Dan,
If we want to make a system to analyse something, you really need to stare at the screen all the time. I think it'd be great if we could somehow implement some features (some simpler than others):
1) decouple "time step" from visualization speed (I already suggested this in another post). Perhaps you could time-step 2min and visualize (render the system) every 10x steps, so that simulation is sped up without losing stability
2) Taken that to the extreme, you could run in "invisible mode", so that no images are rendered at all (but the rest of features are on, see below), one could toggle visibility on and off at any time
This is only useful if the CPU effort in rendering is significant with respect to calculating a step (which I guess is the case).
3) Ideally, one could "record" the whole system evolution. You run it (in visible or invisible mode), and it is "stored" somehow. Then you could watch it again at any speed, watching the same event from different points of view, etc. I don't know if the stored info would be manageable or not
This way, one could set-up a complex system, with many bodies and a short timestep, run it overnight, and analyse it the morning after.
4) It'd be great if there were an "event log" (perhaps there is) with info such as "object X has collided with object Y", with a timestamp (perhaps also positional information, velocity, etc)
5) I'd love to be able to plot some variables. E.g. to plot a chart of velocity of object X and Y, or distance between two objects, etc. Considering the dynamics, some beautiful curves could pop-up (à la Lissajous), especially of you could freely define x and y axes (such as acceleration vs velocity diagrams). If you could render 3-dimensional charts (play x,y,z in a grid-cube) I'm sure it could be pretty interesting. Of course, you should be able to plot several variables at once (different colors). Take into consideration that one could set-up a system, and plot the variables in invisible mode (without watching the system at all).
I think these sort of features would be useful if we are just curious about long-term stability of a system, etc and would greatly help less powerful computers. It could lead to a more "scientific" use. Also for teching purposes (for example, one could plot how total energy is constant in a system, plotting kinetic and potential energy, and alumni would see how one transforms into the other).
Additionally, regarding the "habitable zone" discussion (which I find pretty interesting), one potential feature could be to simulate bodies' temperature depending on the incoming radiation (light) from stars (I think you were already going to implement "light" as a feature) and the Stephan-Boltzman equation (you would need to input the albedo of the body). Of course, this wouldn't take into consideration greenhouse effect (perhaps there is some way), but it could be a nice first step. This variable (sort of "surface temperature") could also be tracked and plotted, etc.
I think most of us are intrigued at the possibility of habitable systems, and I guess it's a cool workstream to deepen on.
My two cents
In any case, congratulations for the program.
Regards
Osezno_