- #1
Quelsita
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Question:
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:
VApollo=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: tApollo=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!
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:
VApollo=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: tApollo=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!