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The record for the fastest speed at which anyone has ever traveled, relative to the Earth, is held by the Apollo X modue at 24,791 mi/h on their return trip from the moon.

At this speed, what is the percent difference between the clocks on the Apollo and the clocks on Earth?

OK, I think I understand how to do the problem, but I'm not getting the answer that our text gives.

I set the moving IRF as the Apollo and the stationary frame as the Earth.

I then found the time elapsed in the frame of the spaceship by using d=vt and the given velocity and the distance from the earth to the moon.

So:

V_{Apollo}=V=24,791mi/h=11082.3m/s

d_{(Earth to Moon)}=3.84x10^8 m

With no time dilation for the ship, the time elapsed then is:

from d=vt: t_{Apollo}=t'=3.84x10^8 m/11082.3m/s = 34649.85 s

I then found the time dilation for the time elapsed in Earth's reference frame using Lorentz tranformation:

t=t^{'}/[tex]\sqrt{1-(V/c)^2}[/tex]

gives an elapsed time in Earth' IRF of 346449.85s

and 346449.85s/34649.85s = 9.985%

The correct answer is 6.82x10^-8 s

Could someone help me figure out where I went wrong? I went over the math a few times, so it must be my logic...

Thanks!

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# Homework Help: Time Dilation question

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