A small asteroid is 1 light year (in the earth’s frame) from earth and is traveling towards the earth at 0. At this time, scientists launch a missile…

A small asteroid is 1 light year (in the earth’s frame) from earth and is traveling towards the

earth at 0.85c. At this time, scientists launch a missile towards the rocket at a speed of 0.75c.

The missile is equipped with a timer that should cause the missile to explode when it reaches

the asteroid.

a) Taking the direction towards the asteroid to be the x-axis, with the earth at

x= 0, find the trajectory x(t) of the asteroid in the frame of the earth.

(b) What is the trajectory

x'(t’) of the asteroid in the missile’s frame? At what value of t’ does the the asteroid meet the missile at

x’= 0?

(c) What should the timer on the missile be set to for the earth to be saved?

(d) What is the velocity of the missile in the asteroid’s reference frame?