The night sky consists of thousands of stars that have traditionally been grouped into constellations. The twelve constellations that lie along the Sun's apparent path on the sky (the so-called Ecliptic) are the familiar ones from the horoscope page in your local newspaper. Here we examine the constellation of Taurus shown in figure 1. The head of the bull consists of the bright stars in the "V"-shape in the lower right part of the image. The bright blue star on the left and another brightish blue star in the lower left corner form the horns.

Figure 1. © Sven Kohle and Till Credner, AlltheSky.com

There are many different stars in this image, varying in both colour and brightness. The brightness variations are caused not only by intrinsic differences in the luminosity of the stars but also because they are located at different distances from Earth. We only see a projection on the sky of the way the stars are really distributed in space. Thus the stars we group together in the constellation Taurus may not be located together in space if we were to make a 3D map of the sky.

Thanks to distance measurements done by the Hipparcos satellite we now know the distances to more than 100,000 stars in the vicinity of the Sun and we can make accurate 3D maps of the locations of the stars. This is shown in an animation that I made of the Taurus constellation.

The Taurus constellation as it appears on the sky is shown again in figure 2a below (including an artificial background). To show the three dimensional structure of the Taurus constellation figure 2b shows the stars in a perspective projection as seen from the Sun. Each star is represented by a sphere of the same size, so nearby stars look like large spheres and distant ones as small spheres (click on the images for a larger version).

Figure 2a

Figure 2b

The animation starts with the image of Taurus as it appears on the sky and then slowly the spheres come into view, showing the 3^rd dimension. Subsequently the constellation is rotated a little bit about the screen's X and Y axes in order to bring out the 3D effect more clearly.

After that the actual motions of the constellation's stars through space are shown. These motions have been measured using a combination of measurements from the Hipparcos satellite (providing the motion of the stars across the sky, i.e., the proper motion) and measurements made from the ground (providing the motion in the line of sight, i.e., the radial velocity). This shows even better than the 3D map that most of the constellation's stars do not belong together and have nothing to do with each other (they fly off in different directions). However there is a group of stars in the centre of the constellation that stay together as they move away. These stars are part of the so-called Hyades cluster. Note that in the sky picture of Taurus it is impossible to pick out a cluster in the bull's head (in contrast the bluish group of stars in the centre right of the image is easily picked out by eye and that's the Pleiades cluster). We really need to know the motions of the stars to identify the cluster! In the second animation (figure 3) the stars from the Taurus constellation which are not members of the Hyades cluster are removed and then the other Hyades cluster stars (from the Hipparcos catalogue) are added. The Hyades stars are then shown rotating around the screen's Y-axis.

Figure 3

The animations, can be downloaded using the links below.

The images in the animation were made using the POV-Ray ray-tracing engine and were turned into animations using Klaus Ehrenfried's PPM2FLI programme. More information on how the animation was made can be found here.

These animations dramatically show the power of making accurate measurements of the positions of stars on the sky, which is what the astronomical discipline of astrometry is concerned with. These accurate position measurements can be used to derive both the distances to the stars and their motions across the sky. The positions measurements are derived from measuring angles between stars all over the sky and the Hipparcos satellite measured these to a precision of 1 thousandth of an arcsecond (one degree is sixty arcminutes and 1 arcminute is sixty arcseconds), which is about 5 billionths of a degree. To put this number into perspective, consider that the full moon spans half a degree on the sky (which is 1 billion milli-arcseconds) and that an angle `as large as' 1 arcsecond corresponds to the apparent size of a Euro coin at a distance of about 4.5 kilometers! For the Taurus stars this accuracy corresponds to knowing their distances with a relative error of a few per cent. For more information on space-astrometry visit the Hipparcos and Gaia web-pages. Gaia is an ESA cornerstone mission which was launched in December 2013 and it is the successor to Hipparcos. It will measure astrometry for over 1 billion stars throughout our Galaxy reaching accuracies of 10 micro-arcseconds. On the pages of the Gaia mission look for the `information sheets' which contain tons of interesting information.

For those interested in more technical information: the distance, structure, dynamics and age of the Hyades cluster were studied with Hipparcos data by Perryman and collaborators (Astronomy & Astrophysics, 331, pages 81-120).