Question

Chapter 05, Problem 090 An interstellar ship has a mass of 8.43 × 106 kg and is initially at rest relative to a star system. (a) What constant acceleration is needed to bring the ship up to a speed of 0.084c (where c is the speed of light, 3.0 × 108 m/s) relative to the star system in 2 days? (b) What is that acceleration in g units (enter the answer in the form N g, where N is a number)? (c) What force is required for the acceleration? (d) If the engines are shut down when 0.084c is reached (the speed then remains constant), how long (in s) does the ship take (from that point on) to journey 9 light-months, the distance that light travels in 9 months? Assume a month has 30 days.

Answer 1

(a)

2 days = 2days x 24hrs/day x 60min/hr x 60 seconds/min = 172800 sec

acceleration = v/t = (0.084 * 3 x 10^8)/172800 = 145.83 m/sec^2

(b)

1 g = 9.806 m/sec^2

Thus:

145.83/9.806 = 14.87 g

(c)

F = M X A = 8.43 x 10^6 x 145.83 = 1.23 x 10^9 newtons

(d)

during the 2 days of constant acceleration, the ship averages 1/2 of its final speed.

it travels 0.084 x 2 x 1/2 = 0.084 light days during those 2 days

the remaining (30*9) - 0.084 = 269.916 light days will require 269.916 days

for a total of 269.916 + 2

= 271.916 days

= 271.916 * 24 * 60 * 60 s

= 23,493,542.4 s