In an attempt to reduce the extraordinarily long travel times for voyaging to di

Question

In an attempt to reduce the extraordinarily long travel times for voyaging to distant stars, some people have suggested traveling at close to the speed of light. Suppose you wish to visit the red giant star Betelgeuse. which is 430 ly away, and that you want your 20.000 kg rocket to move so fast that you age only 36 years during the round trip. How fast, as a fraction of c, must the rocket travel relative to earth? Express your answer to five significant figures. v/c = How much energy is needed to accelerate the rocket to this speed? Express your answer with the appropriate units. E_rocket = Compare this amount of energy to the total energy E$ used by the United States in the year 2015, which was roughly 1.0 times 10^20 J.

Explanation / Answer

a)

T = 36 yrs

v = speed

To = distance / speed = 2 x 430 cy/v = 860 /(v/c)

using the equation

T = To sqrt(1 - (v/c)2)

36 = 860 /(v/c) sqrt(1 - (v/c)2)

v/c = 0.99

B)

E = mc2 / sqrt(1 - (v/c)2)

E = 20000 (3 x 108)2 /sqrt(1 - (0.99)2)

E = 1.29 x 1022 J

b)

E/Eo = (1.29 x 1022)/(1 x 1020 ) = 129

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