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)

Short Outline of the Necessary Fundamental Principles of Newtonian Philosophy Required for an Understanding of the following Theory Six planets, including three with accompanying satellites, move in an orbit around the sun at the mid-point: Mercury, Venus, the earth with its moon, Mars, Jupiter with four satellites, and Saturn with five. These, together with the comets which move toward the sun from all side in a very long orbits, make up a system called the Solar System or also 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 also the force of 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 Kepler's model (according to which the radius vector or the line drawn from the planet to the sun always cuts out on its elliptical path an area proportional to the time) immediately establishes with unequivocal certainty that a force must constantly draw the planet throughout its orbital path towards the mid point of the sun. This sinking force, which governs throughout the entire space of the planetary system and directs itself to the sun, is also 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 distance from the centre increases. This rule is derived infallibly 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 the planets in their movements around the sun occurs also in connection with small systems, namely, with those which are made up of the moons moving about their main planet. Their orbital times are in exactly the same way proportional to the distance and establish a relationship of the force which causes sinking towards the planet, which is 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 diminishes with the distance from the surface gradually 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 distance. Hence people call this frequently reported force gravity.

Moreover, because the idea is highly probable that if a present effect occurs only 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 this body may be, however this occurs, the cause of the effect. Therefore, we have sufficient reason to think that the universal downward movement of the planets towards the sun is an attribute of the power of attraction of the sun and to ascribe this power of attraction in general to all the celestial bodies.

If a body is left free to the influence of this impulse which drives it to sink toward the sun or any 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 force directing it to the side, then, if that force 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 central mass, 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 orbital 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 location the sideways impetus influencing them was the least proportional to the force pulling them to the centre.

In this treatise I will often use the expression a systematic arrangement of the cosmic structure. So that people will have no difficulty clearly imagining what this term might 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, in which 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 thus have fewer interconnections than the others, then I say that these bodies are bound together in a systematic arrangement.