The numerous poorly understood differences between Ganymede and Callisto (the difference in the densities, in the degree of cratering and topography of the surface, the existence proper of craters and a difference of their distribution from that typical of bodies in the inner Solar System, etc.) find readily an explanation within the hypothesis of an explosion of Ganymede's icy envelope saturated by products of the volumetric electrolysis of ice. Similar explosions underwent earlier the ices on Io and Europa, and more recently, on Saturn's satellite Titan. One cannot exclude the possibility that the envelope of Callisto is also saturated by the electrolysis products and is only awaiting a strong impact which would trigger its explosion. The consequences of such an explosion would be devastating for the Earth's biosphere. About 109 ice fragments Φ ⩾ 0.3 km would appear in the orbits of Jovian comet family. Every day, a body causing an explosion ≳ 1 Mt of TNT equivalent would fall on the Earth, once a year- ≳ 103 Mt, and once in a man's life, ≳ 105 Mt. Apart from purely impact effects (super-tsunami, heating of the atmosphere) and the poisoning of the air by such compounds as HCN, CO, etc., impacts in excess of 105 Mt could produce a ‘nuclear winter’ phenomenon resulting from the appearance of huge amounts of dust in the atmosphere. Such impact-related catastrophies led in the past to changes of geological epochs. An analysis is given of possible impact sources. The ~30Myr intervals between mass extinctions can be accounted for by purely random collisions, with only large impacts being capable of producing (1) a nuclear ‘superwinter’ leading to a global catastrophe and (2) an ejection from the Earth of the Aten-type asteroids leading to subsequent secondary mass bombardment. A possibility is pointed out of the appearance of rare (once in about 108 yr) short-period comet showers originating from the detonation of the ices still remaining in the large Trojans. The high priority of a mission to Callisto to determine the degree of saturation of its ices by the electrolysis products and to evaluate its potential hazard for mankind is validated.