Alpha Centauri’s stars energy

[Peppypony]

There’s a moment in one of my stories where a character absorbs all the stars in the Alpha Centauri system and then after that, she wields their power.

I know that’s clearly 4-C, but how high is it exactly?

I asked on FC/OC originally, but that wiki is not as popular, because of that I haven’t had an answer and that’s why I’m asking here instead.

 

[KLOL506]

You will first need its polytropic value if you want to find their GBE.

3GM^2/(r(5-n))

G is gravitational constant of 6.6743015e-11

M is mass in kg

r is radius in meters

n is the polytropic value

Formula is from "An Introduction to the Study of Stellar Structure" by Subrahmanyan Chandrasekhar, Formula 90 to be exact.

 

[Peppypony]

ik what radius and mass is. everything else uhhh… yeah sorry for being dumb but i don’t understand anything there xD

 

[RoTt35]

Alpha Centauri consists of 3 stars: Alpha Centauri A (Rigil Kentaurus), Alpha Centauri B (Toliman) and Alpha Centauri C (Proxima Centauri). The three are main-sequence stars, so they would have a polytropic value of 3

Alpha Centauri A has a mass of 1.0788 M☉ (2.145647e30 kg) and a radius of 1.2175 R☉ (8.4701475e8 meters), so its GRB would be:
(3*6.6743015e-11*(2.145647e30)^2)/(8.4701475e8*(5-3)) = 5.4415503823e41 Joules

Alpha Centauri B has a mass of 0.9092 M☉ (1.808326e30 kg) and a radius of 0.8591 R☉ (5.9767587e8 meters), so its GRB would be:
(3*6.6743015e-11*(1.808326e30)^2)/(5.9767587e8*(5-3)) = 5.4775305839e41 Joules

Alpha Centauri C has a mass of 0.1221 M☉ (2.428471e29 kg) and a radius of 0.1542 R☉ (1.0727694e8 meters), so its GRB would be:
(3*6.6743015e-11*(2.428471e29)^2)/(1.0727694e8*(5-3)) = 5.5037227288e40 Joules

Total Energy: 5.4415503823e41 + 5.4775305839e41 + 5.5037227288e40 = 1.1469453239e42 Joules (4-C: Star level)

 

[Peppypony]

Ok thanks! x3