take this term in an even narrower sense, because I consider the more precise relationships which have united them with each other in a regular and uniform way. The orbits of the planets are, in relation to each other, as nearly as possible on a common plane, namely, on the extended equatorial plane of the sun. The deviations from this rule occur only in connection with the outermost borders of the system, where all movements gradually cease. When therefore a certain number of cosmic bodies, ordered around a common mid-point and moving around it are at the same time restricted to a certain plane, so that they have minimal freedom to deviate on both sides of this plane, and when the deviation occurs gradually only with those which are furthest distant from the mid-point and participate less in the interconnections than the others, then I say that these bodies are bound together in a systematic arrangement.
ON THE SYSTEMATIC ARRANGEMENT OF THE FIXED STARS
The theory of the general arrangement of the cosmic structure has not achieved any remarkable progress since the time of Huygens.13* At this point we still know no more than we already knew then, namely, that six planets with ten companions, all of which have the circle of their orbit set almost on a single plane, and the eternal spheres of the comets, which run riot on all sides, make up a single system, whose mid-point is the sun, towards which everything sinks, around which their movements run, and from which they all are illuminated, warmed, and kept alive, and finally that the fixed stars are just so many suns, the mid-points of similar systems, in which everything may be set up in just as large and orderly a way as in our system and that infinite space teems with cosmic systems, whose number and excellence have a relationship to the infinite nature of their Creator.
The systematic arrangement which took place in the union of the planets which move around the sun disappeared in the crowd of fixed stars, and it seemed as if the rule-governed relationship encountered in miniature does not hold sway on a large scale among the links of all the worlds. The fixed stars were subject to no law, by which their positions were confined relative to each other, and we saw all heaven and the heaven of all heavens filled without order and without design. Since human curiosity limited itself in this way, we did nothing further, other than to infer from this state the immensity of the One who had revealed Himself in such inconceivably huge works and to admire Him.
It was reserved for Mr. Wright, an Englishman from Durham, to take a happy step to an observation which he himself does not seem to have developed into anything insightful and whose useful application he did not sufficiently note. He looked at the fixed stars not as a disorganized and scattered swarm without purpose but found a systematic arrangement in their totality and a general relationship of these stars with respect to a major plane of the space which they occupy.
We wish to improve the idea which he presented and to redirect it, so that it can generate important consequences. The complete confirmation of these is something we leave for future ages.
Anyone who gazes at the starry heavens on a clear night will notice that bright band which presents a steady light through the crowd of stars which have accumulated there more than elsewhere and which perceptibly lose themselves in the huge expanse. People have called this band the Milky Way. Because of the structure of this recognizably distinct area in the sky, it is remarkable that observers of the heavens were not long ago prompted to derive from it strange conclusions about the locations of the fixed stars. For we see that the band has an immense circular orientation and, indeed, in a continuous arrangement taking up the entire heavens. These two factors possess such a precise determination and characteristics so recognizably different from uncertain approximations that from them keen astronomers should long ago naturally have been motivated attentively to investigate the explanation for such a phenomenon.
The stars are not placed on the apparently hollow sphere of the heavens, but from our point of view stand at some distance from each other, some further than others, disappearing into the depths of the heavens. From this phenomenon it follows that, at those distances where they are located one behind the other in relation to us, they do not occur in an equal scattering in every direction, but must be arranged in particular relation to a certain plane which goes through our viewpoint and to which their locations are fixed as closely as possible.
This relationship is such an unambiguous phenomenon that even the remaining stars, which are not included in the white band of the Milky Way, are themselves observed to be that much closer together and more dense, the nearer they are located to the circle of the Milky Way, so that of the 2000 stars which the naked eye perceives in the sky, we find the largest number in a relatively narrow area, the middle of which is taken up by the Milky Way.
