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There are different considerations for the problem: the orbiting masses involved (what is orbiting what?), orbital period (how long for the objects to complete an orbit around their center of mass), the distance of the objects to our measurement device (eg, a telescope on earth), the relative luminosity of the two objects (if they're close together, how do you resolve the darker of the two?), etc. From all these considerations, there are two problems:
1. Measurement technique (getting the data)
2. System dynamics calculations (analyzing the data) For measurement, the article mentions both visual and spectroscopic (wavelength) measurements; overviews of these and other techniques are discussed in [1]. You are correct, distance from the measurement device makes things interesting, especially in the presence of atmospheric distortion, but there are lots of tricks that can improve the effective resolution (eg, speckle imaging, which uses a bunch of images taken in rapid succession [2]). As for the orbital period, think of it like measurements of a line. You don't need every point, just two. If you have several measurements of a celestial body, you can plot them on one of the (MANY) celestial coordinate systems [3] and do some estimates. Longer periods mean more observations for better accuracy, but you don't need to wait for a complete orbital period to get a decent estimate. Hope this at least gives some useful keywords for your searches! [1] https://en.wikipedia.org/wiki/Binary_star#Methods_of_observa...
[2] https://en.wikipedia.org/wiki/Speckle_imaging
[3] http://csep10.phys.utk.edu/astr161/lect/time/coordinates.htm... |