Question

A)How much energy is required to accelerate a spaceship with a rest mass of 131 metric tons to a speed of 0.594 c?

B)Every day our Earth receives 1.55×10²² J energy from the Sun. If we were able to use 0.95 percent of this energy to accelerate spaceships, then how many missions would be possible in one year?

Answer 1

A

K = γ* m₀*c² - m₀*c² = m₀*c² (  γ -1)

γ = 1/sqrt( 1-v²/c² )

= 1/sqrt( 1-0.594^2) =1.2430621

K = 131*10^3*(3*10^8)^2*(1.2430621 -1)

K = 2.865*10²¹ J

B)

Every day our Earth receives 1.55×10²²

useful energy in one day =0.95/100 * 1.55*10^22 J

in one year = 0.95/100 * 1.55*10^22 *365 J =5.374625e22 J

number of mission we can send by this energy

= total energy received / energy required in one mission

= 5.374625e22 / ( 2.8657021*10^21)

=18.7550025 ship

= 19 ship answerr