  We report the mass measurement of $^{56}$Cu, using the LEBIT 9.4T Penning
trap mass spectrometer at the National Superconducting Cyclotron Laboratory at
Michigan State University. The mass of $^{56}$Cu is critical for constraining
the reaction rates of the
$^{55}$Ni(p,$\gamma$)$^{56}$Cu(p,$\gamma$)$^{57}$Zn($\beta^+$)$^{57}$Cu bypass
around the $^{56}$Ni waiting point. Previous recommended mass excess values
have disagreed by several hundred keV. Our new value, ME=$-38 626.7(6.4)$ keV,
is a factor of 30 more precise than the suggested value from the 2012 atomic
mass evaluation [Chin. Phys. C {\bf{36}}, 1603 (2012)], and more than a factor
of 12 more precise than values calculated using local mass extrapolations,
while agreeing with the newest 2016 atomic mass evaluation value [Chin. Phys. C
{\bf{41}}, 030003 (2017)]. The new experimental average was used to calculate
the astrophysical $^{55}$Ni(p,$\gamma$) and $^{57}$Zn($\gamma$,p) reaction
rates and perform reaction network calculations of the rp-process. These show
that the rp-process flow redirects around the $^{56}$Ni waiting point through
the $^{55}$Ni(p,$\gamma$) route, allowing it to proceed to higher masses more
quickly and resulting in a reduction in ashes around this waiting point and an
enhancement to higher-mass ashes.
