Question about semi-major axis mean separation

I am currently doing an assignment but I cannot for the life of me understand what one of terms used means. Notice I am not trying to get help with the assignment itself, but rather to make me understand so I can solve it.

Anyways, in the question (about visual binary stars) I am given their parallax angle etc etc, and I am to find the mass of them. But the sentence I cannot understand is the information given in "The semimajor axis (mean separation) is X.YZ'' and...(continue)", what does it mean? I draw two elliptic orbits and they intersect, I draw the semi-major axes of each ellipse. Is the semi major axis mean separation the angle that is between the semi major axes and the line drawn between each stars center in their elliptic orbits?

Help would be very nice. Thanks in advance!

1 Answer

The semi major axis $$a$$ of an orbit is the same as the arithmetic average of the minimum and maximum distance $$r$$ or the object from the central object in sense of $$a = 0.5\cdot(r_{min} + r_{max})$$; thus semi major axis is sometimes also called mean separation. As such you are given the sum of the semi major axis of two components.

A two-body problem can be reduced / simplified to a mass-less body circling an object of the combined mass - as such you can calculate the combined mass of both stars with the numbers you are given.

• I don't quite see how this answers my question about what the semi-major axis mean separation is. I don't really see the link between semi-major axis and what the mean separation is... – Niklas Stenhall Aug 12 '20 at 7:18
• it's different words for the same thing. – planetmaker Aug 12 '20 at 7:21
• But he gives the mean separation in arcseconds. How is a semi-major axis given in not even a length? Edit: I just forgot to say thank you for answering. I am really grateful! – Niklas Stenhall Aug 12 '20 at 7:27
• Welcome to the real world. No-one was there and could use a car to drive the distance. Instead people have telescopes - and they only measure angular separation. Convert the angular separation into an actual distance with other information you might have about the star or star system like its distance from Earth. – planetmaker Aug 12 '20 at 7:30
• Ah yes. Now it clicked. When you put it that way, it definitely makes sense. Thank you so much! I was stuck being inside the binary star system and didn't even think about the whole picture.*facepalm* – Niklas Stenhall Aug 12 '20 at 7:32