Introduction

For thousands of years, people have been fascinated by the night sky. One aspect of the starry sky that catches many people's imagination is the sheer size of it, which provokes many age-old questions: How large is it, really? What place does Earth occupy in it? Could we ever visit those far-off worlds? Questions like these have fascinated both the lay person and the professional scientist for centuries.

Scientific Background

In light of this, a major scientific goal in astronomy is trying to determine exactly where all of those compelling celestial lights are. In fact, many major astronomical discoveries were directly or indirectly inspired by such determinations:

• 17th century: Galileo attempts to measure stellar parallaxes -- shifts in the positions of nearby stars as the Earth moves in its orbit -- to verify the Copernican heliocentric (Sun-centered) model. Such a measurement would have been strong evidence for the model, but it was beyond the capacity of his primitive telescopes.
• 1728: While searching for stellar parallaxes, James Bradley discovers the "aberration of starlight", an apparent shift in a star's position due to the finite speed of light and the motion of the Earth.
• 1838: Friedrich Bessel determines the first stellar parallax, for the nearby star 61 Cygni. In the next few decades parallaxes would be discovered for other stars, giving us the first indication of the scale of "nearby" stellar space, as well as true luminosities of stars other than the Sun.
• 1912: Henrietta Leavitt discovers the period-luminosity relationship for Cepheid variables, a type of star whose brightness varies periodically. Specifically, she determined that the more luminous a Cepheid variable is, the longer it takes to cycle through a brightness change. By using distances measured for nearby Cepheids (by other methods), the period-luminosity relationship can be expressed quantitatively, and the exact luminosity of a Cepheid given in terms of its period. Since the apparent brightness of any star, as seen from Earth, results from its true luminosity and its distance from Earth, you can determine the distance to any object in the universe, provided you can find Cepheid variables in it.
• 1924: Edwin Hubble finds Cepheid variables in the Andromeda Galaxy, thus determining its distance. The Galaxy turns out to be a gigantic collection of stars well outside our own galaxy (the Milky Way), rather than a group of stars and gas within the Milky Way.
• 1993: Using the recently-refurbished Hubble Space Telescope, astronomers identify Cepheid variables in galaxies more than 10 times farther out than the Andromeda Galaxy, thus firmly linking the Cepheid-based distance scale to the larger, but still poorly calibrated, distance scale based on red shift measurements. In effect, we now had a much more accurate way to determine distances to galaxies so far away that we can't see any details except for the galaxy's spectrum.
• 1997: Data from the Hipparcos satellite show that Cepheids are about 10% more luminous than previously believed, which affects all distances based on Cepheid variables by a corresponding amount. Our best estimates of distances to galaxies increased appreciably as a result of this one measurement.
• 1999: Astronomers using the Hubble Space Telescope complete an eight-year project to measure Cepheids in distant galaxies, as much as 50 times as far from Earth as the Andromeda Galaxy. Combined with the known period-luminosity relation for Cepheids, the distances to these galaxies were established to much higher accuracy than had been done before. Moreover, a comparison of the known Cepheid-based distances to the redshifts of the galaxies allowed astronomers to determine the Hubble constant, a measure of the rate of the Universe's expansion and hence ultimately its age, with an error of ~10%. By contrast, estimates of the Hubble constant varied by 50% or more just a few years previously, depending on how astronomers tried to measure it and how they analyzed their measurements.

In short, knowing where the stars are, and how far away they are, can tell you all sorts of things, ranging from the motion of the Earth to the scale of the entire universe.

Parallax -- the basic measure

The basic measurement for stellar distance data is parallax -- an apparent shift of nearby objects with respect to farther ones, as seen from a moving location. For stellar measurements, the moving object is the Earth, as it moves around the Sun every year. Unfortunately, since stars are so remote, the amount they appear to shift is miniscule (under 1 second of arc, or 1/3600 of a degree), which is why Galileo and his contemporaries failed to see anything.

Parallax Animation Demo

Here's a demo of what parallaxes might look like if the Earth's orbit were much larger (around 1.5 light-years in diameter). Although the motions are exaggerated, the relative amounts of motion are correct: i.e., stars close to the Earth move most, while very distant ones move least. The region portrayed contains a number of interesting objects, including the familiar constellation Orion (to the left), and the nearby stars Epsilon and Omicron² Eridani, among the closest stars to the Sun and widely used in science-fiction novels as potential human and alien outposts.

Click on the star map to load the animation (animated .GIF,
36K).

Ultimately, the various cosmic distance scales out there -- Cepheid variables, spectroscopic methods, red-shift methods for distant galaxies, etc. -- need to be calibrated by other means. A directly-measured parallax with high accuracy is one of the "gold standards" in the astronomical distance measurement game. As a result, a great deal of work has been done to obtain more and better parallax data for more stars.

Hipparcos

For decades, the only way to measure parallaxes was to sit at a telescope (or photographic plates or CCD images), painstakingly measure a whole bunch of star images, and determine the shifts over the course of an Earth orbit. Because of the blurring effects of the Earth's atmosphere, it is difficult to measure these positions more accurately than about 0.01 arcsecond, regardless of the quality of the telescope. With good data (lots of it), and good technique (including multiple lengthy measurements of the same star), this can be pushed down to about 0.002 or 0.003 arcsecond. These lower values are commonplace only for stars that have been extensively studied (e.g., those already known to be very close to the Sun). Ground based parallaxes thus have an accuracy of about 3-10% when the parallax is 0.1 second, which corresponds to about 33 light years.

In other words, for stars like this, uncertainties of 1 to 3 light years in the distance are very typical -- a significant fraction of the distance between the Earth and its closest stellar neighbors. Yet 33 light years is actually a fairly small distance -- only the nearest stars, about 50 out of the several thousand visible to the unaided eye, are this close. At distances over a couple of hundred light years -- which is where an awful lot of interesting stars live -- the uncertainties on ground-based distance data approach or exceed the magnitude of the distance itself. As a result, ground-based parallax measurements don't provide useful information for stars farther out than a couple hundred light years at most, and even for nearby stars often have a surprisingly large error.

In the 1990s, space-based observations changed that. The French satellite Hipparcos obtained detailed positional measurements for almost 120,000 stars, above the blurry atmosphere of Earth. Hipparcos has generally been able to obtain parallaxes with an uncertainty of less than 0.001 second, as against the 0.003 - 0.01 second from typical ground-based measurements. As a result, we now have distance information that's generally three- to tenfold better quality than we had just a few years ago, with literally thousands of stars' positions known to within a fraction of a light-year.

3D Universe and Hipparcos

3D Universe takes the Hipparcos data and presents them in an accessible manner. Although many 3D star maps exist out there, most are either (a) non-stereo renditions (i.e., simple 2D maps with no depth information), or (b) based on pre-Hipparcos data. By contrast, 3D Universe takes you through the new Hipparcos data, showing you directly what the space near Earth -- and, in many cases, hundreds of light-years away from Earth -- looks like. 3D Universe shows how some groups of stars cluster together, representing true groups of stars rather than chance arrangements. It illustrates what star like the Sun look like at various distances, showing how the Sun compares to other stars in the galaxy. Finally, if nothing else, 3D Universe lets you get an extra sense of the scope of the Universe, one you can't get just by looking at the night sky or a flat map of it.