What I have seen from the few star trails I have done, is that the gaps are more evident further away from the centre of the "startrails circle", the centre being the celestial south pole (I think that's its name) in the southern hemisphere. I imagine that it is the same for the northen hemisphere
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To reduce the size of the gaps, take pictures of stars that are closer to the celestial pole. To have the same length (distance) of trail, you would need more exposures, that would however show more of a curve.
To reduce the number of gaps, one need to keep the shutter open for longer, instead of having 120 x 30 second exposures, rather have 10 x 6 minute exposures.
good reading :
http://www.fredmiranda.com/forum/topic/725769/0
qoutes from the page below, the effect/application of focal length:
http://www.brighthub.com …y/articles/42817.aspx?p=2
"•Wide shots having a foreground: These are usually the most spectacular looking images, as the star trails are in context to an appealing foreground. You can experiment depending on your surroundings (a lake, a monument, your tent, etc.) and choose a wide enough focal length to accommodate it. Try to get the Pole Star in frame, as all other stars would be rotating around this one."
"•Zoom in for an abstract effect: Zooming in and filling the frame with only the star trails gives an artistic effect"
a lot of patience required as we learn by trial and error 