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 32 years during the round trip. A) How fast (v) must the rocket travel relative to earth? B) How much energy is needed to accelerate the rocket to this speed? C) How many times larger is this energy than the total energy used by the United States in the year 2000, which was roughly 1.0×1020J?

Explanation / Answer

A)  l/v = 20 years,

so by solving, sqrt(1-v^2/c^2) 430ly / v = 20 years,==> v=0.99973c

B) KE = Mvc = mvc/sqrt(1 - .99973^2) = 20000*.99973*(299E6)^2/sqrt(1 - .99973^2) = 7.69285E+22 J when v = .99973c is the end speed after accelerating.

NOTE: M is relativistic inertia and KE = Mvc is the change in kinetic energy and work applied based on M.

C) That's roughly 100 X's the US annual 2000 use if your number is correct. But, this is important, this assumes 100% efficiency, which is of course impossible.

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