It's a long way to Alpha Centauri

Classical Mechanics Level 3

Even though we have found an Earth sized planet around the nearest star Alpha Centauri B, we're not even close to getting there. To see this let's think about the duration of a flight to Alpha Centauri B, which is about \(4 \times 10^{16}~\mbox{meters}\) away. Imagine a rocket that accelerates at \(0.1g\) for the first two years of its travel before it runs out of fuel and coasts for the rest of the trip at constant velocity. How long does the total trip take in years? Note that the acceleration of our rocket is far beyond the reach of current technology - we're not close to interstellar travel anytime soon.

Details and assumptions

  • There are approximately \(3.15 \times 10^7~\mbox{seconds}\) in a year.
  • Use \(g=9.8~\mbox{m/s}^2\).
  • You can just use Newtonian mechanics.

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