In Star Wars Episode VII: The Force Awakens a new superweapon was unveiled. The so-called Starkiller Base was built into an ice planet. Based on its size and destructive capabilities, the costs for this fearsome base for the First Order could be astronomical. After all the much smaller sized Death Star cost the Galactic Empire on the order of $193 QUINTILLION ($193,000,000,000,000,000,000).1
According to canon, the Starkiller Base has a diameter of 660km, which is verified by it having a diameter roughly 5.5 times that of the Death Star as depicted in Episode VII. As volume rises cubically with diameter, a first pass analysis would state that the Starkiller Base costs: $20.221 SEXTILLION ($20,221,000,000,000,000,000,000).2
However, though the Death Star was constructed from nothing, the Starkiller Base has an entire planet as its foundation. As such, calculating the costs of the Starkiller Base based on planetary volume is not appropriate. Instead, the excavation of the equatorial trench (wrapping around roughly 50% of the planet) would be the majority of the construction. This trench has an approximate depth of 10% of the radius (33km) and width of approximately 25% of the radius (82.5km). Thus the excavated volume is approximately 2,680,000km3. This leads to a cost of approximately $360 QUINTILLION, which is still significantly more expensive than the Death Star.3
The obvious first thought is whether the Starkiller Base would require additional costs as its weapon is able to destroy the entire Hosnian system from a great distance whereas both Death Stars required close proximity to the target and could only destroy one planet per shot. Ultimately this cost is kept comparable as the energy required is collected utilizing the resources provided by a nearby star. Holding onto the energy though should require further resources as the star is absorbed and stored before the weapon is used. To consider this, let us consider the geological makeup of the planet itself. With a diameter of 660km, the volume is 150,532,554 km3. Additionally, given the behavior of our heroes and villains on the surface of the Starkiller Base, there must be Earth-like gravity. Using Newton’s laws of universal gravity, the mass must be approximately 1.6 × 1022 kg.4 Thus the density of the Starkiller Base planet is roughly 106,338 kg/m3. This is just under 5 times the density of osmium, the densest naturally occurring element known to humans, and over 13 times the density of steel. With such high density it is likely this small planet was chosen specifically by the First Order for its ability to store dark energy. As such we can assume that costs are in line with size of the weapon system.
If, however, the planet were able to support life through its natural atmosphere, the costs would be reduced to approximately 2.59% of the total cost.5 That is, if the planet that the Starkiller Base was built into was able to sustain life, its total cost would be a mere $9.315 QUINTILLION or just 4.83% of the cost of the Death Star.
To determine the ability of the Starkiller Base to naturally support life, we need to determine its atmospheric conditions. Reportedly, the atmosphere is breathable, which indicates an Earth-like atmosphere of primarily nitrogen (N2) and oxygen (O2). For completeness we will also consider the average molecule in Earth’s atmosphere (dry air). In a galaxy with interstellar travel and the ability to terraform a planet these may need to be replenished and thus not reduce the costs. So the big question is surrounding the atmospheric escape on the Starkiller Base. This follows rules based on the Maxwell-Boltzmann distribution. In particular, we are interested in the probability that the atmosphere escapes naturally through molecules exceeding the escape velocity. Due to the size and mass of the Starkiller Base, we determine its escape velocity to be approximately 2544 m/s.6 With the Starkiller Base being built on an ice planet, but Rey, Finn, and Kylo Ren all seemingly comfortable on the surface, the temperature is seemingly near 0°C (or 273.15K).Thus with molecular weight of 28 amu for N2, 32 amu for O2, and 29 amu for dry air, we conclude that the probability of molecular escape is so close to 0 to be negligible. Thus without the need for continuous injections of air into the atmosphere, the planet is self-sustaining.7
The only remaining concern is the atmospheric pressure at the bottom of the Starkiller Base trench. With the assumption that the pressure at the surface is 1 atm (i.e., comparable to Earth at sea level), which is implicit in the assumption that the atmosphere is sufficient to support life, then the pressure at the bottom of the trench is 62.3 atm. As 10 meters of depth in water corresponds to approximately 1 atm of pressure, this is about equivalent to a submarine at 623 meters. At this depth, modern American Seawolf class submarines are designed to operate. Since the Starkiller Base will primarily be constructed from the planet itself, the dense natural material (106,338 kg/m3) would act as the hull on a submarine keeping the humans safe.
TL;DR: The Starkiller Base costs $9.315 QUINTILLION or 4.83% of the cost of the first Death Star.
1. Assuming a diameter of 140km for the first Death Star. This has since been retconned to anywhere from 120km to 160km.↩
2. Starkiller Base cost = Death Star cost × (Starkiller Base volume / Death Star volume) = $193 QUINTILLION × (330/70)^3 = $20.221 SEXTILLION.↩
3. Excavation may be cheaper, especially as the extracted minerals can be sold for profit.↩
4. Newton’s laws state that planetary mass is equal to the square of planetary radius (330 km) multiplied by the acceleration due to gravity (9.81 m/s2) and divided by the universal gravitational constant.↩
5. It costs roughly 38.67 times more (pound for pound) to send a living human than lifeless cargo. The original cost computations assumed an artificial atmosphere would be required to keep humans alive, without that we can divide the cost for the Starkiller Base by 38.67.↩
6. Escape velocity is the square root of twice the multiplication of the acceleration due to gravity (9.81 m/s2) and planetary radius (330 km).↩
7. Water vapor would escape the atmosphere at a slow rate, but as must water would remain as ice on such a planet, this can be neglected without concern.↩