Double Stars pp 42-44 | Cite as

# The Methods by Danjon and Rabe

## Abstract

The eccentricity *e* affects not only the position of the primary star in the orbit but also the rate of change of angular velocity over the revolution. Thus, *e* can in principle be determined from the shape of the curve θ(*t*) without using separations. Consider now two opposite points of the orbit. (*θ*_{2} – *θ*_{
1} = 180°) Then *v*_{2} – *v*_{1} — 180° also holds, as the projection effects are the same, but *M*2 *— M*1 does not equal 180° except if *e =* 0, or if the two points are on the major axis. Graph the function *M*_{2} - *M*_{1} - 180° for a number of pairs of opposite points over the orbit; then its zero points determine periastron and apastron, and the extremum values depend only on *e* = sin *φ*. In fact, they equal 2*φ* + sin 2*φ* The remaining elements are readily found, as corresponding pairs (*θ*, *v*) are now known.

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