A few clarifying comments to the above thread:
The key reason for space based virtualization is timeliness - right now storing and dumping raw data results in yesterday's data tomorrow. Using the VM allows for the ability to move some of the ground processing software up to the vehicle, to either preprocess radar data or at the very least determining which images are just of clouds and not worth wasting the bandwidth to downlink.
Radiation is an issue, but you need to think of the VM as a "mission coprocessor" like an old math coprocessor. The VM is not running the satellite (spinning wheels, firing thrusters, orienting the vehicle, health & status, GPS, etc.), it is just (pre)processing payload data. The VM hardware will be shielded (either aluminum as stated above or high z materials) and as with virtualization can be restarted from a previous checkpointed/saved state after a fault.
As the mission progresses new code can be loaded to the VM to further exploit the data, without worrying about interfering with the flight control software or hardware.
Extending this concept across the constellation would allow for enabling "virtual persistence" of a target region, with each satellite handing off its current VM state or subset of data to the next satellite about to rise over the area. Also allows for satellites to become multi-use vehicles, either over an orbit or throughout their lifetime.
With respect to overflight time, 10-15 minutes is what a LEO vehicle has to a groundsite - been that way since Sputnik - its just physics. All contacts between the ground and the vehicle are worked out like a TV schedule, with the vehicle turning on a few seconds before the overflight so the ground can lock up on the signal. The real issue is the frequency - at UHF you can be 30 degrees wrong and still find the signal, at S-band its about 5 deg and Ka 0.1 deg. TLEs were made to point S-band antennas - higher frequencies like X and Ka require the owner operator to perform their own precision orbit determination to guarantee the link closes and every second of a pass is used.