Star Trails

Imagine we pointed a camera at the night sky towards north. Normally the iris (the hole which the light passes through to get on the film) is open for a very short time, perhaps a tenth of a second. What if we fixed it so that the iris was open for several hours? What would we see when the film was developed?

These curves are called star trails. Normally we do not see the stars moving (as the Earth rotates) as it happens too slowly. We know they do move because their position changes with time. These pictures clearly show us that the Earth rotates. Notice that the North star, Polaris, leaves a small trail itself showing that it isn't exactly North.

Here is a picture of star trails taken with a camera on a very long exposure setting. (about 30 mins)

pic D. Drumm

We can use this image to calculate how long it takes the Earth to rotate, i.e. the length of a sidereal day. Remember that this is 4 minutes shorter than an average solar day.

Basically, if it takes time T for the Earth to rotate 360⁰ and it takes time t for it to rotate θ degrees then, because the angular velocity (the number of degrees swept out per minute) is constant then;

We need to know the time over which the exposure was taken and we need to measure the angle that a trail (pick a big one) makes with the celestial pole. Then we can bung these numbers into the equation above and get a value for T.

I suggest you do all the time measurements in minutes for simplicity.

Example

The angle on the diagram above = 7.5 ⁰. The exposure time was 30 minutes.

So T = (360/7.5) x 30 = 1440 minutes.  (The actual time is 1436 minutes, or 23 hours and 56 minutes. Why is our answer slightly different?)

Astrophotography

It is possible to get good pictures of objects in the night sky under certain conditions:

• a good clear night

• a fast film - 400 or 800 ASA

• an exposure time of 1 minute - any more would leave a star trail

If we want to take a picture of a very faint star then we can use a very long exposure. This time, however, we do not want the image of the star to move and leave a trail.

One solution is to use a telescope with a motorised mount that corrects for the Earth's rotation, following the star through the sky.

Another is to use an autoguider. If you were to use an eyepiece with crosshairs one could centre these on the star in question then manually move the telescope over a period of time to keep it centred in the crosshairs. This is a very tedious process. An auto-guider does this automatically. The image falls on a CCD (the light sensitive part of a digital camera) and a computer controls the telescopes motors so that the star is followed automatically.

pic  www.Meade.com		pic NASA   Credit: Jimmy Westlake
A popular digital imager with auto-guider software for a computer.	Crosshairs on an eyepiece.	What do you think the straight lines are?