Birkeland's experimental attempts to explain the aurora borealis, he was fascinated by aurorae and related phenomena. His first work on the subject attempted to model mathematically the paths taken by charged particles perturbed by the influence of a magnetized sphere, and Størmer eventually published over 48 papers on the motion of charged particles. By modeling the problem using differential equations and polar coordinates, Størmer was able to show that the radius of curvature of any particle's path is proportional to the square of its distance from the sphere's center. To solve the resulting differential equations numerically, he used Verlet integration, which is therefore also known as Störmer's method. Ernst Brüche and Willard Harrison Bennett verified experimentally Størmer's predicted particle motions; Bennett called his experimental apparatus "Störmertron" in honor of Størmer. Størmer's calculations showed that small variations in the trajectories of particles approaching the earth would be magnified by the effects of the Earth's magnetic field, explaining the convoluted shapes of aurorae. Størmer also considered the possibility that particles might be trapped within the geomagnetic field, and worked out the orbits of these trapped particles. Størmer's work on this subject applies to what are today called the magnetospheric ring current and Van Allen radiation belts. As well as modeling these phenomena mathematically, Størmer took many photographs of aurorae, from 20 different observatories across Norway. He measured their heights and latitudes by triangulation from multiple observatories, and showed that the aurora are typically as high as 100 kilometers above ground. He classified them by their shapes, and discovered in 1926 the "solar-illuminated aurora", a phenomenon that can occur at twilight when the upper parts of an aurora are lit by the sun; these aurorae can be as high as 1000 km above ground. Størmer's book, From the Depths of Space to the Heart of the Atom, describing his work in this area, was translated into five different languages from the original Norwegian. A second book, The Polar Aurora (Oxford Press, 1955), contains both his experimental work on aurorae and his mathematical attempts to model them. In his review of this book, Canadian astronomer John F. Heard calls Størmer "the acknowledged authority" on aurorae. Heard writes, "The Polar Aurora will undoubtedly remain for many years a standard reference book; it belongs on the desk of anyone whose work or interest is involved with aurorae." Other astrophysical phenomena investigated by Størmer include pulsations of