The Castor binary system Some binary systems are sufficiently close to Earth and the stars are well enough separated that we can see the two stars individually in a telescope and track their motion over a period of time. We term such systems visual binaries.
Example: The Castor System
The adjacent image shows one example, the star Castor, which is actually a visual binary as observed through a telescope (it was the first binary discovered, by Herschell in 1790). In this case the plot is of the orbit of one star relative to the other and the year of the observation is given at the corresponding point on the orbit.
Orbits for binary star systems
Orbits for Binary Systems
In reality, binary star systems are governed by Kepler’s laws, as modified by Newton to account for the effect of the center of mass. Then each star executes an elliptical orbit such that at any instant the two stars are on opposite sides of the center of mass. The orbits generally are as depicted in the following figure.
Sirius and Companion
The Sirius Binary System
An example is shown in the image to the left of the Sirius binary star system, which consists of a more normal main sequence star (Sirius A) and a white dwarf companion (Sirius B).
The image adjacent right shows a telescopic view of the Sirius system. The faint point of light indicated by the arrow is Sirius B, almost lost in the glare of the much brighter Sirius A.
The orbits are drawn to scale, but the sizes of the two stars are not to scale in this image. Both stars would be but points of light at this scale, and Sirius A is considerably larger than the Sun while the white dwarf Sirius B is about the size of the Earth.
One important consideration for visual binary orbitals is that the plane of orbital revolution for such systems is not usually perpendicular to our line of sight. In general, there is some tilt angle i, as illustrated in the adjacent figure.
Thus, when we see the orbit of a visual binary we do not see the actual orbit but only the projection of that orbit on the celestial sphere. For example, if the orbit looks like an ellipse, that could be because the orbit actually is elliptical, or because the true orbit is a circle but we are seeing it from an angle that makes the circle look flattened and therefore elliptical. In many cases it is possible to determine the angle i by careful measurement in order to deduce the true orbits of the binary system. In other cases we cannot and the angle i remains uncertain.