First, thank-you all for your suggestions, they've been most helpful.  In fact,
I've used almost all of them in one way or another.

It's becoming obvious, however, that I'm going to need the big guns for this
project, as my last render took... 16 hours..?  My tiny little core duo tablet
just isn't up to the task of giving me timely results on test renders, even
without radiosity.

I adapted the method Thomas suggested, using the following settings:

media {
     intervals 10
     scattering {
          5, <0.05, 0.17, 0.3>*0.05
          extinction 1.0
          eccentricity -0.23
          }
     samples 50
     absorption rgb <0.95, 0.55, 0.3>*0.05
     density {
          function {exp( -(sqrt(x*x+y*y+z*z)-63870)/4 )}
          density_map {
               [0 rgb 0.0]
               [1 rgb 0.1]
               }
          }
     }

Radiosity (The good settings):

radiosity {
     pretrace_start 0.01
     pretrace_end   0.005
     count 600

     nearest_count 12
     error_bound 0.1
     recursion_limit 3
     low_error_factor 0.2
     gray_threshold 0.2
     minimum_reuse 0.015
     brightness 0.58

     adc_bailout 0.01/2
     }

I know that 1 interval is supposed to be sufficient, and it may have to do with
my scale, but with only 1 interval I get a ring-effect in the media radiating
outward from the point of greatest light intensity.

The absorption was added because the original media gave the planet a reddish
cast.

These settings seem to work fairly well, except that the atmosphere is a too
dense.

The big guns:

Asus M4A79T Deluxe motherboard
AMD 3.0Ghz Hexacore processor
8Gb ram
1 TB Western Digital Caviar Black HD
Radeon HD 5870 graphics card

Regards,
A.D.B.

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