TECHNICAL NOTE D
In the sample of the sixty nearest stars to the Earth we include the Sun. Accompanying seven of these stars is at least one dark unseen body. These unseen bodies are inferred because a wobble is detected in the peculiar motion of the star associated with the dark body (as in Figure 1). Including the unseen bodies as small stars we find sixty-seven stars grouped into forty-five systems. There are three triples, sixteen doubles, and twenty-six single stars. Sixty-one percent of these objects are thus components in a double or triple star system.
There are potentially many binaries in the Galaxy. Since faint companions are unlikely to be detected by any means, many of the binary systems which exist will not be recognized by observers.
In general, binaries fall into groups separable only by the technique used for their detection. Where the principals sufficiently separate they can be resolved by visual observation through a telescope: these are the visual binaries. When the principals are closer together spectroscopic detection is sometimes possible. For very close pairs eclipses are sometimes seen as the stars orbit one another. In some cases other phenomena are seen which show regular periodicity betraying the binary nature of the system. Discovery of this type has become increasingly frequent in recent years, greatly expanding the number of known binary systems.
Visual observation of the binary companion depends upon several factors: the proximity of the binary system to the Earth; a sufficient separation of the principals to allow resolution of their images by a telescope; and the occurrence of small differences in the luminosities of the principals, otherwise the view of the => companion will be obscured by the light of the => primary.
Tens of thousand of binary systems can be resolved by telescope into two separate stars. In about twelve percent of these visual binaries the orbital motion can be measured, but only a few satisfactory orbital analyses have been completed  . Where the orbit of the companion relative to the primary star can be measured, and where the distance to the principals can be measured, the physical separation of the pair is known. If the period of revolution of the binary is known, then, temporarily accepting Kepler's Harmonic Law, which is based upon Universal Gravitation as the only force binding the principals, the total mass of the binary system can be calculated (Chapter Three). This calculation based upon Kepler's Harmonic Law is the primary clue to the masses of all stars  (but see Chapter Two).
Allen (1963) tabulates the distribution of the stars against the calculated total "mass" of the binary system. For systems equal to or greater in mass than the Sun, only thirty-two percent of the stars are not members of double or multiple star systems. In those star systems of lesser "mass" the percentage of single stars rises dramatically  . For the mass range 0.5 to 0.25 Sun, eighty-five percent of the stars appear single. No star below 0.1 Sun seems to have a companion (ibid). This surely indicates that the ability to see companions near such poorly luminous stars is limited, if not nil.
For a typical visual binary one revolution of the companion about the primary takes a few decades. The orbits of the companions have dimensions comparable to the orbits of the major planets in the Solar System, but their shapes are much more elliptical than are the planetary orbits (see Figure 39). For a typical visual binary superposed on the Solar System the => apastron (near Neptune) is three times as distant as the => periastron (near Saturn).
The shorter the orbital period for revolution, the more circular the orbit of the companion. Systems which revolve in less than ten days have relative orbits whose shape resembles the orbits of the planets Mars and Saturn. Where the orbit is less than 100 days the orbit is less elliptical than the orbit of the planet Mercury. For orbits over 100 days distinctly elliptical orbits are noted and apastron is about twice as distant as periastron. These orbits are more elliptical than the orbit of the planet Pluto, where aphelion is sixty-seven per cent further than perihelion.
Figure 39. Binary Orbits of Short Period
Binary stars show a relationship between the shape of their relative orbit and their period of revolution in that orbit. For those pairs orbiting in times from a few days to a few weeks the orbits are found to be somewhat like the more elliptical planetary orbits found in the solar system. Elliptical orbits are described in terms of their difference from a circular orbit using a quantity called eccentricity. Eccentricities for closed orbits have values between 0 (a circle) and nearly 1 (which would be a parabola). The ellipse above the graph shows how the eccentricity is measured for a particular ellipse.
In some binary systems the separation of the components is too small to allow resolution in a telescope. Sometimes the detection of the binary still can be made because when the distance between the principals is small enough the stars move in orbit with high velocities. The binary can be observed because a Doppler shift occurs in the spectrum lines of the orbiting companion.
Spectroscopic detection favors binary systems in which the stars are highly luminous and especially where the orbiting star is equal in brightness to, or brighter than, the more stationary primary. The orbital periods for spectroscopically detected binaries range from days to weeks. In such systems the orbital period is determined from the time taken for the spectrum lines to shift through one complete cycle; canceling the motion of the binary system itself, the spectrum of the companion shows a velocity of approach, then no velocity, a velocity of recession, no velocity, finally returning to a velocity of approach.
