Relativity : Traveling to Andromeda galaxy

AI Thread Summary
To determine the speed required for an astronaut to travel to the Andromeda galaxy in 30 years of spaceship time, the concepts of length contraction and time dilation from relativity must be applied. The astronaut needs to account for the distance of 2 million light years and the effects of traveling at relativistic speeds. By using the equations for length contraction (L = L_0/γ) and time dilation (ΔT = γΔT_0), the astronaut can relate the proper distance and time experienced on the spaceship to the distance and time measured from Earth. The challenge lies in correctly equating these equations to find the necessary speed. Assistance is requested to clarify how to set up these calculations effectively.
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Homework Statement


An astronaut wishes to visit the Andromeda galaxy 2 million light years from Earth. He wishes the one way trip to take him 30 years (ie in the frame of reference of the spaceship). Assuming that his speed is constant, how fast must he travel?


Homework Equations


L = L_0/\gamma
\Delta T = \gamma \Delta T_0


The Attempt at a Solution


I know that by increasing velocity of the spacecraft , you can effectively length contract the distance between Earth and the galaxy, however, i do not know how i should equate the equations. Any help will be greatly appreciated.
 
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