The Fedora Core 9 Release Notes specify the absolute minimum system requirements.
x_86
The Fedora Core 9 specifications are written for Intel Processors but the equivalent processors from other manufacturers (AMD, Cyrix, and VIA) may be substituted with no problem.
Installation via text mode requires:
200 MHz Pentium-class processor or better
128 MB of RAM.
Installation via graphical mode requires:
400 MHz Pentium II processor or better.
Minimum RAM: 192MB.
Recommended RAM: 256MB.
x86_64
Installation via text mode requires:
128 MB of RAM
Installation via graphical mode requires:
Minimum RAM: 384MB.
Recommended RAM: 512MB.
PPC
Fedora Core 9 supports the "New World" generation of Apple Power Macintosh, shipped from circa 1999 onward (Older versions need a special boot loader); IBM RS/6000, pSeries, iSeries, and Cell Broadband Engine machines; Sony PlayStation 3; Genesi Pegasos II; Efika; and the P.A. Semiconductor 'Electra' machines. The minimum recommended CPU is the PowerPC G3 / POWER3.
Installation via text mode requires:
233 MHz G3 or better
128MB of RAM
Installation via graphical mode requires:
400 MHz G3 or better
256MB of RAM