Earth is on the move. We rotate at over 1000 mph and move around the Sun at a speed of around 25000 mph. It may seem so slow to see the day and night pass over the hours, but were really moving fast.
When we photograph the night sky we have to get all of the light we can as the stars will trail if we allow the exposure to be too long. There are some "rules" for shooting the night sky that you can follow to help you reduce the number of errors photographing the night sky.
Today's digital cameras can accomplish a lot when capturing light. Taking star trails is nothing new. It's been done on film camera for years. The advantage we have now is we have post processing software that can help us maximize the effect. Better still we have software specific to the task of taking star trails and some good programs are free like Startrails (http://www.startrails.de/html/software.html). I like free and it’s easier than stacking all those photos in Photoshop.
To shoot star trails you should use an intervalometer. This device will automatically expose for the time you set it for and reset the shutter for the next shot. Since you will need at least 100 shots to get a decent star trail its a lot better than triggering your camera every 15 seconds or so.
The best "Rule" for full frame cameras is the Rule of 500. This means if you use a 24mm lens you can expose for almost 21 seconds. Hence 500/24=20.8333. If you use a camera with a crop sensor your formula will be a little different. A Canon 60D for example we need to divide the result in seconds by 1.6 taking into account the crop factor of a Canon 60D and other similar cameras. So when shooting with Canon with a crop sensor a 24mm would work out to be 500/24=20.833 then taking that answer and dividing it by 1.6 which then equals 13 seconds. Nikon has a slightly larger crop sensor and the factor is about 1.5. So a 24mm can expose to almost 14 seconds.
What you will find in practice is that if you push the exposure time to the theoretical limit of your exposure your stars will come out oblong. The larger your print, the more apparent the the oblong stars become when you print your photos especially if the photo is 12x18 or larger.
Of course you can break out your old slide rules (pre-computer age sticks with lots of math on them) and calculate:
The Earth's rotation is 0.0042 arc degrees per second or 1 degree rotation per 238 seconds. 238 / Pixels per Degree = Rule
FOV = 2arctan((horizontal dimension of sensor x crop factor)/(2 x ( focal length x crop factor )) Yeah, that's what I thought. Trig was not my thing in high school.
I shoot using both the Canon 6D and a modified Canon 60D with the cut-off filter removed. I shoot with a 24mm at f/2.0 to f/4 as my main lens on my Canon 6D. I use a 10-22mm at f3.5 for my Canon 60D crop sensor camera. For the full frame camera I expose up to 15 seconds because my prints may be 16x20 or larger. I can push the ISO up as high as 6400 on the Canon 6D before the noise becomes really apparent. It depends on how hot it is outside at night. When you live in the Mojave desert it can still be over 100 degrees at midnight in the summer. If the camera is already hot the noise will be overwhelming. On the Canon 60D it can be as low as 15 seconds or as high as 30 seconds depending how wide I am shooting. Typically that is around 10-14mm on the Canon 60D.
Keep in mind as the software stacks all of these photos the apparent brightness will increase in the landscape so stack using an average so you don't blow out the results. You can also end up with too many trailing stars, satellites, sky glow from light pollution and high flying aircraft. Take a little time and practice and try different f/stops for your star trails.
Finally you need to find the North Star - Polaris. Locate the Big Dipper otherwise know as Ursa Major (Big Bear). the two pointer stars in the dipper will point you to the Ursa Minor (little Bear) and the Polaris. Instructions are here - http://www.wikihow.com/Find-the-North-Star.
If you live in the Southern Hemisphere (O' how I envy you) find the Southern Cross and head down from there to the constellation of Octans. There is no particular star to center on but if you are shooting wide angle you'll find it in your photos.
When you shoot star trails the stars that are closer to the poles will seem to move less than stars along the celestial Equator. You have to think as if you are inside a big globe. If you know where the pole is then go South 90 degrees that is the Equator. Nearly all of your Zodiac constellations travel along this line. Stars will trail much faster along this line due to its apparent motion. Even if your are doing star trails you don't want your individual shots turning out oblong stars. Occasionally you will get a bright meteor or an Iridium Flash which can be spectacular as your stars will be pin points. Those types of shots can be money and they are desirable with clients.
Free Startrail software can be found here - http://www.startrails.de/html/software.html
Let me know how your shots turn out.