Nineteen percent of all bright stars show variable Doppler shift in their spectrum, implying a companion (usually unseen). Of these, forty-seven percent show double spectrum lines; the duplication arises because the motion of both of the principals is detected, indicating that the two stars are comparable in brightness.
Lastly, some binary systems are detected because the light received from the stars is seen to vary as the principals eclipse one another. The stars in these eclipsing binary systems usually revolve about one another in less than one month. If indeed these light variations are eclipses, the principals are very close together or, alternatively, at least one, and sometimes both, of the stars have a very large radius compared to the Sun. Orbits have been calculated for almost 100 eclipsing binaries.
About nine percent of the spectroscopic binaries are also eclipsing binaries. To have such a high percentage of eclipsing systems in the spectroscopic binary sample is surely an anomaly.
Eclipsing binaries include principals with the smallest separation; the close binary stars belong to this group. About sixty percent of eclipsing systems can be described as detached, which means that the light curves of the eclipse produced as one star obscures the other show that the principal bodies are roughly spherical in shape; the Algol star system falls into this group of eclipsing star systems.
The remaining eclipsing binaries are the semi-detached star systems. Here the surface of at least one of the principals is distorted into an ellipsoidal shape, and forms at the extreme a teardrop-shaped body "in contact" with the other star. The Beta Lyrae system is a semi-detached binary. Though there is no physical distinction between all of the detached binary systems, that group transacts differently and less strongly than the remainder of the sample, all close binaries. These binary stars transact much more strongly because of the proximity of the two stars. The behavior of the close binaries can be characterized by its violence, in some examples episodic, in others sustained. Here the stars are in competition with the locally available energy supply and for the space with its infra-charge.
Of special interest are the so-called contact binaries, systems in which one of the stars has seemingly expanded so as to touch, or in some cases even to envelop the companion star within its tenuous atmosphere. Some contact binary systems appear to revolve about one another in a small fraction of one day.
Seldom do the close binaries resolve into two stars, nor do their spectra often show duplication. They are the binary systems with the greatest internal transaction. Many of them show gas flowing between the stars (Chapter Ten), some exhibit emission lines, in other one of the components, usually a dwarf star, erupts regularly (ibid). This eruptive behavior seems to be linked to the gas flow, which produces a hot spot on the recipient star, representing a cataclysmic extreme in activity of the type exhibited by the close binary group as a whole.
Systems containing the dwarf novae fall into a group which also resembles systems containing old novae and W Ursae Majoris binaries (Glasby, p146). All of the principals are underluminous. In contrast, many close binaries contain one "overly large" principal. The Wolf-Rayet stars are found paired with a smaller overluminous companion (Glasby, p143). Frequently, B-emission stars are members of close binary systems (Maraschi et al.). As early as 1938 Haffner and Heckmann proposed that in open star clusters, stars lying above the Main Sequence (overluminous stars) were members of binary systems. It seems that a property common to close binary systems is deviant luminosity of one or both principals. This may indicate the importance both of the transaction between the components in such systems, and of the competition of these stars for the contents of their surroundings. We maintain that these transactions are electrical.
In summary, the close binary stars feature one principal which is a degenerate object. At least one of the principals shows anomalous luminosity. Transactions within these systems produce various degrees of violent outburst: some flicker (Chapter Ten), all exchange material and, we believe, electric charge. These unusual characteristics of close binary systems appear to represent a competition for space and electrical charge; some scholars, perplexed by these same behaviors, have proposed that unimaginable concentrations of matter have been observed and are causing the observed violence. From the evidence presented in this book, it seems that Solaria Binaria quantavoluted through the gambit of close binary phenomena before its principals became detached and its binary nature became disguised. The electrified star system, simple in concept and understandable in its development, was the stage on which the pageant of mythology, pre-history, and written history begins to unfold as parts of the common cosmic voyage.
126. Batten (1967) notes the great difference between the number of systems known to exist and those which have been studied. A highly special sample has well determined orbits, even fewer systems have known masses. Typical orbits are given in Allen.
127. We use the term massing in preference to weighing. An example of massing using Kepler's Harmonic Law; the satellite Triton is 353 megameters form Neptune: the Moon is 384 megameters from the Earth. If both Earth and Neptune had the same mass, the periods of revolution for Triton and Moon about their primaries would be about the same. They are not; the Moon takes 22.3 days to orbit while Triton orbits in 5.9 days. This leads astronomers to conclude that Neptune is 17 times the mass of Earth. Any transaction equal to 17 times the gravitational pull of one Earth mass on Triton would suffice to cause Triton's rapid orbiting of Neptune as observed. So with the stars: the more intensive the transaction between the principals, the more rapidly the pair will orbit about one another.
128. In systems which show no evidence of any periodic phenomenon, the star's mass has been inferred using theoretical considerations (see Chapter Three).