Remarkable data indicate the presence of a massive black hole at the center of our Milky Way galaxy. One of the two W. M. Keck 10 meter diameter telescopes in Hawaii was used by Andrea Ghez and her colleagues to observe infrared light coming directly through the dust surrounding the central region of our galaxy (visible light is multiply scattered by the dust, blocking a direct view). Stars were observed for several consecutive years to determine their orbits near a motionless center that is completely invisible ("black") in the infrared but whose precise location is known due to its strong output of radio waves, which are observed by radio telescopes. The data were used to show that the object at the center must have a mass that is huge compared to the mass of our own Sun, whose mass is a "mere" 2 ✕ 10³⁰ kg.

Here are positions from 1995 to 2008 of one of the stars, called S0-20, orbiting around the galactic center. The orbit looks nearly circular with the radius shown.

(a) Using the positions and times shown above, what is the approximate speed of this star in m/s? Also express the speed as a fraction of the speed of light.

v =	1805598.898 m/s
v/c =

(b) This is an extraordinarily high speed for a macroscopic object. Is it reasonable to approximate the star's momentum as mv? (Some other stars near the galactic center with highly elliptical orbits move even faster when they are closest to the center.)

yes, v << c

no, v comparable to c

(c) Based on your value for the speed of the S0-20 star, calculate the mass of the massive black hole about which this star is orbiting. (This result differs somewhat from that obtained by Ghez and colleagues, who did a careful analysis of the elliptical orbits of several stars. Although the orbit of the star looks circular in the figure above, it is actually an ellipse seen at an angle.)

kg

(d) How many of our Suns does this represent? .

Suns

It is thought that all galaxies may have such a black hole at their centers, as a result of long periods of mass accumulation. When many bodies orbit each other, sometimes an object happens in an interaction to acquire enough speed to escape from the group, and the remaining objects are left closer together. Some simulations show that over time, as much as half the mass may be ejected, with agglomeration of the remaining mass. This could be part of the mechanism for forming massive black holes.

For more information, see the home page of Andrea Ghez, http://www.astro.ucla.edu/faculty/ghez.htm. The papers available there refer to "arcseconds," which is an angular measure of how far apart objects appear on the sky, and to "parsecs," which is a distance equal to 3.3 light-years (a light-year is the distance light goes in one year)