Skimming Cosmic Rays on the external Solar atmosphere can be showering in gamma, electron
and energetic muon pairs. Such secondaries of TeV or higher energy could reach Earth along a
thin frontal solar ring. The skimming gamma and electron rays are abundant, but originated in
a very thin layer of the solar atmosphere, disturbed and obstacled in their propagation by solar
corona fields and plasma scattering. On the contrary, secondary TeVs-PeVs muons are much
rare, but are much more penetrating : they may escape from deeper solar edges along large cord
distances, forming a thicker solar ring areas, shining brighter towards our Earth. Being muons of
opposite charges, their trajectories are splitted in a twin ring of muons signals that should finally
exit the Sun, decays in flight, reaching array detectors on Earth. These muons and their decay in
electron pairs, even partially deflected up a few TeVs, must lead to rare gamma-like, air-showers, in
LHAASO array detector, falling inside or around the same solar shadows. These rare gamma-like
airshowers must be soon disentangled and observable within an energy range of a few up to tens
TeV energy.
A more rare, more exciting, signal must also occur from the entire lunar surface or disk, by
upward escaping TeVs muons toward the Earth, made by tens TeV muon astrophysical neutrinos
, interacting in a few kilometer lunar crust depth, shining around a 6 − 60 TeV energy windows,
as above, as detectable electron air-shower. Such a lunar mass volume, as a calorimeter for
astrophysical neutrinos, is at least a million times larger than the IceCube one, but their arrival
solid angle is extremely small. Therefore this lunar disk area signals will be hardly observable in
present LHAASO, even within several years or decades. However future larger area, LHAASO
like arrays, might be opening the road to a guaranteed lunar induced neutrino muon Astronomy.
The first expected solar (and lunar) air-shower rate and geometry in their LHAASO shadows are
described.