After evidence was obtained in 1920s that the university is expanding, it became reasonable to ask: will the universe 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 brake the expansion and “close” the universe is equivalent to there hydrogen atoms per cubic meter. 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 center of rotation. It has been known for some time that outside the bright nucleus of a typical spiral galaxy luminosity falls off rapidly with distance from the center. If luminosity were a true indicator of mass, most of the mass would be concentrated toward the center. Outside the nucleus the rotational velocity would decrease geometrically with distance from the center, 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 center or increases slightly. This unexpected result indicates that the falloff in luminous mass with distance from the center 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 or 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.
十九世纪二十年代，人们证明宇宙是在不断扩大的，于是有人问：宇宙会继续无限地扩大下去，还是已经有足够大的质量来维系天体间的相互吸引使宇宙停止扩大。计算得出,使宇宙停止扩大所需要的临界密度等于三个氢原子/立方米。但是我们可以观测到的宇宙(星系中的可见物质)的密度小于该临界密度。如果要让宇宙停止扩大，那就必须要有超过可见物质密度约70倍的不可见物质存在。
为了寻找这些“丢失的物质”，我们研究了星系在据其环绕中心不同位置的环绕速度。我们曾经认为在典型螺旋星系的明亮中心以外，亮度随距中心距离的增加而急剧减弱。如果亮度标志着质量，那么大部分质量就应该集中在星系的中心。而根据开普勒定律，随着距中心距离的增加环绕速度应该呈几何递减。可是，我们发现螺旋星系中天体的环绕速度保持不变或是随距离增加稍稍变快。这个出乎意料的结果表明随距中心距离的增加，不可见物质质量的增加抵消了可见物质质量的减少。
我们的研究结果表明占宇宙质量90%的物质不能发出可从地球上观测到的光。这种暗物质可能是特别暗的质量轻的恒星，大的行星如木星或者是大、小黑洞。虽然还没有确定这些质量是否足以使宇宙停止扩大，一些物理学家认为这些推测正趋向接近临界值，这是意义重大的。
