At this point, to clear any confusion, we will
work out an example. Suppose an astronaut decides to fly to Pluto
from Earth (a distance of 6x1012 m) at about 0.5 c (k
= 1.73).
According to the astronaut, the time he travels satisfies:
6 x 1012 = ( k - 1/k) c T / 2
Solving gives T = 9.7 hours. On Earth the time when the astronaut
lands is
Te = (k+1/k)T/2 = 11.2 hours
So the astronaut has aged 1.5 hours less than the people on
Earth. If the astronaut then returns to Earth at the same speed,
he will have aged 19.4 hours, while everyone on Earth has aged
22.4 hours, a difference of 3 hours!.
Suppose that while orbtiting Pluto, the
astronaut launches a probe which travels at 0.5 c.
Nonrelativistic physics states that the probe travels at the
speed of light, but this is cannot be!.
Using the equation previously derived, the k-factor relating time
on the probe to time on Earth is k = (1.73)x(1.73) = 2.99. Then
the people on Earth claim that the speed of the probe is:
v = ( k - 1/k ) c / ( k + 1/k) = 0.8 c
So to people on Earth the probe travels at 0.8 c.
Lesson 5