Question

Assume that 437 days is a reasonable limit for how long a human can endure constant-velocity space travel. Proxima Centauri, the star closest to our Sun, is 4.24 light years away from Earth. Part A If you wanted to fly to Proxima Centauri within the 437-day limit in a rocket of mass 1.50×106 kg , how much energy would be required to accelerate the rocket to the necessary speed in the Earth reference frame? For this rough estimate, ignore the energy required to stop, and disregard the hundreds of days required at each end of the journey for acceleration. Express your answer with the appropriate units. Part B Compare your answer with 0.6× 1021J, the yearly worldwide energy consumption predicted for 2015.

Answer 1

The distance between Earth and Proxima Centauri, d = 4.24 light years

d = 4.011 * 10^16 m

Ttime taken , t = 437 days

= 437 * 365 * 24*3600

t = 1.38*10^10 s

the speed of the rocket , v = d/t

v = 4.011 * 10^16 / ( 1.38 * 10^10)

v = 2.91 * 10^6 m/s

the energy required , E = 0.5 * m * v^2

E = 0.5 * 1.3 * 10^6 * (2.91 * 10^6)^2

E = 5.5 * 10^18 J

the energy required is 5.5 * 10^18 J

the yearly worldwide energy consumption predicted for 2015 ,

E' = 0.6 * 10^21 J

E/E' = 5.5 * 10^18 J /( 0.6 * 10^21 J)

E/E' = 9.17 * 10^-3