Powered by OpenAIRE graph
Found an issue? Give us feedback
addClaim

This Research product is the result of merged Research products in OpenAIRE.

You have already added 0 works in your ORCID record related to the merged Research product.

The Orbital Elements of a Visual Binary

Authors: Wulff D. Heintz;

The Orbital Elements of a Visual Binary

Abstract

The orbit of a visual pair describes, in the form of seven so-called orbital elements, the motion of the companion relative to the primary star, such as is obtained from the relative observations. In the two-body problem with the masses M1 and M2, the radius vector r, and the constant of gravitation k2, the relative motion is represented by the second-order differential equation $${d^2}r/d{t^2} = - {k^2}\left( {{M_1} = {M_2}} \right)r/|r{|^3}$$ (4) . Its six scalar constants of integration correspond to six elements which suffice to specify a particular solution if the total mass M1 + M2 is assumed to be known. This holds for the solar system but not for double stars. The Kepler laws describe the solutions of Equation (4), and the 1st and 2nd laws are readily utilized: the motion proceeds in a conic section (an ellipse, if periodic) with the primary star in the focus, and the area swept by the radius vector in the conic section is constant per unit of time. The 3rd law (formula 1), although equally valid, cannot be applied until the orbit is known, and a determination of the unknown total mass is attempted. The semiaxis major, therefore, is an independent element and, moreover, from visual and all positional data known only in arc sec, not in linear measure such as astronomical units or kilometers.

Related Organizations
  • BIP!
    Impact byBIP!
    citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    1
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Upload OA version
Are you the author? Do you have the OA version of this publication?