140 Questioning the Universe: Concepts in Physics
orbit. For this speed, (u/c)
2
= (5/186,000)
2
= 7.2 × 10
−10
. This explains why
we do not experience time dilation in our ordinary lives.
4. When speeds get very close to c so that the ratio (u/c) gets close to 1.0, then
the difference between T and T
0
can be substantial. For instance, at a speed
of 150,000 miles/s, which is close to 80%, the speed of light (u/c = 0.8)
√{1 − (u/c)
2
} = √{1 − .8
2
} = √{1 − .64} = √.36 = 0.6
or
1/√{1 − (u/c)
2
} = 1/0.6 = 1.67
or
T = 1.67T
0
Let us make sure we understand the meaning of this result. If an observer
on rocket ship A measures a time of 1 min for some event that occurs on
his rocket, then observer B, who is on a rocket with a relative speed of 80%