  The planetary system around the naked-eye star $\nu^2$ Lupi (HD 136352;
TOI-2011) is composed of three exoplanets with masses of 4.7, 11.2, and 8.6
Earth masses. The TESS and CHEOPS missions revealed that all three planets are
transiting and have radii straddling the radius gap separating volatile-rich
and volatile-poor super-earths. Only a partial transit of planet d had been
covered so we re-observed an inferior conjunction of the long-period 8.6
Earth-mass exoplanet $\nu^2$ Lup d with the CHEOPS space telescope. We
confirmed its transiting nature by covering its whole 9.1 h transit for the
first time. We refined the planet transit ephemeris to P = 107.1361
(+0.0019/-0.0022) days and Tc = 2,459,009.7759 (+0.0101/-0.0096) BJD_TDB,
improving by ~40 times on the previously reported transit timing uncertainty.
This refined ephemeris will enable further follow-up of this outstanding
long-period transiting planet to search for atmospheric signatures or explore
the planet's Hill sphere in search for an exomoon. In fact, the CHEOPS
observations also cover the transit of a large fraction of the planet's Hill
sphere, which is as large as the Earth's, opening the tantalising possibility
of catching transiting exomoons. We conducted a search for exomoon signals in
this single-epoch light curve but found no conclusive photometric signature of
additional transiting bodies larger than Mars. Yet, only a sustained follow-up
of $\nu^2$ Lup d transits will warrant a comprehensive search for a moon around
this outstanding exoplanet.
