How common are Earth-size planets in habitable zones of Sun-like stars?
In plain words
The fraction of Sun-like stars with an Earth-size planet at a distance where water could be liquid sets how many targets future telescopes can study. Current estimates differ by about a factor of ten.
Precise statement
Measure $\eta_{\mathrm{Earth}}$, the number per G and K dwarf of planets with $R = 0.5-1.5\,R_{\mathrm{earth}}$ in the conservative habitable zone. Kepler-based estimates span roughly 0.05-0.6 because of extrapolation in period and radius and stellar property uncertainties. The answer is a value with uncertainty below $\sim 30\%$.
What would settle it
A transit survey of bright Sun-like stars with sensitivity to Earth analogs over multi-year baselines (e.g., ESA PLATO), with radial-velocity mass follow-up.
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