Requested by Matt.
To call Iokath a planet is technically incorrect, and an insult to the brilliant design of the artificial world. A massive sphere constructed around--and fully enveloping--an undersized and unremarkable star, Iokath absorbs all of the energy released by its "sun," maximizing solar efficiency.
All the orbital bodies in the system--every planet, moon, and asteroid--were demolished and salvaged for core elements to create this technological marvel. The salvage was processed and repurposed to create a self-sustaining ecosphere that could be altered and expanded to meet the ever-changing needs of the builders and their society. The self-contained nature of Iokath allows for complete control and customization of every aspect of the environment--a theoretically perfect world.
With the system's star hidden by the surrounding sphere, Iokath is undetectable from a distance, and its impenetrable exterior defenses make it virtually unassailable. Combined with the technological superiority of the builders, it was impervious to any outside threat... but Iokath couldn't protect itself from enemies within."
Sounds fun.
Calculation
Low end
It's described as a undersized star, so I'll use VB 10 as a baseline.
VB 10 has a Radius of 0.102 Solar Radius, which is about 695,700 kilometers
0.102 * 695,700 = 70,961.4 km
(4 × pi × 70,961.4^3)/3 = 1.4967702e+15 km^3
So 1.4967702000000001e+24 m^3
However it was pretty hollow. Not sure how hollow, so 90% to be safe.
1.4967702000000001e+24 - 90% = 1.4967702e+23 m^3
Density of the lower mantel of the Earth is 4,400 kg. Matt said they're made of that, or something.
1.4967702e+23 * 4,400 = 6.5857889e+26 kg
Importing the values into this calculator yields 2.447501268e+35 J
58.49 Yottatons
Edit: The link uses some coding to switch formulas without switching URLs. This is what it should look like.
High end
It was suggested I should use Proxima Centuari instead.
Proxima has a radius of 0.1542 SR, so 107,323.2 km
(4 × pi × 107,323.2^3)/3 = 5.1780883e+15 km^3
So 5.1780882999999997e+24 m^3
5.1780882999999997e+24 - 90% = 5.1780883e+23
5.1780883e+23 * 4,400 = 2.2783589e+27 kg
Inputting the values and we get 1.93682620438e+37 J
4.629 Ninatons
Results
- Low end: 58.49 Yottatons
- High end: 4.629 Ninatons