On my PC Processor (CPU): Intel(R) Core(TM) i5 CPU 750 @ 2.67GHz Speed: 1,197.00 MHz
Cores: 4 with graphic card ATI Radeon 4870

I'm running
OS: Linux 2.6.27.45-0.1-default x86_64 System: openSUSE 11.1 (x86_64)
KDE: 4.1.3 (KDE 4.1.3) "release 4.11.1"

and display system Mesa Project
Model: Software Rasterizer, Driver: 2.1 Mesa 7.2

but at star of Google Earth ver. 5.1 I receive message You are currently running Google Aarth in 'OpenGL' with software emulation and will run very slowly. And that is thrue.

What have I to do, what tests to make and how?

BR georg

You need to install the proprietary drivers for your video card.

http://en.opensuse.org/ATI_drivers

Either that, or you need to install updated versions of the open source drivers, if they are packaged for Opensuse at all.