Perhaps the most striking case, for which we have substantially accurate data, is the star β Aurigæ; which, during the general spectroscopic survey of the heavens undertaken by Professor Pickering of Harvard, in connexion with the Draper Memorial, was discovered to show a spectrum with the lines some days double and alternate days single. Clearly it must consist of a pair of luminous objects revolving in a plane approximately containing the line of vision; the revolution being completed every four days. For the lines will then be optically displaced by the motion, during part of the orbit—those of the advancing body to the right, those of the receding body to the left,—while in that part of the orbit which lies athwart the direction of vision, the spectrum lines will return to their proper places,—opening out again to a maximum, in the opposite direction, at the next quadrant.
The amount of displacement can be roughly estimated, enabling us to calculate the speed with which the sources of light were moving.
Professor Pickering, in a brief statement in Nature, Vol. XLI, page 403, 1889, says that the velocity amounts to about 150 miles per second, and that it is roughly the same for both components.
Taking these data:—
Equality and uniformity of speeds,
150 miles per second each,
Period 4 days,
we have all the data necessary to determine the masses; and likewise the gravitative pull between them. For the star must consist of two equal bodies, revolving about a common centre of gravity midway between them, in nearly circular orbits.
The speed and period together easily give the radius of the circular orbit as about 8 million miles.
Equating centrifugal and centripetal forces
mv² / r = γ m² / (2r)²
and comparing the value of 4r³ / T² so obtained with the r³ / T² of the earth, we find the mass of each body must be about 30,000 times that of the earth, or about 1/10th that of the sun.