# Calculating the orbits of binary stars around their barycentre

I've been building a world, partly for test reasons (making sure my spreadsheet works, and so i know what i need to add to it) and partly for fun, but for calender reasons i need to know the orbital period of my binary star system.

More specifically, as i am putting this in a spreadsheet, i need the calculations to figure out the orbital period - preferably dumbed down a little as, when searching myself, i couldn't make heads or tails of it.

Star 1:

Mass: 1.07 Solar Masses

Distance from Barycentre: 0.0709724389 AU

Star 2

Mass: 0.853 Solar Masses

Distance from Barycentre: 0.0890275611 AU

Orbital Eccentricity: 0.41

• You need the masses of both bodies and the distance between their centers to calculate the orbital period (you can express the mass in terms of solar masses if it's more convenient). Jul 20, 2017 at 20:12
• I've added those to the question. Jul 20, 2017 at 20:31
• Your distances from the barycenter of the system only apply if the orbits are circular, otherwise you'll have to qualify them. I assume these are the maximum distances from each other?
– Pak
Jul 20, 2017 at 21:18
• No. Their absolute max separation is 0.4512... i'm getting the sinking feeling that i've been worldbuilding wrong Jul 20, 2017 at 21:23
• Barycenter, from ancient Greek barys (heavy); from the same Greek word we have barometer (measures the weight of the atmosphere) and baritone (deep voice). Jul 20, 2017 at 21:45