In the late stages of stellar core-collapse , prior to core bounce , electron captures on medium-heavy nuclei drive deleptonization and simulations require the use of accurate reaction rates . Nuclei with neutron number near N = 50 , just above atomic number Z = 28 , play an important role , but rates used in astrophysical simulations rely primarily on a relatively simple single-state approximation . In order to improve the accuracy of astrophysical simulations , experimental data are needed to test the electron-capture rates and to guide the development of better theoretical models . This work presents the results of the ^ { 86 } Kr ( t , ^ { 3 } He+ \gamma ) experiment at the NSCL , from which an upper limit for the Gamow-Teller strength up to an excitation energy in ^ { 86 } Br of 5 MeV is extracted . The derived upper limit for the electron-capture rate on ^ { 86 } Kr indicates that the rate estimated through the single-state approximation is too high and that rates based on Gamow-Teller strengths estimated in shell-model and QRPA calculations are more accurate . The QRPA calculations tested in this manner were used for estimating the electron capture rates for 78 isotopes near N = 50 and above Z = 28 . The impact of using these new electron-capture rates in simulations of supernovae instead of the rates based on the single-state approximation is investigated , indicating a significant reduction in the deleptonization that affects multi-messenger signals , such as the emission of neutrinos and gravitational waves .