The visible disk of our Milky Way galaxy is about 10° light-years in diameter. A cosmic-ray proton enters the galactic plane with speed v = 0.99c. How long would it take the proton to cross the galaxy from our point of view? What would be the corresponding time if measured from proton's frame? How wide is the galactic plane to the proton, in its direction of motion? 

In order to prolong one's life, observer A starts a journey leaving observer B behind. If A moves a round trip at the steady rate of 5 x 10²m/s for 102s according to the clock of B, how much less have A aged than B?

The distance of a star from the Sun, as measured in the rest frame of the Sun and star, is 5.3 light-years. Consider a spaceship that departs the solar system at a speed c bound for the star, when the two clocks: one at the Sun and the other at the spaceship, are synchronized at t = 0.

Calculate the time of arrival of the spaceship in the rest frame of the Sun:

(a) as measured by the Sun clock. 

(b) as measured by the spaceship clock.