8-16. A spaceship transporting passengers bound for a planet in the Vega system leaves Earth at speed (3/5)c, when both its clock and the clock on Earth read 1-0. Twenty weeks later, according to their own clock, Earthlings realize that a saboteur may be aboard the ship, so thcy immediately transmit a radio message at v-c toward the ship, informing the ship of their suspicion. Upon receiving the message, the ship's computer immediately discovers the saboteur lurking in one Chapter 8 / The Lorentz Transformation of the ship's lifeboats, so instantly fires the lifeboat at speed (35/37)c relative to the ship, back toward Earth, returning the saboteur to stand trial. (a) Draw a series of four pictures in Earth's reference frame, illustrating the important events in the story. Then, calculating in Earth's frame, answer the following. (b) What does the ship-clock read (in weeks) when Earth sends the original message? (c) How far is the ship from Earth (in light-weeks) when the message is sent? (d) What does the Earth's clock read (in weeks) when the ship receives the message? (e) What does the ship's clock read when it receives the message? (f) How far is the ship from Earth when it receives the message? (g) How fast does the lifeboat travel in Earth's frame of reference? (h) What does Earth's clock read when the lifeboat arrives? (i) Suppose the lifeboat clock reads zero when it is launched from the ship. What time does it read when it reaches Earth? (j) How much younger is the saboteur than she would have been had she stayed on Earth instead of going off on the ship and returning in the lifeboat?