Autotheist's Science Corner

Lesson 4 - An Example

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
T_e = (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.