Mounting a Camera/Telescope
Yes, you can do this at home!
The easiest way to determine the maximum exposure you can use without any star trails or blurring for your camera and lens is to use the following equation:
Exposure (t) seconds = Magic_Number * cosine(Declination) / Focal Length (mm)
The Declination of the object in the sky can be obtained from tables and charts. As the declination approaches 0 degrees the cosine approaches 1, and as the declination goes to 90 degrees at the poles the cosine value becomes 0. This equation is to be applied for celestial objects between those two extremes.
The Focal Length is the effective focal length of your optical system. Often times this is simply the number printed on the zoom lens.
The harder number to find is the "Magic_Number". The magic number is a factor that is found through experimentation and will vary for different cameras.
Using a fixed mount and your camera you can set up a basic test to learn what the maximum exposure time for any camera will be, shooting at any declination. You need a good clear night and some time to accumulate the data. I originally did this experiment using film (Kodak Tri-X) and can assure you it is much easier with a digital camera!
To save you the cost of processing some film the numbers I use are 1000 for very grainy film and 300 for pretty good film.
How to get the Magic_Number for your camera:
Use a standard lens, (50mm is recommended), find a place you take longer exposures of the stars near the celestial equator. The best (easiest) target is the belt of Orion. The northern most star of the belt almost lies on the celestial equator (declination is zero). Orion is not visible all year long, so you may need to consult a star atlas for other candidates. Sometimes the planets are in the right position making for another easy target.
On a clear night with the best possible conditions (fair temperature, low humidity, no winds) set up your tripod and camera facing Orion. Focus the camera as best you can manually. Automatic focus is not going work. Using a cable release (or remote control) take a series of pictures starting at 5 seconds and incrementing by another five seconds up to about 45 seconds. The result will be a set of images at 5, 10, 15, 20, 25, 30, 35, 40, and 45 seconds.
Take the images back to the computer and zoom in on each of them. The examples above show a series of photos taken with a 50mm lens and a Canon Digital Rebel. Each exposure was progressively longer and in exposure 3 you begin to see trails.
Now look at your own pictures. At what exposure do you start to see streaks or star trails? At what exposure do you see no movement at all?
I recommend that you repeat this experiment a few times to make sure your data is consistent.
Multiple the time exposure of the longest exposure that does not show any star trails by the focal length of the lens in use. For example, let's say that you notice no trail at an exposure of 10 seconds and do notice the start of one at 15 when using a 50mm lens. Multiple 10 by 50 for a factor of 500. If the movement shows up slightly at 10 seconds but not at all at 5 seconds then use the five value to achieve the starting factor. If you want to try for a more precise factor then repeat the experiment bracketing the two values and use a smaller increment.
The factor just found by experiment can be plugged into the equation above as the "Magic_Number".
