  The detection of the first exoplanet paved the way into the era of transit
photometry space missions with a revolutionary photometric precision that aim
at discovering new exoplanetary systems around different types of stars. With
this high precision, it is possible to derive very accurately the radii of
exoplanets which is crucial for constraining their type and composition.
However, it requires an accurate description of host stars, especially their
center-to-limb variation of intensities (so called limb darkening) as it
affects the planet-to-star radius ratio determination. We aim at improving the
accuracy of limb darkening calculations for stars with a wide range of
fundamental parameters. We used the recently developed 1D MPS-ATLAS code to
compute model atmosphere structures and to synthesize stellar limb darkening on
a very fine grid of stellar parameters. For the computations we utilized the
most accurate information on chemical element abundances and mixing length
parameters including convective overshoot. The stellar limb darkening was
fitted using the two most accurate limb darkening laws: the power-2 and
4-parameters non-linear laws. We present a new extensive library of stellar
model atmospheric structures, the synthesized stellar limb darkening curves,
and the coefficients of parameterized limb-darkening laws on a very fine grid
of stellar parameters in the Kepler, TESS, CHEOPS, and PLATO passbands. The
fine grid allows overcoming the sizable errors introduced by the need to
interpolate. Our computations of solar limb darkening are in a good agreement
with available solar measurements at different view angles and wavelengths. Our
computations of stellar limb darkening agree well with available measurements
of Kepler stars. A new grid of stellar model structures, limb darkening and
their fitted coefficients in different broad filters is provided in CDS.
