Abstract
SPECTROSCOPIC VELOCITIES OF BINARIES.—The determination of the elements of double-star orbits from spectroscopic measurements has been attempted by two methods. That due to Dr. Wilsing, which is a very convenient one, is only applicable to cases of small eccentricities; another method, developed by Dr. Rambaut, is not subject to this limitation, but is rather elaborate. In No. 3242 of the Astronomische Nachrichten, Prof. R. Lehmann-Filhés works out a metho 1 somewhat akin to that of Dr. Rambaut, but which he claims to have discovered independently, and which does not require difficult calculations or constructions. If both components of a spectroscopic double are bright enough to give a measurable spectrum, as is the case with β Aurigæ and ζ Unæ Majoris, the velocities as determined from the displacement of the lines in the spectrum are taken as relative, and the investigation then deals with the motion of one mass with respect to the other considered as stationary. If, on the contrary, only one of the components gives a measurable spectrum, as in the case of Algol and? Virgin!?, the motion must be referred to the centre of gravity of the system, the radial velocity of which must be determined and subtracted from the observed velocities. The period of the star is easily determined by obierving a considerable number of periodic varialions, and all observations can then be reduced to a single revolution by adding or subtracting multiples of the period. These spectroscopic velocities are then plotted as ordinates with the times as ai scissas, and a wavy curve is thus obtained showing the maximum and minimum velocities relative to the solar system. If lhese velocities are referred to the centre of gravity of the system, the areas of the curve above the axis of abscissa must be equal to those below, i.e. the total displacements must neutralise each oiher. This gives a condition which the curve must lulf?l, aud which serves to control the observed velocities. Another condition is that the area inleicepted between the maximum positive ordinate and the next point of intersection with the axis of abcissie niust be equal to the area of the curve between that point and the maximum negative ordinate, this representing the motion of the star from the ascending to the descending node. Prof. Lehmann-Filres gives simple formulae lor determining the vaiicus elements of the orbit from the corrected curve. Comparing his mtthod wilh that of Dr. Rambaut lor the case of? Auriga?, he finds 0?58 for ihe eccentricity, where the latter lound? 156, and 57° 93 lor the longitude of the arcending codr, against Dr. Rambaut's 57°'43"showing differences which are well within the errors ol observation. The real daily rrotion is fouid to be 9O°726, corresponding to a pericd ol 3'g6Sdays. The apparent semi-major axisof theoibit comes out as 7,516,000 Engh>h miles, "hich agrees very closely with the value obtained by Dr. Rambaut, viz. 7,500,000.
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Our Astronomical Column. Nature 50, 327 (1894). https://doi.org/10.1038/050327a0
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DOI: https://doi.org/10.1038/050327a0