  The detection of very-high-energy (VHE) neutrinos ($E_\nu \gtrsim 10$ PeV) is
a challenge that future generations of experiments are being designed and
constructed to address. One promising method relies on using the Earth as a
neutrino target for indirect detection of skimming tau neutrinos interacting
within the Earth and producing tau leptons that are able to escape and decay in
the atmosphere. The tau decay produces upward-moving Extensive Air Showers
(EASs). A space-based or suborbital instrument observing the ground near the
Earth limb can search for the beamed Cherenkov signal produced by the up-going
EAS resulting from the tau-lepton decay. In this paper, we derive the
geometrical constraints for such an observation in general and for the specific
case of the Probe Of Extreme Multi-Messenger Astrophysics (POEMMA) mission
currently under study, focusing on the Cherenkov signal detection. We show
that, using reasonable orbital parameters, POEMMA can achieve full-sky coverage
to search for potential neutrino sources over the length of its mission. We
also show that follow-up of a transient Target-of-Opportunity (ToO), such as a
flaring source, can be achieved within an orbit time scale depending on the
source location on the celestial sphere and its relative position with respect
to the Sun and the Moon.
