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            After evidence was obtained in the 1920s that the universe is expanding, it became reasonable to ask: will the universe continue to expand indefinitely, or is there enough mass in it for the mutual attraction of its constituents to bring this expansion to a halt? It can be calculated that the critical density of matter needed to break the expansion and “close” the universe, is equivalent to three hydrogen atoms per cubic metre. But the density of the observable universe-luminous matter in the form of galaxies-comes to only a fraction of this. If the expansion of the universe is to stop, there must be enough invisible matter in the universe to exceed the luminous matter in density by a factor of roughly 70.
            Our contribution to the search for this “missing matter” has been to study the rotational velocity of galaxies at various distances from their centre of rotation. It has been known for some time that outside the bright nucleus of typical spiral galaxy luminosity falls off rapidly with distance from the centre. If luminosity is a true indicator of mass, most of the mass would be concentrated toward the centre. Outside the nucleus the rotational velocity would decrease geometrically with the distance from the centre, in conformity with Kepler’s law. Instead we have found that the rotational velocity in spiral galaxies either remains constant with increasing distance from the centre or increases slightly. This unexpected result indicates that the falloff in luminous mass with distance from the centre is balanced by an increase in nonluminous mass.
            Our findings suggest that as much as 90 percent of the mass of the universe is not radiating at any wavelength with enough intensity to be detected on the Earth. Such dark matter could be in the form of extremely dim stars of low mass of large planets like Jupiter, or of black holes, either small of massive. While it has not yet been determined whether this mass is sufficient to “close” the universe, some physicists consider it significant that estimates are converging on the critical value.