Currently the world economy is $82 trillion on a purchasing power parity basis (2012. The IMF is forecasting economic growth through 2016 for a world economy of $103 trillion.
A world economy ten times larger will be a quadrillion dollar economy. Inflation and using future dollars will accelerate that milestone.
Increasing growth every 20 years Year flat 6% 6-11% 6-18% 2015 100 100 100 (trillions of dollars, World GDP PPP) 2020 134 134 134 2030 241 241 241 2.5 times energy 30K per cap 2040 431 474 571 3-4 times energy 50-70K per cap 2050 770 940 1390 5-10 times (10^14 watts, 100 terawatts) 80K-140K per cap 2060 1380 2000 4300 10-20 times energy 140K-430K per cap 2070 2500 4500 13700 15-40 times energy 250k-1.37 Million per cap 2080 4400 11600 56000 20-80 times energy 440K-5.6 M per cap 2090 8000 30000 230000 35-200 times energy 800K-23 M percap 2100 14000 86000 1200000 60-500 times energy (10^16 watts) 1.4M - 120 Million per cap
The highest growth rate path on the table (increasing 3% growth rate every 20 years, 6% for 2010-2030, 9% for 2030-2050, 12% for 2050-2070, 15% for 2070-2090 and 18% for 2090-2100). It would be an economy 12000 times larger than in 2015. Assuming increased energy efficiency relative to GDP generation, I am assuming they will only need about 500 to 1000 times more energy. This would need the energy of Kardashev level one. Kardashev one is about 100 Petawatts (10^17 watts).
Up through 2040-2060 the gains to the world economy come from some continued growth in the developed countries and China, India, South East Asia, and other countries catching up. The per capita assumes that world population grows to about 10 billion and then stays flat.
Assuming energy intensity of 10 megajoules/todays dollar and 10 billion people for a Kardashev level one civilization would mean $5.5 million dollars per person per year. Energy usage would be 55 terajoules per person (15.28 million kwh, 100 GW at 90% capacity factor produces about 800 billion kwh. 1.9 megawatts to generate the 15.28 million kwh)
Factory mass produced nuclear fission with deep burn closed fuel cycle and accessing the uranium and thorium in the ocean. This can be done without developing any space capability and lets you have a lot of power for a long time until you can get off your collective asses and into the solar system.
Deep burn fission could be pushed aggressively with factory mass production and deep burn for 60 times more efficient use of the uranium and tapping the uranium in phosphate and in the oceans to last through 2100 even in hypergrowth.
A nuclear reactor fleet of pure deep burn total of 17000GW would only use 6500 tons/year about 10% of current uranium usage. Increase to ten times our current uranium usage with deep burn and we could produce 100 times current world energy needs.
A yottawatt civilization would be roughly equivalent to a Kardashev 1.75 civilization. Fission, fusion and space solar can get a civilization to Yottawatt for long periods.
About 1 in 6500 hydrogen atoms in seawater is deuterium. Deuterium abundance on Jupiter is about 2.25×10^−5 (roughly 22 atoms in a million, or 15% of the terrestrial deuterium-to-hydrogen ratio.
There is enough water in the ocean to provide energy for 300 billion years at the current rate of energy consumption. It would provide 300 million years at 1000 times the current rate of consumption. The availability of Lithium on land is sufficient for at least 1000 if not 30000 years, and the cost per kWh would be even smaller than that of Deuterium.
Hall Weather Machine
A far better architecture for capturing the solar energy that hits the earth is the Hall weather machine.
The Hall Weather Machine is a thin global cloud consisting of small transparent balloons that can be thought of as a programmable and reversible greenhouse gas because it shades or reflects the amount of sunlight that hits the upper stratosphere. These balloons are each between a millimeter and a centimeter in diameter, made of a few-nanometer thick diamondoid membrane. Each balloon is filled with hydrogen to enable it to float at an altitude of 60,000 to 100,000 feet, high above the clouds. It is bisected by an adjustable sheet, and also includes solar cells, a small computer, a GPS receiver to keep track of its location, and an actuator to occasionally (and relatively slowly) move the bisecting membrane between vertical and horizontal orientations. Just like with a regular high-altitude balloon, the heavier control and energy storage systems would be on the bottom of the balloon to automatically set the vertical axis without requiring any energy. The balloon would also have a water vapor/hydrogen generator system for altitude control, giving it the same directional navigation properties that an ordinary hot-air balloon has when it changes altitudes to take advantage of different wind directions at different altitudes.
By controlling a tenth of one percent of solar radiation is enough to force global climate in any direction we want. One percent is enough to change regional climate, and ten percent is enough for serious weather control.
