Elon Musk
c.ai
To reach 1% of c, the ship would need approximately 750 tons of antimatter. This would be sufficient to produce over 4 trillion joules of energy, which should be more than enough to accelerate to 1% of c, assuming constant thrust is applied. Of course, as you approach the speed of light, relativity would become a factor and the amount of energy needed to reach a particular velocity would increase exponentially, so the exact amount of antimatter needed to obtain 1% of c would depend on the rate of acceleration being applied.
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ScottBaker
Assuming we start with 1lb of antimatter from the Earth-based particle accelerator, then transfer it to the magnetic containment field at the front of the spaceship at a point when traditional chemical-based rockets have already propelled it safely out of Earth's orbit, how much energy would be left over for propulsion after capturing the energy from the initial 1lb matter-antimatter explosion to make more antimatter?
Elon Musk
c.ai
The energy released by one pound of matter-antimatter annihilation is equivalent to about 18 megatons of TNT. So, assuming a conversion efficiency of 100% (which is not realistic, but for the sake of simplicity, let's say it is for the time being), the spaceship would be left with about 17.7 megatons of energy for thrust, which would be enough to accelerate to about 35% the speed of light. The problem with reaching this level of speed is that relativity becomes a significant factor at extremely high speeds and the energy required to reach such speeds begins to increase dramatically.
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ScottBaker
Factoring in relativity, and also that we can only accelerate up to 1G so as not to crush the human inhabitants of the spaceship, how much of C could we achieve this way?
Elon Musk
c.ai
If we are being realistic, and considering the effects of relativity as we approach the speed of light, the amount of mass of the ship will become more and more significant and the energy required to accelerate it will grow exponentially with velocity. This would mean that with a constant rate of acceleration at 1G, we could probably only reach about 50% of C before the energy requirements for continued acceleration become truly astronomical. The upside is that time dilation would also become a factor, so time from the point of view of someone on the ship would seem to slow down exponentially at these speeds, and even more exponentially as we approached C.
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