Binary Star Separation in AU

 

Start with the arc length equation:

 

  

 

Where

         S = arc length

         R = radius

       = angle in radians

 

Note that S and R must be in the same units. For S in AU, R must be in AU. To convert from parsecs, there are 206265 AU/pc. To convert from seconds of arc to radians, there are 206265 seconds of arc per radian.

 

 

Therefore:

 

Using this relationship and data from the forth edition of Stars and Planets by Jay Pasachoff (Peterson Field Guide), the following separations can be calculated:

 

Albireo  34 sec, 385 ly, 4015AU

Almaak 10 sec, 355 ly, 1089AU

Mizar 14.4 sec,  78 ly,   345AU