Euclid preparation: I. The Euclid Wide Survey
  Euclid is an ESA mission designed to constrain the properties of dark energy
and gravity via weak gravitational lensing and galaxy clustering. It will carry
out a wide area imaging and spectroscopy survey (EWS) in visible and
near-infrared, covering roughly 15,000 square degrees of extragalactic sky on
six years. The wide-field telescope and instruments are optimized for pristine
PSF and reduced straylight, producing very crisp images. This paper presents
the building of the Euclid reference survey: the sequence of pointings of EWS,
Deep fields, Auxiliary fields for calibrations, and spacecraft movements
followed by Euclid as it operates in a step-and-stare mode from its orbit
around the Lagrange point L2. Each EWS pointing has four dithered frames; we
simulate the dither pattern at pixel level to analyse the effective coverage.
We use up-to-date models for the sky background to define the Euclid
region-of-interest (RoI). The building of the reference survey is highly
constrained from calibration cadences, spacecraft constraints and background
levels; synergies with ground-based coverage are also considered. Via
purposely-built software optimized to prioritize best sky areas, produce a
compact coverage, and ensure thermal stability, we generate a schedule for the
Auxiliary and Deep fields observations and schedule the RoI with EWS transit
observations. The resulting reference survey RSD_2021A fulfills all constraints
and is a good proxy for the final solution. Its wide survey covers 14,500
square degrees. The limiting AB magnitudes ($5\sigma$ point-like source)
achieved in its footprint are estimated to be 26.2 (visible) and 24.5
(near-infrared); for spectroscopy, the H$_\alpha$ line flux limit is $2\times
10^{-16}$ erg cm$^{-2}$ s$^{-1}$ at 1600 nm; and for diffuse emission the
surface brightness limits are 29.8 (visible) and 28.4 (near-infrared) mag
arcsec$^{-2}$.
