ACTUAL DIMENSIONS OF THE STARS
We have seen that the distances of the stars from the solar system are
immense beyond conception, and millions upon millions of them are
probably forever beyond our power of ascertaining by direct measurement
what their distance really is. After we had found the sun's distance and
measured the angle filled by his disk, it was easy to calculate his
actual size. This direct method, however, fails when we try to apply it
to the stars, because their distances are so vast that no star's disk
fills an angle of any appreciable size; and even if we try to get a disk
with the highest magnifying powers of a great telescope our efforts end
only in failure. There is, indeed, no instrumentally appreciable angle
to measure.
How then shall we ascertain the actual dimensions of the vast spheres
which we know the stars actually are, as they exist in the remotest
regions of space? Clearly by indirect methods only, and it must be said
that astronomers have as yet no general method that yields very
satisfactory results for stellar dimensions. The actual magnitude of the
variable system of Algol, Beta Persei, is among the best known of all
the stars, because the spectroscope measures the rate of approach and
recession of Algol when its invisible satellite is in opposite parts of
the orbit; the law of gravitation gives the mass of the star and the
size of its orbit, and so the length of the eclipse gives the actual
size of the dark, eclipsing body. This figures out to be practically the
same size as that of our sun, while Algol's own diameter is rather
larger, exceeding a million miles.
If we try to estimate sizes of stars by their brightness merely, we are
soon astray. Differences of brightness are due to difference of
dimensions, of course, or of light-giving area; but differences of
distance also affect the brightness, inversely as the squares of the
distances, while differences of temperature and constitution affect, in
very marked degree, the intrinsic brilliance of the light-emitting
surface of the star. There are big stars and little stars, stars
relatively near to us and stars exceedingly remote, and stars highly
incandescent as well as others feebly glowing.
We have already shown how the angular diameters subtended by many of the
stars have been estimated, through the relation of surface brightness
and spectral type. Antares and Betelgeuse appear to be the most inviting
for investigation, because their estimated angular diameters are about
one-twentieth of a second of arc. This is the way in which their direct
measurement is being attempted.
As early as 1890, Michelson of Chicago suggested the application of
interference methods to the accurate measurement of very small angles,
such as the diameters of the minor planets, and the satellites of
Jupiter and Saturn, as well as the arc distance between the components
of double stars. Two portions of the object glass are used, as far apart
as possible on the same diameter, and the interference fringes produced
at the focus of the objective are then the subject of observation. These
fringes form a series of equidistant interference bands, and are most
distinct when the light comes from a source subtending an infinitesimal
angle. If the object presents an appreciable angle, the visibility is
less and may even become zero.
Michelson tested this method on the satellites of Jupiter at the Lick
Observatory in 1891, and showed its accuracy and practicability.
Nevertheless, the method has not been taken up by astronomers, until
very recently at the Mount Wilson Observatory, where Anderson has
applied it to the measurement of close double stars. It is found that,
contrary to general expectation, the method gives excellent results,
even if the "seeing" is not the best--2 on a scale of 10, for instance.
To simplify the manipulation of the interferometer, a small plate with
two apertures in it is placed in the converging beam of light coming
from the telescope objective or mirror. The interference fringes formed
in the focal plane are then viewed with an eyepiece of very high power,
many thousand diameters. The resolving power of the interferometer is
found to be somewhat more than double that of a telescope of the same
aperture. By applying the interferometer method to Capella, arc
distances of much less than one-twentieth of a second of arc were
measured. More recently the method has been applied to the great star
Betelgeuse in Orion, whose angular diameter was found to be 0".46,
corresponding to an actual diameter of 260,000,000 miles, if the star's
parallax is as small as it appears to be.