This problem is shamelessly taken from Taylor and Wheeler's book Spacetime Physics with only small modifications.
This project must be done by individuals. You must hand in a printed copy of your work to me by the scheduled time, or place it in the mailbox outside my office door.
You are standing alone at dusk, with the setting Sun and planet Venus low in the western sky, and the full Moon rising above the Eastern horizon. A spaceship approaches from the East and lands next to you. The aliens who step out of it tell you that they come from a distant planet which lies due East, far beyond the rising Moon. They have been travelling straight to Earth, with a speed such that their "gamma" factor during the trip was gamma = 5/3.
At the instant the aliens land, you notice the Sun change color to an eerie purple. The aliens admit that earlier, on their way to the Earth, they accidently fired a powerful laser towards the Sun which caused the Sun's outer layers to explode. "Sorry," they say. The aliens warn you that the explosion sent out a powerful pulse of energetic particles, travelling at half the speed of light, which will destroy the Earth when they reach it. As they are talking, you notice that the planet Venus suddenly changes color. "See what we mean?" say the aliens.
You ask the aliens if they can take you and your little dog Toto away with them before the Earth is destroyed. They agree, and you all hop into their spaceship. They point the ship due East, away from the Sun, and plan a course at their top speed, which will yield gamma = 25/7. The ship takes off exactly 7 minutes after it landed on the Earth next to you.
Do you (and the aliens, and Toto) make it safely out of the solar system? Explain in detail.
Make a space-time diagram to illustrate the events in this story.
This page maintained by Michael Richmond. Last modified Oct 12, 2008.