Question

An astronaut moves away from earth at a speed of light. If an observer on earth measures the astronaut's size what change would he or she measure? Would the astronaut measures any change?

Answer 1

The speed of astronaut relative earth is at a speed of light. The astronaut's size is
L=L_0 √(1-c^2/c^2 )=0.
Thus, an observer on earth cannot see astronaut now.
Also, the astronaut cannot measure any change because he is situated in his own rest frame.