440
Relativity
P39.15
(a)
Since your ship is identical to his, and you are at rest with respect to your own ship, its
length is
20 0
.
m
.
(b)
His ship is in motion relative to you, so you measure its length contracted to
19 0
.
m
.
(c)
We have
L
L
v
c
p
=
−
1
2
2
from which
L
L
v
c
p
=
=
=
−
19 0
0 950
1
2
2
.
.
m
20.0 m
and
v
c
=
0 312
.
.
*P39.16
In the Earth frame, Speedo’s trip lasts for a time
∆
∆
t
x
v
=
=
=
20 0
21 05
.
.
ly
0.950 ly yr
yr .
Speedo’s age advances only by the proper time interval
∆
∆
t
t
p
=
=
−
=
γ
21 05
6 574
.
.
yr
1
0.95
yr
2
during his trip.
Similarly for Goslo,
∆
∆
t
x
v
v
c
p
=
−
=
−
=
1
20 0
1
0 75
17 64
2
2
2
.
.
.
ly
0.750 ly yr
yr .
While Speedo has landed on Planet X and is waiting for his brother, he ages by
20 0
20 0
5 614
.
.
.
ly
0.750 ly yr
ly
0.950 ly yr
yr
−
=
.
Then
Goslo
ends up older by
17 64
6 574
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 Fall '11
 Staff
 Physics, General Relativity, Spacetime, Yr, Speedo

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