Ok so its a few steps but nothing crazy.embokim wrote:Suppose that now after a series of observations astronomers have deduced some properties of this pair of

stars. The parallax angle of this system is 0.0555…”. The mean separation of these two stars appears to

be 1.11”.

What is the semimajor axis of this binary star system, in AU?

How would you solve this question?

Thank You so much!

First you want to take the parallax angle and find the distance in parsecs to the system. d =1/theta.

Once you have the distance to the system, you can use the Small Angle formula to find the D, diameter in parsecs (or AU ish, there is a trick here to avoid conversions but lets keep it simple). 1.11" = 206265D/d

Now that you have the diameter of the system, the semi major axis is half of that and in AU, so use parsec to AU conversion and divide by 2. This problem makes a lot of assumptions about the observers being on earth and that the system's major axis is moving along a "transverse" line, but this method should work for the information that is given.