I have been trying to texture a domesky with a starfield for an animated space scene but the texture looks stretched and distorted when applied to the dome. the texture works as a simple background but not on the dome. what am I doing wrong?

Are you using a tileable texture and set the repeats to number that works?

This is one of the problems of trying to fit a flat, square image onto a round object.

If you're not familiar with projection mapping, consider a cross section of your sky dome and decal...
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The vertical line to the right is a cross section of your decal image, and the two lumps represent stars. Project the top and bottom of each star horizontally onto the sky dome, and you can see how the star nearer the pole takes up more space on the dome surface than the star nearer the equator. I reckon this is the distortion you're seeing. (That was only a partial explanation, but enough to get you going.)

If you have Photoshop you can distort your decal image such that the projection distortions you are getting will not show up. For an example of how to do this, see Vern's Spherical Mapping Tutorial (click the links to the left of the image on that page to see the before/after images).

Alternatively, you could decal your sky dome as if it was a cube, using several decals (e.g. front, back, left, right, top). You'll still get distortions, but they won't be as apparent. See Yves' Mapping A Starry Sky Tutorial for an example of this.

Honestly, the best thing for a starfield is Julian's awesome Starsphere. You can find it here.

Just download it, and open it up. It is way easier to use than trying to set up a mapped object. It also renders much faster and looks great with motion blur.