Star Trails

13.19 - Be able to use star trail photographs to determine the length of the sidereal day

You can see evidence of the apparent motion of stars by photographing them over a long time using a long exposure. Not all cameras will let you do this so see if you can borrow an advanced one from someone.

If you photograph a star, any star over a period of time you will find the photograph will be of a bright trail. This is because the Earth is rotating and the camera sees the star moving. If you look at the position of a star in the sky at 8pm and then look again at 10pm you will find it has moved. If you take a long exposure photo of stars but aim at or near the pole star you will find several circles of light surrounding it. Not only is this attractive and you have created art but it also shows the motion of stars around the North Pole. Polaris will not have moved very much compared to other stars if you have done it correctly.

Star Trail Calculations

By looking at how much a prominent star in a star trail photograph has moved we can work out the exposure time of the image.

How far the star rotates is really saying how far the Earth has moved and so how long the picture was taken for.

Here is another way of saying this:

Angle of arc
Time exposure
24 hours

Measure the angle between each tip of the trail, using Polaris as the centre guide. You might notice that Polaris is a little blurry. That is because it is just less than a degree away from the true northern rotation point.

In the example on the right the first star has moved 90°. In a day it would move 360°. You can't get a star trail of that length unless you go near the poles in winter.

So 360° = 24 hours
90° is a 1/4 of 360 so 1/4 of 24 is 6 hours.




Question 1

The angle measurement between the trail tips and Polaris is 45°. How many hours was the image exposed for?

360 divide 45 is 8.
24 (hours) divide 8 = 3.


Question 2

The angle measurement between the trail tips and Polaris is 145°. How many hours was the image exposed for?

Angle is approx 145°.
360 divide 145 is approximately 2.5.
24 divide 2.5 is 9.6 hours.


Question 3

If you were told an image was exposed for 1 hour what angle might you expect a prominent star to have moved?

24 divide 1 is 24.
360 divide 24 is 15 °.