What Is the Meteor's Altitude Due to Length Contraction?

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SUMMARY

The discussion centers on calculating the altitude of a meteor as perceived by an observer on Earth versus an alien on the meteor, utilizing the principles of length contraction in special relativity. The Earth observer measures the meteor at an altitude of 650 meters while it travels at 0.92c. The correct approach involves using the formula L = Lo / γ, where Lo is the proper length (650m) and γ is the Lorentz factor. The conclusion is that the two inertial frames are not identical, leading to differing measurements of altitude due to relativistic effects.

PREREQUISITES
  • Understanding of special relativity concepts, particularly length contraction.
  • Familiarity with the Lorentz factor (γ) and its calculation.
  • Basic knowledge of inertial frames of reference.
  • Ability to apply mathematical formulas in physics contexts.
NEXT STEPS
  • Study the derivation and implications of the Lorentz factor (γ).
  • Learn about the principles of relativistic length contraction in detail.
  • Explore examples of relativistic effects in different inertial frames.
  • Investigate the relationship between speed and time dilation in special relativity.
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Students of physics, educators teaching special relativity, and anyone interested in understanding relativistic effects on measurements in different frames of reference.

debroglieman
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An observer on Earth sees a meteor approaching rapidly, heading directly for the Earth's surface. At a certain instant, the Earth observer sees the meteor at 650m altitude. If the meteor is traveling at 0.92c, as recorded by an Earth radar, what would be the altitude as measured by the alien resting on the meteor?



L=Lo (ɣ)



I know the solution is to plug in Lo = 650 and solve for L, but not know why this is so. It seems that the two inertial frames are identical, and as such the answer should be 650m? Advice/solution appreciated.
 
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No. The inertial frames are (not) identical (but symmetric), but measurements from them disagree anyway, such as those of distance. Remember that lengths appear* to change from frames of reference moving WRT the object whose length is being measured.

*for lack of better wording
 
Okay, so how do I know what is Lo and what is L?
 

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