Not sure if this belongs here or in the off-topic, but it's about space, and it deals with math, so...
The ISS masses (at the time of posting) 369 914 kilograms, and has been estimated to have cost between 35-160 billion USD so far. This would be a cost per kilogram of $ 94 616.58.
This is in contrast with $ 54 750 for platinum, and $ 43 330 for gold. Of course, the ISS actually works and does stuff, whereas 369 914 kilograms of gold or platinum would just sit there.
As a space enthusiast, have you ever wondered how spaceflight would be motivated by a rare, extremely valuable resource somewhere else in space?
In Avatar, the rare mineral- unobtanium- that can only be found on the planet of the film's setting, 4.4 lightyears away from Earth, is said to cost 20 million USD back on Earth.
The interstellar spacecraft (called an ISV) shown in the film has a payload capacity of 350 tons. Let's be a bit pessimistic and say it's carrying 250 tons of unobtanium, and 100 tons of other stuff... such as the crates the unobtanium is shipped in, or other peripheral cargo.
That would be five trillion dollars.
The mass figures for the ISV are unfortunately absent. Let's say it masses 2500 tons, and it has the same dollars/kg value as the ISS. That would be a 236.5 billion dollar spacecraft.
We are never given thrust or ISP figures for the ISV, but from what I can make out the engines are some sort of hybrid between an antimatter-plasma core, and a photon drive (yeah... :shifty
. For simplicity's sake, let's assume it has the same performance as a proper antimatter beam core engine. For a dV of 0.7 C (the ISV's top speed), that is a mass ratio of 8.15. Assuming, again, that this is a beam core engine, that would mean 10187.5 tons of antimatter.
Although other estimates of antimatter production are more pessimistic, considering that this is an interstellar spacecraft utilising large amounts of it, the optimistic estimates are probably best. With the $25 million/gram figure, that is 254.6 quadrillion USD, which is maybe a tad high. :facepalm:
Assuming the total cost of antimatter is a trillion USD, it would need to have a cost of 98 $/gram, and 98159.50 $/kilogram. Which is orders of magnitude lower than any real antimatter cost estimate.
However, the cost of antimatter depends on the cost of power, and if cheap fusion power were available, it could reduce the costs somewhat. One of the major uses of unobtanium is described by the director as integral to the construction of fusion powerplants, so this is conveniently self-explanatory.
The ISV refuels with deuterium and hydrogen mined from the atmosphere of Polyphemus (the parent planet in the film), but it is unclear if antimatter is produced there as well. Presumably the ISV cannot carry antimatter for it's return to Earth, but I would find the production of antimatter in such a remote location to be rather difficult.
However, the ISV is not accelerated and decelerated purely by the engines; it combines the use of engines with the use of a lightsail, pushed by lasers from our solar system.
To accelerate the the ISV (that we've now assumed is about 2500 tons in mass) at 1.5 G, one would need 340 meganewtons of force. Atomic Rockets says light sail power outputs and accelerations boil down to 6.7 newtons per gigawatt. In this case that is 50 746 268.65 gigawatts, or 50.7 petawatts.
That is 3171 times the power usage by the entire planet today. And around half of what it would take to become a type 1 civilisation. Earth's energy budget is 174 petawatts.
That is the output energy. The best experimental lasers have an efficiency of 0.65, and if this laser had the same efficiency, it would nee an input power of 78 petawatts. It would also have to get rid of 27.3 petawatts of waste heat. Presumably this laser is a collection of lasers rather than a gigantic, monolithic system.
The laser would have to have a vanishingly good cost for what it does. As another, total thumbsuck, that would probably only be plausible once humans use 0.7 C spacecraft for pleasure cruises, let's say the operation of the laser for the duration of the flight is another trillion dollars.
The spacecraft will need maybe, 100 billion dollars to operate for each flight. The auxilliary landing shuttles, being larger yet more futuristic than STS, could maybe have an operating cost for the entire mission of 2 billion dollars each. Of course the base, the mine, the avatar program and the absurdly large private military that is operating is going to cost more, but I doubt it would be the same as the GDP of a small country. The Iraq war has cost 737 billion dollars, and the operation in the film seems to be a good deal smaller than a whole war.
So they can somehow get the cost of thousands of tons of antimatter down to a trillion dollars, the operating and power cost of a laser array that conjures notions of the Death Star down to a trillion dollars, and operate an interstellar spacecraft for a 100 billion, and various other things for another 50 billion, they could still make a profit of 2.8 trillion dollars.
However, how a society that is able to produce thousands of tons of antimatter, and run such a gigantic laser array is not able to make a simple chemical compound escapes me.
Of course, it's also possible that, due to the fact that the film is set in the future, and the future is portrayed as the ungodly love child of times square and a poor suburb of Soweto, 20 million USD might be 20 000 USD in today's money.
