If we assume the meter class telescope + power supplies and whatever else masses ~ 1 metric ton, it would take 1,853,298,442,530,598,439 Joules - 1.8 quintillion - 1.853 * 10^18 - to accelerate it to .2c. Only ~ 442 Megatons of TNT. Keep in mind, that is assuming 100% efficiency, which would be impossible with a light sail or any other known technology.
With all the various inefficiencies in power collection/generation, laser generation, momentum/power transfer, etc. we'd be talking probably somewhere around 5% end-to-end power transfer - if we were lucky. Which is still way better than the rocket equation (probably).
So to get the required 1.853 * 10^18 J at 5% efficiency, we'd need say 20x more power at earth to accelerate it (if 5% efficiency). So 3.706 * 10^19 J. Which starts get more concerning, at 8,840 gigatons of TNT.
Let's take the most efficient means we can imagine to produce energy, direct matter annihilation. Annihilating 1KG of mass (using 500g of Anti-matter, 500g of Matter) produces 8.986 * 10^16 J of energy. If we could somehow feed the resulting energy directly into the laser for accelerating the craft, and assume near 100% efficiency in doing so, before laser losses - we'd only need roughly 1000 KG of matter/anti-matter to do so.
Not bad!
But wait, our more likely end-to-end efficiency is at best 1%. Hmm. Which would require 100 times the input energy to spacecraft acceleration. 44 Gigatons of TNT or 1.853 * 10^20 J.
5KG of matter/antimatter.
Which is definitely not a significant fraction of earths mass, but yikes. I wouldn't want to pay that energy bill!
51,480,512,292,500 kWh (the 'wall plug equivalent') at my current rates would be $26 trillion dollars!
With all the various inefficiencies in power collection/generation, laser generation, momentum/power transfer, etc. we'd be talking probably somewhere around 5% end-to-end power transfer - if we were lucky. Which is still way better than the rocket equation (probably).
So to get the required 1.853 * 10^18 J at 5% efficiency, we'd need say 20x more power at earth to accelerate it (if 5% efficiency). So 3.706 * 10^19 J. Which starts get more concerning, at 8,840 gigatons of TNT.
Let's take the most efficient means we can imagine to produce energy, direct matter annihilation. Annihilating 1KG of mass (using 500g of Anti-matter, 500g of Matter) produces 8.986 * 10^16 J of energy. If we could somehow feed the resulting energy directly into the laser for accelerating the craft, and assume near 100% efficiency in doing so, before laser losses - we'd only need roughly 1000 KG of matter/anti-matter to do so.
Not bad!
But wait, our more likely end-to-end efficiency is at best 1%. Hmm. Which would require 100 times the input energy to spacecraft acceleration. 44 Gigatons of TNT or 1.853 * 10^20 J.
5KG of matter/antimatter.
Which is definitely not a significant fraction of earths mass, but yikes. I wouldn't want to pay that energy bill!
51,480,512,292,500 kWh (the 'wall plug equivalent') at my current rates would be $26 trillion dollars!