A geometrically determined distance to a far-off black hole

To find the distance to a nearby star, astronomers consider a triangle whose base is a diameter of Earth’s orbit and whose opposite vertex is the star, which apparently shifts position as Earth executes its orbit. Simple trigonometry establishes the distance. Applicable to objects up to a kiloparsec (about 3300 light-years) away, that technique is the basis for the lowest rung of the cosmic distance ladder, the interlocking set of distance determinations that extend to the far reaches of the cosmos. Now Sebastian F. Hönig (then at the University of Copenhagen, now at the University of Southampton) and colleagues have used an analogous geometry to obtain the distance to an object many megaparsecs away: the black hole in the galaxy NGC 4151. As illustrated in the figure, the analogue of the Earth-orbit diameter is the inner diameter of a dust torus that surrounds the black hole. The violent and...