Velocity required to reach star in 10 onboard years

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SUMMARY

To travel to the Pleiades, located 130 parsecs away, in 10 onboard years, a spacecraft must achieve a velocity expressed as a fraction of the speed of light (v/c). The relationship between time experienced onboard and the distance traveled is governed by the time dilation equation, ΔT = γΔT₀, where γ (gamma) represents the Lorentz factor. The onboard observer perceives the distance contracted due to relativistic effects, necessitating the use of the length contraction formula to determine the effective distance. Accurate calculations require understanding of both time dilation and length contraction principles in special relativity.

PREREQUISITES
  • Understanding of special relativity concepts, including time dilation and length contraction.
  • Familiarity with the Lorentz factor (γ) and its calculation.
  • Basic knowledge of distance measurement in parsecs.
  • Ability to manipulate and solve equations involving velocity and distance (d=vt).
NEXT STEPS
  • Study the derivation and implications of the Lorentz factor (γ) in special relativity.
  • Learn how to apply the length contraction formula in relativistic contexts.
  • Explore practical examples of time dilation in high-velocity scenarios.
  • Investigate the implications of traveling at relativistic speeds on spacecraft design and mission planning.
USEFUL FOR

Students of physics, particularly those studying special relativity, astrophysicists, and anyone interested in theoretical space travel and relativistic effects.

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



[tex] \Delta T = \gamma \Delta T_0[/tex]

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.
 
Physics news on Phys.org
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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