In an attempt to use Cepheid variables to determine the distance to the Centaurus cluster , we have obtained images of NGC 4603 with the Hubble Space Telescope for 9 epochs ( totalling 24 orbits ) over 14 months in the F555W filter and 2 epochs ( totalling 6 orbits ) in the F814W filter . This galaxy has been suggested to lie within the “ Cen30 ” portion of the Centaurus cluster , which is concentrated around a heliocentric redshift of \approx 3000 { km s ^ { \scriptscriptstyle - 1 } } , and is the most distant object for which this method has been attempted . Previous distance estimates for Cen30 have varied significantly and some have presented disagreements with the peculiar velocity predicted on the basis of full-sky redshift surveys of galaxies , motivating our investigation . Using our WFPC2 observations , we have found 61 candidate Cepheid variable stars with well-determined oscillation periods and mean magnitudes ; however , a significant fraction of these candidates are likely to be nonvariable stars whose magnitude measurement errors happen to fit a Cepheid light curve of significant amplitude for some choice of period and phase . Through a maximum likelihood technique , we determine that we have observed 43 \pm 7 real Cepheids ( with zero excluded at > 9 \sigma ) and that NGC 4603 has a distance modulus of 32.61 _ { -0.10 } ^ { +0.11 } ( random , 1 \sigma ) ^ { +0.24 } _ { -0.25 } ( systematic , adding in quadrature ) , corresponding to a distance of 33.3 ^ { +1.7 } _ { -1.5 } ( random , 1 \sigma ) ^ { +3.8 } _ { -3.7 } ( systematic ) Mpc . This result is consistent with a number of recent estimates of the distance to NGC 4603 or Cen30 and implies a small peculiar velocity consistent with predictions from the IRAS 1.2 Jy redshift survey if the galaxy lies in the foreground of the cluster .