Willem de Sitter - Radius Quotes

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In both the solutions A and B the curvature is positive, in both three-dimensional space is finite: the universe has a definite size, we can speak of its radius, and, in the case A, of its total mass. In the case A... the density is proportional to the curvature... Thus, if we wish to have a finite density in a static universe, we must have a finite positive curvature.

Willem de Sitter
In the "static" universe expansion is impossible, the "empty" universe does expand. Therefore we may be tempted to consider the empty universe as the most likely approximation; and we can proceed to compute the radius of curvature of the universe, supposing it to be of the empty type, from the observed rate of expansion.

Willem de Sitter
It is easy to compute the density of a static universe of a radius of two thousand million lightyears, and it comes out only very little larger than the observed density. The actual universe is thus very far from empty, it is, on the contrary, nearly full.

Willem de Sitter
The way in which the universe expands is determined by the variation of this [radius of curvature] R with the time. There are three types, or families, of non-static universes... the oscillating universes, and the expanding universes of the first and of the second kind.... each of these is a representative of a family, comprising an infinite number of members differing in size and shape.... In the expanding family of the first kind the radius is continually increasing from... zero... In the expanding series of the second type the radius has at the initial time a certain minimum value, different for the different members of the family. [Both kinds of expanding families] become infinite after an infinite time.

Willem de Sitter
Let the universe have only two dimensions, and let it be the surface of an india rubber ball. It is only the surface that is the universe, not the ball itself.... Let there be specks of dust fixed to the surface to represent the different galactic systems. If the ball is inflated, the universe expands, and these specks of dust will recede from each other, their mutual distances, measured along the surface, will increase in the same rate as the radius of the ball. An observer in any one of the specks will see all the others receding from himself, but it does not follow that he is the centre of the universe. The universe (which is the surface of the ball, not the ball itself) has no centre.

Willem de Sitter