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RJLiberator
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Homework Statement
The International Space Agency is designing a spaceship to reach the star Proxima Centauri, 4 cyrs (light years) away so that the on-board crew will age 4 years from departure to arrival. How fast must the ship travel?
Homework Equations
t(moving clock) = t(stationary clock)*sqrt(1-V^2/c^2)
t(between ship light clock ticks to us) = 2D/(sqrt(c^2-V^2)) = t(between ticks of our own light clock)/(sqrt(1-V^2/c^2))
The Attempt at a Solution
We must identify which frames we are in.
We are wondering how fast the ship must travel, V, to people on Earth.
The crew must age 4 years, so we take t' = 4 years, the time it takes for the crew to age (ship frame).
The ship must travel a distance of 4 c*yrs, which is in the Earth frame, so we say L = 4c*yrs.
This seems like insufficient information.
L = 4c*yrs
V = ?? unknown, need.
t = unknown
t' = 4 years
V' = ??
L' =?
I suppose, if I can say L' = 4 c*yrs, then I can say that the speed the ship is going at is c (speed of light), but then the equations start to break down so that seems like a dead end.
I know that the time of the clock on the ship must be a shorter time change than that of Earth frame.
Is there anything that I am stating as false?