Exercise
https://texercises.com/exercise/distance-of-alioth/
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The following quantities appear in the problem: Länge \(\ell\) / Geschwindigkeit \(v\) /
The following formulas must be used to solve the exercise: \(\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \quad \) \(\ell = \frac{\ell_0}{\gamma} \quad \)
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Exercise:
In an Earth reference frame Alioth the third star in the handle of the Plough or Big Dipper is light years away. How fast would you have to travel so that to you the distance would be only light years?

Solution:
If the distance to the star must be reduced by a factor of gamma fracell_ell fraclzOlO fraclzl g you have to travel so fast that the velocity corresponds to this Lorentz-factor: v sqrt-fracgamma^ c . c &approx .e
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Exercise:
In an Earth reference frame Alioth the third star in the handle of the Plough or Big Dipper is light years away. How fast would you have to travel so that to you the distance would be only light years?

Solution:
If the distance to the star must be reduced by a factor of gamma fracell_ell fraclzOlO fraclzl g you have to travel so fast that the velocity corresponds to this Lorentz-factor: v sqrt-fracgamma^ c . c &approx .e
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Tags
contraction, einstein, length, lorentz, lorentz-transformation, physics, relativity, special, transformation
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Difficulty
(2, default)
Points
2 (default)
Language
ENG (English)
Type
Calculative / Quantity
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