Hamsphere 2 does run under Linux as did Hamsphere 1. Save the java file to your desktop and just double click on it or right click and run with Java Runtime (provided you have it installed). Only problem I have come across is that the frequency readout font is too large and overlaps VFO 2 info a bit.
Also you can't run another program which requires audio like Fldigi because there seems to be a limitation with ALSA audio and it only permits one program to access it at a time (unless somebody has a solution).
I use ubuntu Linux wich installs pulseaudio server by default. It is a program wich acts as a mixer and is very useful if you have a sound card with a stupid driver which does not support multiple programs playing audio at the same time.
Hamsphere is a java program using java's sampled audio classes. One can setup the default sound device by editing the "sound.properties" file under the library "/etc/java*" (java-6-openjdk or java-6-sun on my machine).
# OpenJDK on Ubuntu is configured to use PulseAudio by default
# PulseAudio not running? Please give feedback on LP: #407299.