In that case, the entire operation would be far from plausible.
The ISS masses (at the time of posting) 369 914 kilograms, and has been estimated to have cost between 35-160 billion USD so far. This would be a cost per kilogram of $ 94 616.58.
This is in contrast with $ 54 750 for platinum, and $ 43 330 for gold. Of course, the ISS actually works and does stuff, whereas 369 914 kilograms of gold or platinum would just sit there.
As a space enthusiast, have you ever wondered how spaceflight would be motivated by a rare, extremely valuable resource somewhere else in space?
In Avatar, the rare mineral- unobtanium- that can only be found on the planet of the film's setting, 4.4 lightyears away from Earth, is said to cost 20 million USD back on Earth.
The interstellar spacecraft (called an ISV) shown in the film has a payload capacity of 350 tons. Let's be a bit pessimistic and say it's carrying 250 tons of unobtanium, and 100 tons of other stuff... such as the crates the unobtanium is shipped in, or other peripheral cargo.
That would be five trillion dollars.
The mass figures for the ISV are unfortunately absent. Let's say it masses 2500 tons, and it has the same dollars/kg value as the ISS. That would be a 236.5 billion dollar spacecraft.
We are never given thrust or ISP figures for the ISV, but from what I can make out the engines are some sort of hybrid between an antimatter-plasma core, and a photon drive (yeah... :shifty
. For simplicity's sake, let's assume it has the same performance as a proper antimatter beam core engine. For a dV of 0.7 C (the ISV's top speed), that is a mass ratio of 8.15. Assuming, again, that this is a beam core engine, that would mean 10187.5 tons of antimatter.Although other estimates of antimatter production are more pessimistic, considering that this is an interstellar spacecraft utilising large amounts of it, the optimistic estimates are probably best. With the $25 million/gram figure, that is 254.6 quadrillion USD, which is maybe a tad high. :facepalm:
Assuming the total cost of antimatter is a trillion USD, it would need to have a cost of 98 $/gram, and 98159.50 $/kilogram. Which is orders of magnitude lower than any real antimatter cost estimate.
However, the cost of antimatter depends on the cost of power, and if cheap fusion power were available, it could reduce the costs somewhat. One of the major uses of unobtanium is described by the director as integral to the construction of fusion powerplants, so this is conveniently self-explanatory.
The ISV refuels with deuterium and hydrogen mined from the atmosphere of Polyphemus (the parent planet in the film), but it is unclear if antimatter is produced there as well. Presumably the ISV cannot carry antimatter for it's return to Earth, but I would find the production of antimatter in such a remote location to be rather difficult.
However, the ISV is not accelerated and decelerated purely by the engines; it combines the use of engines with the use of a lightsail, pushed by lasers from our solar system.
To accelerate the the ISV (that we've now assumed is about 2500 tons in mass) at 1.5 G, one would need 340 meganewtons of force. Atomic Rockets says light sail power outputs and accelerations boil down to 6.7 newtons per gigawatt. In this case that is 50 746 268.65 gigawatts, or 50.7 petawatts.
That is 3171 times the power usage by the entire planet today. And around half of what it would take to become a type 1 civilisation. Earth's energy budget is 174 petawatts.
That is the output energy. The best experimental lasers have an efficiency of 0.65, and if this laser had the same efficiency, it would nee an input power of 78 petawatts. It would also have to get rid of 27.3 petawatts of waste heat. Presumably this laser is a collection of lasers rather than a gigantic, monolithic system.
The laser would have to have a vanishingly good cost for what it does. As another, total thumbsuck, that would probably only be plausible once humans use 0.7 C spacecraft for pleasure cruises, let's say the operation of the laser for the duration of the flight is another trillion dollars.
The spacecraft will need maybe, 100 billion dollars to operate for each flight. The auxilliary landing shuttles, being larger yet more futuristic than STS, could maybe have an operating cost for the entire mission of 2 billion dollars each. Of course the base, the mine, the avatar program and the absurdly large private military that is operating is going to cost more, but I doubt it would be the same as the GDP of a small country. The Iraq war has cost 737 billion dollars, and the operation in the film seems to be a good deal smaller than a whole war.
So they can somehow get the cost of thousands of tons of antimatter down to a trillion dollars, the operating and power cost of a laser array that conjures notions of the Death Star down to a trillion dollars, and operate an interstellar spacecraft for a 100 billion, and various other things for another 50 billion, they could still make a profit of 2.8 trillion dollars.
However, how a society that is able to produce thousands of tons of antimatter, and run such a gigantic laser array is not able to make a simple chemical compound escapes me.
Of course, it's also possible that, due to the fact that the film is set in the future, and the future is portrayed as the ungodly love child of times square and a poor suburb of Soweto, 20 million USD might be 20 000 USD in today's money.
In that case, the entire operation would be far from plausible.
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