When the spacecraft's fusion efficiency is 0.01%, the spacecraft's fusion fuel is 1t, and the total

Azzalictpdv 2022-05-10 Answered
When the spacecraft's fusion efficiency is 0.01%, the spacecraft's fusion fuel is 1t, and the total mass of the spacecraft is 1.2t, the friend bet the final speed of the spacecraft is 80% of the speed of light. The state of the fuel at nuclear fusion is assumed to be D + T and 0.01% of the maximum energy of the fusion of the fuel, although the fusion method has not yet been firmly determined. I am curious about the answer of the final speed of this space ship.
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Answers (1)

Superina0xb4i
Answered 2022-05-11 Author has 17 answers
Restating the numbers to make sure they're right:
- After burning the fuel, the remaining mass is 200kg
- Of the 1000kg of fuel burned, 0.1kg (0.01%) is turned into kinetic energy of the remaining mass.
If so, here's how you calculate the result:
γ = E / m = 200.1 / 200 = 1.0005
From γ = 1 / 1 v 2 / c 2 , we get v 2 / c 2 = 1 1 / γ 2
Plugging in the numbers:
v = c 1 1 / 1.0005 2 = 0.032 c or about 9,500 km/sec.
Fast, but not 0.8c. That would require γ = 1.67, which in turn requires a much higher efficiency and more fuel.
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