I've been reminded of a useful resource that we have on this website for any budding astrophotographer. Malcolm put together a spreadsheet for use in our first "Introduction to Astrophotography" workshop in February last year which shows the maximum exposure time to prevent star trailing using an undriven tripod mounted digital camera.
A direct link to the document is here.
Obviously, if you want to see star trails, simply expose for longer than these exposure times!
The exposure time is dependent on the focal length of your lens. The "general" guideline for preventing star trails is that you should exposure for a period, in seconds, less than 600 divided by the focal length of your lens. So, for example, using a 50mm lens, you should expose for less than 600 / 50 = 12 seconds to avoid star trailing.
However, this exposure time is also dependent on the declination of the area of sky you are imaging. Objects close to a declination +90 degrees (i.e. close to Polaris) will not be rotating as quickly as those at a declination of zero degrees (for example, the belt of Orion). The spreadsheet is useful, as it takes these differences into account.
Hi
While a useful guide, it should be remembered that imaging is subject to trial and error. It is certainly more art than science. I use maths to given me a ball park for imaging settings but after that its playing about. The figures quoted on the excel sheet should be considered a starting point rather than an absolute. A 50mm lens designed for a 35mm / FX sensor will act like a 75mm on an APS sensor camera. Although the magnification is not increased, when viewed or printed at 'normal' size the image will be magnified and star trailing will be evident if the exposure is too long. In fact star trailing is always evident, it is only the degree of magnification used to view it that makes it visible or not.
Personally I use the playback and zoom function of the camera to assess images for star trail to see if I can get away with a certain exposure.