Either “su” and leave off the sudo or make sure you’re user account is a sudo’er
sudo chcon -t textrel_shlib_t '/opt/google-earth/librender.so'
sudo chcon -t textrel_shlib_t '/opt/google-earth/libauth.so'
sudo chcon -t textrel_shlib_t '/opt/google-earth/libminizip.so'
sudo chcon -t textrel_shlib_t '/opt/google-earth/libevll.so'
sudo chcon -t textrel_shlib_t '/opt/google-earth/libmeasure.so'
sudo chcon -t textrel_shlib_t '/opt/google-earth/liblayer.so'
sudo chcon -t textrel_shlib_t '/opt/google-earth/libflightsim.so'
sudo chcon -t textrel_shlib_t '/opt/google-earth/libnavigate.so'
sudo chcon -t textrel_shlib_t '/opt/google-earth/libgooglesearch.so'
sudo chcon -t textrel_shlib_t '/opt/google-earth/libinput_plugin.so'
sudo chcon -t textrel_shlib_t '/opt/google-earth/libgps.so'
sudo chcon -t textrel_shlib_t '/opt/google-earth/libbasicingest.so'
sudo chcon -t textrel_shlib_t '/opt/google-earth/libminizip.so'
sudo chcon -t textrel_shlib_t '/opt/google-earth/libmoduleframework.so'
sudo chcon -t textrel_shlib_t '/opt/google-earth/libgoogleearth_lib.so'
sudo chcon -t textrel_shlib_t '/opt/google-earth/libcollada.so'
Keep and eye on SELinux after to make sure any others haven’t been added.
Download the required 32 bit packages (to let you run it on a 64 bit system) use:
http://bigjim-network.be/2009/06/24/google-earth-on-fedora-11-64-bit/