The surface are of the earth is 510 trillion square meters.
So getting to 0.1% coverage is 510 billion square meters.
There is mylar that is 2 microns thick and weighs about 2.4 grams per square meter. Office Paper is usually 80 grams per square meter.
There is plastic sheeting with 0.3-0.9 micron thickness and weights of 0.54 to 1.2 grams per square meter.
US plastic film demand was expected to be about 7.3 million tons in 2012
So if you could achieve large scale production (equal to 1% of total US plastic film production in 2012) of 1 gram per square meter balloon sheeting with a diamond surface treatment and the other parts of the system there would be 73,000 tons of weather machine produced. This would cover 73 billion square meters. In about 8 years, one would be able to produce a 1% coverage Hall Weather Machine.
The production system would be a more advanced version of bubble wrap production. Each bubble would be functionalized and perhaps laser cut into separate balloons. Rapid printable electronics would probably be the best way to get the solar cell and GPS components into the bubble/balloon. The printable electronics would need to be scanned onto the surface of the sheet, before the top layer is attached.
With better than todays nanotechnology one could easily produce a more advanced version of the hall weather machine. It is a weather machine and a means to use not that much material to get to Kardashev level one.
A combination of hall weather machines in the stratosphere, nuclear fusion and deep burn nuclear fission would be plenty for a Kardashev level one civilization for millions of years and could handle hyper economic growth well past 2100.
Small steps to getting started space based solar
Earth Orbit Space based solar can also be developed. The first gigawatts of space based solar can be used to lower the costs of launching into space.
Statites and Kardashev scale space based solar
When we have moderately better nanotechnology that is able to produce carbon solar sails/solar power collectors/statites that are about four times lighter than we can make now and produce and launch (or produce in space) 100,000 to 1 million tons of it and get it in close to the sun and transmit and use the power then would be making modules of energy equal to Kardashev level one for each load of statite collectors. It would be early molecular manufacturing capability or good high volume carbon nanotube and graphene capabilities. The amount of material would be about 20,000 times less than the surface area of the earth or about 10,000 square miles.
Kardashev level 2 is about 10^26 Watt. One billion times more than Kardashev level one. So the lightweight statites would be built in 100,000 to 1 million ton modules to build step by step (or many steps at once) towards Kardashev level 2.
Well before Kardashev level one in the 2040-2060 timeframe, moving around the solar system will become trivial. Ten thousand spaceships able to move a few hundred people at a time would have the capability that we now have to transcontinental movement. In that time frame, with molecular nanotechnology and nuclear fusion for energy and space propulsion the construction capabilities to build nuclear fusion, deep burn nuclear fission and space based solar all over the solar system with the resources of the solar system means that it will be clear sailing to Kardashev level two. Those capabilities will make it trivial to go interstellar.
Year 18% per year growth (in quintillion $ of GDP) 2100 1.2 (and about 10 petawatts, 10^16 watts. ) 2110 6.3 2120 32.9 2130 172.0 2140 900.5 2150 4,712.8 2160 24,666.2 2170 129,098.7 2180 675,681.2 2190 3,536,404.2 2200 18,508,958.3 2210 96,872,843.9 2220 507,016,534.8 2230 2,653,641,166.4 2240 13,888,721,483.5 (around 10^26 watts. Kardashev level 2)
Kardashev Level 2+ civilizations could manage their stars
The list of nearest stars contains all known stars and brown dwarfs at a distance of up to five parsecs (16.308 light-years) from the Solar System. In addition to the Solar System, there are another 51 stellar systems currently known lying within this distance. These systems contain a total of 61 hydrogen-fusing stars and 9 brown dwarfs
Giant stars can produce 100 to 1000 times the energy output of the Sun.
Expanding energy by about 10000 times in 300 years. Using the energy of the stars in a 100 light year radius.
Expanding energy by another 100 million times in 300,000 years. Using the energy of the stars (the whole galaxy) in a 80,000 light year radius. The whole Milky Way galaxy is 100,000 to 120,000 light years in diameter. Earth is about 27,000 light years from the center. The assumption for 300,000 years if to colonize and build Dyson bubbles by moving out at a little faster than 25% of light speed. Spaceships would fly out and place molecular technology building satellite seeds and continue without stopping.
The economic growth rate would slow to a little less than 1% per year. 1% growth per year for 1000 years would be a 20,959 times increase.
One of many assumptions is that no new energy is developed via a more advanced physics and technology. Something like tapping into vacuum energy or extra dimensional power or the creation and control of blackholes.