Question

How much energy is required to accelerate a spaceship with a rest mass of 126 metric tons to a speed of 0.589 c?
Every day our Earth receives 1.55×10²² J energy from the Sun. If we were able to use 1.05 percent of this energy to accelerate spaceships, then how many missions would be possible in one year?

Answer 1

FOr the energy needed

energy needed to accelerate = total energy - rest energy

energy needed to accelerate = m * c^2 - m0 * c^2

energy needed to accelerate = m0 * c^2/sqrt(1 - (v/c)^2) - m0 * c^2

energy needed to accelerate = 126 * 1000 * (3 *10^8)^2 * (1/sqrt(1 - 0.589^2) - 1)

energy needed to accelerate = 2.69 *10^21 J

the energy needed to accelerate is 2.69 *10²¹ J

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let the number of missions needed in one year is N

N * energy of each mission = total energy received at earth

N * 2.69 *10^21 = 1.55 * 10^22 * 0.0105

solving for N

N = 0.061

the number of mission taken in one year is 0.061

hence, 0 missions per year are possible