How do you go about getting a 3-D picture of the big dipper?

You need to know not only the relative positions of the Big Dipper stars on the sky, but also their distances. The positions of the stars are given in coordinates called right ascension (RA) and declination (Dec). The RAs are usually given in units of hours, which relate to how the sky appears to rotate once a day in (approximately) 24 hours. The Decs tell how far the stars are north of the projection of the Earth's equator on the sky. These positions are fairly easy to measure, by just noting where the stars seems to be in the sky as we see them. The distances to the stars are much harder to measure. The Big Dipper stars are close enough to the Earth so that they seem to move around in the sky a little bit when they are viewed at different times of the year from the Earth as it moves in its orbit around the Sun. This small change in position during the year is called parallax by astronomers. The farther from the Sun, the less the stars move around. The best parallaxes come from a space satellite mission called HIPPARCOS. The HIPPARCOS results show that the Big Dipper stars are between about 80 and 120 light years from the Earth, with errors of a light year or two. With the direction and distance to each star in the Big Dipper, one can then make a 3-D plot of the stars' positions. The stars at either "end" of the Dipper (at the end of the "handle" and the outside "lip" of the bowl) are the farthest away from us. The other fice stars in the middle turn out to be at almost the same distance (80 light years) from us. So, one should envision the ends of the Dipper being the farthest away from us, while the stars in the middle form a nearly flat pattern as viewed from the Earth. Answered by David B. Shaffer, Ph.D. in astronomy, from Caltech.