Radio atmospheric km. For ELF waves (< 3 kHz), ray theory becomes invalid, and only mode theory is appropriate. Here, the zeroth mode begins to dominate and is responsible for the second window at greater distances. Resonant waves of this zeroth mode can be excited in the Earth–ionosphere waveguide cavity, mainly by the continuing current components of lightning flowing between two return strokes. Their wavelengths are integral fractions of the Earth's circumference, and their resonance frequencies can thus be approximately determined by "f" ≃ "mc"/(2π"a") ≃ 7.5 "m" Hz (with "m" = 1, 2, ...; "a" the Earth's radius and "c" the
International Union of Radio Science Geophysical Union) as well as the "Journal of Atmospheric and Solar-Terrestrial Physics". URSI's original objective (to encourage "scientific studies of radiotelegraphy, especially those which require international cooperation") has been broadened to include all radio science, from telecommunications to radio astronomy, acquisition of radar information about distant passive objects, studies of the radiation stimulated or spontaneously emitted by these objects, biological effects of electromagnetic radiation and active modification of objects by radio waves, within the spectrum from extremely low frequency to the optical domain. A few Commissions are engaged with international projects in cooperation with other international bodies, for example with