Introduction

Many methods have been given for the calculation of a visual binary orbit. The motion of the Earth can be neglected, but the measurement errors are much larger than errors in positions of planets, asteroids or comets. Therefore these methods are entirely different from calculating an orbit in our planetary system. The decision about whether to calculate an orbit or not may depend on the following considerations:

For the first calculation of an orbit:

• Is the observational material good and complete enough to give a reliable value for the important quantity a3/P2?

• Are there only a few recent measurements and does the companion approach a critical phase of the orbit, so that a first preliminary result will attract the observer's attention to the pair?

For the improvement of an orbit:

• Are there large (or growing) deviations between observed positions and calculated positions?

• Will the new orbit give a significantly more reliable result for a3/P2?

Rating the observational material: with a strongly marked curvature, even a comparatively short arc may suffice to give a reliable orbit, provided that the observations are consistent; see the two "well-determined"

Figure 8.1. Well-determined arcs, undetermined arcs and the complete ellipses.

arcs in Figure 8.1. Now have a look at the two "undetermined" arcs. Even high-precision measurements will not allow us to calculate a preliminary orbit. Any result will have to be graded "undetermined". Substantial revisions are to be expected - see the complete ellipses. In the example, the dotted ellipse results in a mass seven times larger than the solid one!

In the case of the first calculation of an orbit the observed arc will determine which method should be used. If there is any hope that the observational material will allow a least-square fit applied to a set of provisional elements, a simple geometrical method is sufficient to obtain an initial set of elements. If the observed arc is undefined or too short to draw the complete ellipse, a dynamical method is required like the method by Thiele and van den Bos.

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