How much energy is required to accelerate a spaceship with a rest mass of 108 metric tons to a speed of 0.566 c? Every day our Earth receives 1.55×1022 J energy from the Sun. If we were able to use 0.85 percent of this energy to accelerate spaceships, then how many missions would be possible in one year? Please show the math step by step in part A
1→Relativistic kinetic energy equation shows that the energy of an object approaches infinity as the velocity approaches the speed of light. Thus it is impossible to accelerate an object across this boundary.
relatistivic KE is:
KE = mc²(γ–1)
where,
γ = 1/√(1–V²/c²)
108 metric tons = 108000 kg
γ = 1/√(1–0.566²) = 1.213
KE = (108000 kg) * (3 * 10^8)² * (1.213 -1 )
KE = 2.07 * 10^21 Joules
2→
In one year we would receive = 1.55 * 10^22 * 365
= 5.6575 * 10^24 J
0.85 % of this is: 0.85* 10^-2 * 5.6575 * 10^24
= 4.8088 x10^22 J
If each mission requires the spaceship to accelerate to 0.566c then the total number of possible missions is:
(4.8088 * 10^22)/(2.07 * 10^21) = 23.226
That's a minimum of 23 missions in a year.
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