INTRODUCTION

Various measurement techniques have since been used, both through direct observation of the galactic center, and through observation of objects moving around the center. What are these techniques, and what have been the results?

More than a century later, the Dutch astronomer Jacobus Cornelius Kapteyn used the same counting technique (this time by means of photographic plates) in what became a decade-long collaborative effort involving over 40 observatories worldwide. In 1922 he published his magnum opus, First Attempt at a Theory of the Arrangement and Motion of the Sidereal System in which he placed the Sun very close to the center of the Galaxy, giving a value of R₀ of about 2,000 light-years.

Meanwhile, in 1912, American astronomer Henrietta Swan Leavitt discovered the period-luminosity relationship of cepheid variable stars, which states that the longer the period of pulsation, the more luminous the star. This relationship was then used by the American astronomer Harlow Shapley to find the distance—and spatial distribution with respect to the galactic system—to every one of the 93 globular clusters known at the time.

A globular cluster is group of stars that formed out of the same molecular cloud, and which remains bound together by the mutual gravitational attraction of its components. Globulars contain an average of 100,000 to 1 million stars [Darling], usually arranged in a spherical or slightly elliptical pattern. They are almost always found outside of the galactic disk, orbiting the galactic center from within the halo at high inclinations—which was precisely what Shapley found.

By locating the center of distribution of globulars, Shapley was able to conclude—in 1918—that the galactic center was located not in our own region, but in the direction of the constellation Sagittarius, at a distance of about 50,000 light-years (a value of R₀ which is almost double the modern value). He was the first to ascertain—more or less correctly—our true place in the Milky Way.

Later, in 1927, Dutch astronomer Jan Hendrik Oort—aided by Kapteyn's proper motion data and Swedish astronomer Bertil Lindblad's mathematical models—established that our Galaxy is a rotating system, and that its center lies about 20,000 light-years away, also in the direction of Sagittarius.

Distribution of globular clusters—
This method—the same used by Shapley in 1918—has remained a classic technique to obtain a value for R₀. Studies made in the 1970s and 1980s by various teams (Vaucouleurs & Buta, Racine & Harris, etc.) using corrections for interstellar absorption—which was unknown to Hubble, and was indeed the reason for his overestimation—have obtained values for R₀ ranging from 22,800 to 24,500 light years, much closer to the actual value than that originally derived by Shapley.

Red Giants and Mira-type variable stars—
Red giants and Mira-type variables abound in the inner bulge of the Galaxy, so—as long as we could determine their luminosity—they may be used as "interstellar yardsticks" to the center of our Milky Way. Mira variables actually show in the infrared a clear period-luminosity relationship, but this has not been very well calibrated, which somewhat limits the usefulness of the technique. A study based on a large sample of giant "red clump" stars was made in 1997 by Bohdan Paczynski and Krzysztof Z. Stanek, giving a value for R₀ of 27,400 ± 1,300 light years [Paczynski, Stanek, 1997].

RR Lyrae-type variable stars—
These are standard "interstellar yardsticks", with a fixed absolute magnitude of +0.6, that have been used since the time of Shapley (even though he unknowingly took them to be ordinary cepheids). In 1995, Bruce W. Carney and Jon P. Fulbright conducted infrared observations of about 60 RR Lyraes in the Milky Way's inner regions, yielding for R₀ a value of 25,400 light years [Carney, 1995].

Among these rare species, one may find "numerous supernova remnants, massive star-forming clouds, strong X-ray and gamma-ray sources, and towering magnetic structures which protrude from the galactic plane" [Reid, 2000]. The galactic nucleus itself seems to be occupied by a compact, extremely massive object—very probably a black hole—which emits strongly in the radio frequencies, and is known as Sagittarius A* (read: "Sagittarius A-star"). It is in the study of this object (and its associated stars and clouds) that an accurate value for R₀ will eventually be found.

The following techniques have been recently suggested or carried out:

Water (H₂O) Masers—
Masers (microwave amplification by stimulated emission of radiation) are the microwave analog of what we call lasers in the optical spectrum. This type of radiation is frequently found in interstellar clouds orbiting near the galactic nucleus. It originates when water molecules suspended in the clouds become excited by luminous, high-energy stars in the surrounding area, causing the molecules to emit coherent microwave photons. Radio astronomer Mark Jonathan Reid detected the proper motion of these masers in 1993, thus enabling him to establish the rotational center of the clouds. His value for R₀—26,000 ± 1,600 light years—is regarded as one of the most accurate ever obtained [Reid, 1993].

Trigonometric Parallax—
The parallactic displacement of the Milky Way nucleus in relation to extra-galactic objects—as attributed to our movement around the galactic center—has recently been detected. This feat has been achived by M. J. Reid—along with Anthony Readhead, René Vermuelen and Robert Treuhaft—using the VLBA (Very Long Baseline Array) radio telescope. The 1999 study found that the value for R₀ is 26,000 light years, and that the length of the "cosmic year" (that is, the time the Sun takes to move around the center of the Milky Way) is about 226 million years [NRAO, 1999].

Keplerian orbits of stars—
It has been suggested that the Keplerian orbits of stars moving around Sagittarius A* could be resolved—from astrometric and Doppler shift measurements—thus revealing the whole system's distance, the same way as with normal binary stars. Preliminary results giving a value for R₀ of 26,000 ± 1,300 light years have been obtained—through this technique—by a research team led by Frank Eisenhauer, using the ESO's Very Large Telescope [Eisenhauer et al, 2003].

An accurate determination of the mass of our Galaxy will, in turn, allow for a more complete understanding of its components, including the 90% or so of unaccounted mass that seems to exist. This will lead to better models of our own Milky Way, and galaxies in general, which in turn will help to answer some of the great cosmological questions of our time, such as how and when the universe started, and what its final destination could be.