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One of the biggest problems we can encounter while dealing with thelimb-darkening coefficients for stellar atmospheric models with sphericalsymmetry is the difficulty of adjusting both the limb and the central partssimultaneously. In particular, the regions near the drop-offs are not wellreproduced for most models, depending on Teff, log g, or wavelength. Even ifthe law with four terms is used, these disagreements still persist. Here weintroduce a new method that considerably improves the description of both thelimb and the central parts and that will allow users to test models of stellaratmospheres with spherical symmetry more accurately in environments such asexoplanetary transits, eclipsing binaries, etc.  The method introduced here is simple. Instead of considering all the $\mu $points in the adjustment, as is traditional, we consider only the points untilthe drop-off ($\mu_{cri}$) of each model. From this point, we impose acondition ${I(\mu)}/{I (1)} = 0$. All calculations were performed by adoptingthe least-squares method.  The resulting coefficients using this new method reproduce the intensitydistribution of the PHOENIX spherical models (COND and DRIFT) quite well forthe photometric systems of the space missions {{\sc TESS}}, {{\sc KEPLER}},{{\sc COROT}}, and {{\sc MOST}}. The calculations cover the following ranges oflocal gravity and effective temperatures:  2.5 $\leq$ log g $\leq$ 6.0 and 1500 K $\leq$ T$_{\rm eff}$  $\leq$ 12000 K. The new spherical coefficients can easily be adapted to themost commonly used light curve synthesis codes.

astronomy and astrophysics

A new method to compute limb-darkening coefficients for stellar  atmosphere models with spherical symmetry: the space missions TESS, Kepler,  Corot, and MOST