  We present a measurement of the lifetime of ground state atomic carbon,
C(^3P), against ionization processes in interplanetary space and compare it to
the lifetime expected from the dominant physical processes likely to occur in
this medium. Our measurement is based on analysis of a far ultraviolet (FUV)
image of comet C/2004 Q2 (Machholz) recorded by the Galaxy Evolution Explorer
(GALEX) on 2005 March 1. The bright CI 1561 A and 1657 A multiplets dominate
the GALEX FUV band. We used the image to create high S/N radial profiles that
extended beyond one million km from the comet nucleus. Our measurements yielded
a total carbon lifetime of 7.1 -- 9.6 x 10^5 s (scaled to 1 AU). Which compares
favorably to calculations assuming solar photoionization, solar wind proton
change exchange and solar wind electron impact ionization are the dominant
processes occurring in this medium and that comet Machholz was embedded in the
slow solar wind. The shape of the CI profiles inside 3x10^5 km suggests that
either the CO lifetime is shorter than previously thought and/or a
shorter-lived carbon-bearing parent molecule, such as CH_4 is providing the
majority of the carbon in this region of the coma of comet Machholz.
