What is the best sky projection to use for my purposes?

[Simfish]

So basically I want to write some code in Python to project the movement of the moon and sun across the night sky. Basically, I need a projection such that the shape of the moon won't change as it moves in the sky (especially when it's near the horizon) - the objects have to look fairly good rather than ugly and distorted. My postdoc hypothesizes that a Lambert conformal projection (which preserves angles) would be the best projection to use. What are your thoughts?

She also suggested that I try out a variety of projections on planetarium software, although the planetarium software I've downloaded don't have a lot of projections to compare with (in particular, none of them have both a Lambert conformal and a stereographic projection). Is there planetarium software that allows you to experiment with a wide variety of projections? Would a stereographic projection work well (compared to a Lambert conformal projection?)

I think another key thing is this: what we're trying to plot should look more like a constellation map than like a view of the sky from a particular person's perspective.

 

[icez]

Most planetarium software that I know of only project the position of astronomical objects. The objects themselves are basically static images that are increased or decreased in size according to the zoom level.

Also, since you mention that the primary purpose of your script is to generate constellation maps, I don't believe that having or not having distorted stars would matter much.

Personally, I would go with stereographic projection, to conserve shapes near a point of interest.