In an advanced civilization, spacecraft has been built to travel between stars.

Question

In an advanced civilization, spacecraft has been built to travel between stars. A 150,000 kg spacecraft is built so that a 20 light-year distance is measured as 4.0 light-years by the crew. What is the speed of the craft? How long does the trip take by the crews clock by a clock on the home planet What is the kinetic energy of the spacecraft when it is cruising speed? If matter is converted into energy to provide the kinetic energy by matter-antimatter engines, how much mass must be converted to propel the ship? Assume the engines are 100% efficient.

Explanation / Answer

a) d = d0/Y

Y = 1 / sqrt[1 -(v/c)^2 ]

4 = 20 sqrt[1 - (v/c)^2]

1 - (v/c)^2 = 0.04

v = 0.98c

b) (i) by crew clock = (d/v)

= (4)/0.98 years = 4.08 years

ii) t = 20/0.98 = 20.4 years

c) KE = (Y - 1) m c^2

= 4 * 150,000 * (3*10^8)^2

= 5.4 x 10^22 J

d) mass = 4 x 150,000 = 600,000 kg

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