I already like this event.Ughhhh I hate essay questions...they're not good for the test taker or the grader >.> (well, I guess that depends on the person). I would imagine there's a few ways to do this? I would very much ask the grader if you can. I think you kind of have to make some observations here to actually get it. Of course, you have to make it under the constraints given (that is it's a visual binary and decently far away). Unfortunately or fortunately you could use a lot of ways to figure this out then? I question also whether I should assume that they meant trigonometric parallax, spectroscopic parallax...I'll try to use a method without just in case.There was a question I ran into that didn't quite make sense to my partner or I. The question went something like this: "You locate a visual binary in the night sky that is too far for the distance to be determined with parallax. How do you determine the distance?"
No other details were provided, which game my partner and I a bit of a headache :/
Do you have to assume other things in order to solve it? It was an essay question
You could find the angular size of the system by observation. Using spectroscopy you could maybe derive a velocity graph. You could also find the temperature of each star and probably the luminosity of each star dependinggggg on the system. You could maybe use some sort of mass-luminosity relation and then find the mass of each star (I know I'm being cheap there, but they do exist and you just need to figure out the spectral class and luminosity class of the objects...if it can't be applied I could list other ways of doing this, whatever). With that, you can find the mass of the system, then I would hope you can find the period of orbit either by observation or from your velocity graph. With period and mass you can find the physical semi-major axis. With that and the observed angular size of the system, you can then use the small-angle formula to I believe get the distance to the system.
Phew, hope that helped!
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