Neutrino signals by Upward Tau airshowering at Earth horizons and by Muon airshowering at Moon shadows

International audienceNeutrinos are invisible, but their interactions with matter and their leptons signature leave an observable trace. Due to the huge atmospheric neutrino noise produced by cosmic ray rainpresent detectors are hidden deep in underground, as SK or IceCube detectors. At highest energy, atmospheric signal are found to be overcome by a new flavor signature. Because of it at those edges there is much hope for revealing highest energy neutrino as an astronomy, well above tens TeVs.We remind that the three neutrinos and antineutrinos flavors show different roles. Traces of GeVs-TeVs electrons radiate a lot, so they are short (on the order of meters) within solid matter.Muons, even if unstable, they radiate much less, so they are much more long life and penetrating (range of kilometers at TeVs eneregy in matter). These muons may be born inside a rock andescape from matter, as skimming from mountains; they may also decay over great distances, much larger than the size of Earth. In analogy, taus, the third and most unstable leptons, are hardlyformed from cosmic rays secondaries. Therefore they arise mainly from astrophysical neutrinos, that are democratically mixed during stellar and cosmic oscillating flights. Tau are also the most penetrating in principle but because they are extremely unstable, they are relevant only at PeVs energy edges. They may rise as a inner cascade and a later decay as a larger shower in icy: the so called double bang. The tau penetrability range and decay in rock, at PeV energy, is around 49 meters; the , onceescape in air , may decay in air-shower. For instance their escaping from a mountain or from the Earth, is amplified in a widest area and by richest secondaries as rare upgoing airshowers. Therefore, for more than twenty years they have been advocated and proposed as a new filtered neutrinos astronomy no longer hidden in underground detectors, free from most atmospheric noises. These are the signals searched by present ongoing experiments from mountains, valleys and from space: the tau airshowers. Nevertheless also muons at TeVs or higher energy can in principle decay in flight, but mainly onlyfrom the Moon distances. Their secondary electron may trace wide airshower on Earth atmosphere as gamma ones. Because the terrestrial and nearby magnetic fields, the bending begin to fadeabove 6.4 TeV; just above 61.2 TeVs the muons are mostly no longer able to decay in flight. Therefore, rarest gamma-like airshower in largest LHAASO like array, in the 6.4 TeVE 61.2 TeV windows, may be discovered in future years. The widest thousands of kilometer-size gamma array such as GRAND ARRAY can detect these trough going muons escaping from the Moon, decayingas electron or gamma on terrestrial airshowers.More energetic and fragmented decays can also rarely occur, from PeVs tau from the Moon. The corresponding solar shadow is opaque to neutrinos. But their skimming PeVs CRs could still shinemore likely muons, whose decay in flight may also soon rise as a gamma corona halo around our Sun, with a possibly already detectable signal in LHAASO