The system in question is Spica (the A and B components are accurate, the others are suspected to exist but there's little data on them so the data for those are mostly extrapolated/fictional). So far I've got this data (mass in solar mases, luminosity in Sols, Radius in Sols, Distance in AU):
Code: Select all
Mass Lum Rad Dist
A 11 13400 7.8 -
B 7 1700 4 0.12
C 6 900 3 4
D 4 250 2.5 40
E 0.6 0.08 0.54 10000
What I'm assuming is that there are nested barycentres here: I calculate the AB pair barycentre. Then I treat those two stars as a single mass to calculate where the AB-C barycentre is. I do the same to calculate where the ABC-D barycentre is. And again for the ABCD-E barycentre.
Is this how you're supposed to calculate where the barycentres are?
One thing I'm not sure about is if the separations shown are the distances between each star and A, or each star and its local barycenter. Apparently the formula to calculate a barycentre is:
r1 = rtot(m2/(m1+m2)) where r1 is the distance from the centre of the more massive star, rtot is the separation between the two stars, and m1 and m2 are the masses of the two stars. I'm using the distances shown as the rtot distance in this formula, is that what one is supposed to do?
If I do that, then I get these distances:
AB Barycentre = 0.047 AU from A
AB-C Barycentre = 1 AU from AB Bary
ABC-D Bary = 5.7143 AU from ABC Bary
ABCD-E Bary = 209 AU from ABCD Bary
The next problem of course is "how do I show this in Celestia"? Is it possible to 'nest' stellar barycentres like this yet? And how do you calculate the orbital periods of the stars around their barycentres?