Startrail photographs are long exposure photographs which show the apparent movement of stars through the sky in a circular motion.
These photographs can be taken to measure the rotation of the earth (or length of the sidereal day) or simply because they produce a very interesting and artistic image.

To take Startrail Photos you will need:

A DSLR Camera
A sturdy Tripod
A Shutter Remote or Intervalometer
A clear sky
Time
A computer to enhance the images (optional)

There are two methods that you can use to create Startrail Photographs and I will cover both in this instructable.

Step 1: Method One - Continuous Long Exposure

This method is the most simple of the two but has the downside of resulting in an image that can be effected by noise and visible light pollution.

To take Startrail Photographs with one continuous exposure is very simple:

Set your camera up on a tripod pointing at the sky.
Focus your camera to Infinity (the furthest distance possible that the lens can focus on).
Set your cameras exposure to 'Bulb'. This means the sensor will continue to record light for as long as the shutter button is held down.
Usea shutter remote with a lockable shutter button to take an exposure (Or if you do not have access to this you could simply use duct tape to hold down the shutter release button; if you are going to do this be very careful, when applying the tape, to avoid moving the camera because even the slightest movement could ruin the whole exposure.) .
After the camera has been exposed for as long as you would like (I would recommend 30 minutes as the minimum time the camera has to be exposed in order to capture any noticeable trails.) release the shutter button and the camera will save the picture to your memory card.
The end.

For this method I would recommend using a relatively low ISO to try and minimise noise. The aperture is yours to experiment with as different apertures will produce different effects on the image.

Step 2: Method Two - Multiple Images Blended Together

This method is not as simple as the first however I believe it produces significantly better images which do not have the same problems of noise and light pollution.

For this method you will need an intervalometer ( I use the Neewer RM-VPR1 which costs £15, however some camereas have built in intervalometers).

Set up your Camera, with its aperture open wide, pointed up at the stars.The open aperture will make the stars much brighter but because of the nature of this method it will not result in as much light pollution as the first method.
Set your shutter speed to the longest length possible (on my camera this is 30 seconds) and your ISO relatively low (I tend to use ISO 200).
Plug the Intervalometer into your DSLR and set it to take a photo every 30 seconds; this is the same as taking pictures constantly because each exposure is 30 seconds long.
Leave the camera to take pictures for the length of time you wish to capture startrails for (as before I recommend 30 minutes as the minimum).
After you have left your camera taking pictures for the desired length of time you can stop the intervalometer. You will notice when you look at the images that they do not look like startrail images but instead look like static photos of the stars. However if you cycle through the pictures on your camera quickly you will see a time-lapse of the stars moving across the sky.
Although this time-lapse is fun to watch on your camera it is not the startrail image you wanted to take so you must import your photos onto a computer and save them all in one folder.
Download an application called Startrails which is available for Windows. When you open the application it will show a blank interface but that is what it is supposed to look like.
Head to the top of the application and click 'Open images' this will then prompt you to select the folder where you saved your images. Once you import the images you need to press the button labeled 'Startrails' and you will be presented with some options, one of the options is for blendmode i reccomend using 'Lighten-Screen-Blend' because this produces a significantly better final product.
Export your startrail photograph from the program (an additional feature the program offers is to export the startrail as a time-lapse video).

Step 3: Extras - Light Painting and Sidereal Day Calculations

As I mentioned at the start of this instructable startrails are not only for creating stunning visual photographs but they can also be used to the length of the sidereal day; if you would like more information on how to measure the sidereal day (time taken by the earth to rotate exactly 360 degrees.) click here for an article explaining the calculations required.

Taking startrail photographs can be a time consuming process so why not use up some of that time by adding some light-art to your startrail masterpiece.
Light painting is done by moving a light source (torch/flashlight) around during a long exposure photograph and can create some very interesting effects (I used light painting to draw a stick-man looking up at the night sky with a telescope on the startrail photograph above.)
Please be careful if you decide to use light painting and you are using the first method of startrail photography because if you mess up your light painting you will ruin your whole exposure whereas if you are using the second method you can always delete the one exposure with the light painting and it will not have a significant effect on the final product.