Velocity required to reach star in 10 onboard years

AI Thread Summary
To reach the Pleiades, located 130 parsecs away, in 10 years according to the onboard clock, one must calculate the required velocity as a fraction of the speed of light. The relevant equation involves time dilation, expressed as ΔT = γ ΔT₀, where γ is the Lorentz factor. The onboard observer experiences length contraction, which affects the perceived distance. The user is seeking guidance on how to set up the problem, particularly in applying the length contraction formula to determine the effective distance traveled. Clarifying the setup will enable them to perform the necessary calculations.
alanthreonus
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Homework Statement



You wish to travel to the Pleiades (at a distance of 130 pc) in 10 years, according to the clock
that you carry. How fast do you have to travel to accomplish this (express the velocity as a
fraction of speed of light, v/c)?

Homework Equations



<br /> \Delta T = \gamma \Delta T_0<br />

The Attempt at a Solution



I've been stuck on this for hours, and I really don't know how I'm supposed to set this up. If someone could just help me set it up, I can do all the calculations myself.
 
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d=vt. You know t=10 years. d can be found via the length contraction formula: to an onboard observer, the distance to the Pleiades seems contracted by a factor of gamma.
 
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