Now, if we imagine a plane drawn through the starry heavens and extending an unlimited distance and assume that all the fixed stars and all the solar systems have a common spatial relationship to this plane, so that they are closer to it than to any other areas, then the eye which is located on this common plane, as it looks out into this field of stars, into the hollow spherical surface of the firmament, will see the thickest accumulation of stars in the direction of the drawn plane, in the form of an area illuminated with more lights. This band of light will sweep out in the direction of a huge circle, because the onlookerās viewpoint is on the plane itself. This area will be swarming with stars. Because of the undifferentiated smallness of bright points, a single one of which escapes the eye, and because of the apparent density of a uniform white gleam, it will look, in a word, like a Milky Way. The rest of the heavenly host, whose relationship with the drawn plane becomes less and less apparent or which are also located closer to the observerās position, will be seen as more scattered, although their accumulation will be related to this same plane. From this, finally, it follows that, because from our solar system we see this arrangement of fixed stars in the orientation of a very large circle, our solar system is located in precisely the same large plane and makes one system with the others.
In order that much better to penetrate the composition of the common interrelationship governing this cosmic structure, we wish to try to discover the cause which has arranged the locations of the fixed stars, relating them to a single common plane.
The Sun does not limit the extent of its powers of attraction to the narrow region of the planetary system. According to all appearance, this power extends an infinite distance. The comets which go very far above Saturnās orbit are forced by the sunās powers of attraction to turn back again and to move in orbits. Whether it is more likely for the nature of a force apparently incorporated into the essence of matter to act without limits and whether, in addition, it will be really recognized as such by those who assume Newtonās principles, we wish only to have it conceded that this power of attraction of the sun extends approximately to the nearest fixed star and that the fixed stars act on each other as just so many suns to the same extent. Thus, it follows that the entire host of fixed stars strives to come closer together through this power of attraction, so that all the world systems are in a situation where sooner or later they fall into one clump, through this reciprocal moving closer together, which is continuous and unhindered, unless these systems are saved from this disaster by forces which pull away from the central point, as with the spheres in our planetary system. These forces bend the heavenly bodies away from falling in a straight line and, working together with the forces of attraction, bring about the timeless orbits. Thus the structure of creation is preserved from collapse and has been skilfully created to last eternally.
Hence, all the suns in the firmament have orbiting motions, either around one common central point or around many. But with them, we can everywhere apply the analogy of what we observe about the orbital paths of our solar system, namely, that just as that very cause which has imparted to the planets a force moving them away from the centre, through which they maintain their orbits, has directed their orbital paths so that they are all related to a single plane, so also the cause, whatever it might be, which has given the suns of the higher world as well as so many wandering stars of the higher world structure the force of their orbit has at the same time brought their orbits as much as possible into one plane and has worked to limit deviation from this plane.
According to this conception, we can picture the system of fixed stars to a certain extent by means of the planetary system, if we magnify the latter infinitely. For if instead of six planets with their ten satellites we assume many thousands of similar bodies, and instead of the twenty-eight or thirty comets which we have observed, we assume a hundred or a thousand times more of them, and if we think of these particular bodies as generating their own light, then to the eye of the observer who looks out at them from the Earth there would appear exactly the same light as appears from the fixed stars of the Milky Way. For the planets we have imagined, because of their close relationship to the same common plane in which we find ourselves with our Earth, would display a densely lit area made up of countless stars, whose direction went in a very large circle. This band of light would have a sufficient number of stars everywhere, although, according to this hypothesis, as moving stars, they are not fixed to a single spot. For, because of their movement, there would always be enough stars on anyone side, even though other stars had moved from that location.
The width of this illuminated zone, which projects a sort of zodiac, will be set by the different levels of deviation of designated erratic stars from their reference plane and by the inclination of their orbits in relation to this same plane. Since most of them are near this plane, their number will appear more scattered in relation to the extent they are distant from it. However, the comets, which occupy all regions without distinction, will cover the field of the heavens on both sides.
The shape of the heaven of fixed stars thus has no cause other than the same systematic arrangement on a grand scale as the cosmic structure of the planetary system on a small scale, since all the suns make up one system, whose common interconnecting plane is the Milky Way. Those which are the least related to this plane will be seen to the side; for that very reason, however, they are less dense, more widely scattered, and less frequent. They are, so to speak, comets among the suns.
This new theory, however, attributes a forward motion to the suns, and yet everyone acknowledges that they are motionless and that they have been fixed in their positions from the start. The name which the fixed stars have acquired from this seems confirmed and unambiguous because of all the centuries of observation. This difficulty, if soundly based, would destroy the proposed theory. But this l...