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https://texercises.com/exercise/alien-spaceship/
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The following quantities appear in the problem: Zeit \(t\) / Geschwindigkeit \(v\) / Strecke \(s\) /
The following formulas must be used to solve the exercise: \(s = vt \quad \) \(\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \quad \) \(t = \gamma t_0 \quad \)
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Exercise:
An alien spaceship from Sirius laO covers the distance to Earth in taO of its proper time. Calculate the Lorentz factor and the time the journey take as measured from an observer on Earth. vspacemm Interpret the result in both reference frames spaceship and Earth.

Solution:
For an observer at rest with respect to the Earth the distance to Sirius proper length can be expressed as lambda v t beta c gamma tau ctausqrt-fracgamma^gamma ctausqrtgamma^- It follows for the Lorentz factor gamma gaF sqrt+leftfraclactimestaright^ resultgaP The time for an observer in the rest frame of the Earth is t tF gatimesta resulttP In the reference frame of the Earth a trip from Sirius to Earth cannot be shorter than tminP travel time at the speed of light. The result reflects this fact. In the reference frame of the spaceship the distance to sirius is elllambda/gammalP. This is much shorter than laO so the travel time can be less than tminP.
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Exercise:
An alien spaceship from Sirius laO covers the distance to Earth in taO of its proper time. Calculate the Lorentz factor and the time the journey take as measured from an observer on Earth. vspacemm Interpret the result in both reference frames spaceship and Earth.

Solution:
For an observer at rest with respect to the Earth the distance to Sirius proper length can be expressed as lambda v t beta c gamma tau ctausqrt-fracgamma^gamma ctausqrtgamma^- It follows for the Lorentz factor gamma gaF sqrt+leftfraclactimestaright^ resultgaP The time for an observer in the rest frame of the Earth is t tF gatimesta resulttP In the reference frame of the Earth a trip from Sirius to Earth cannot be shorter than tminP travel time at the speed of light. The result reflects this fact. In the reference frame of the spaceship the distance to sirius is elllambda/gammalP. This is much shorter than laO so the travel time can be less than tminP.
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special relativity
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lorentz factor, time dilation
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ENG (English)
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Calculative / Quantity
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