On this page, we will revisit the Asteroid problem. We will have a spaceship moving at half the speed of light towards the right. You can change that velocity by moving the upper blue point. The “asteroid” is 3 units long in the unprimed system.
Position 1: We start at the time –9 time units in the unprimed system.
The coordinate systems have a common origin at the point where the spaceship passes in front of the asteroid. At that moment, according to the frame of reference of the asteroid, two lanterns, one at each end of the asteroid, will flash.
The simulation looks something like this:
- Move the movable point at (7, 9) to the spaceship’s position, and read off the time:
- In the primed system.
- Find the same time using some appropriate calculations.
The green line is the x-axis, the now-axis according to the spaceship. Now, we can start the time by clicking the Move button.
Position 2: The time will tick on until the moment the people in the Spaceship think that the right lantern has flashed. It’s not the moment when people on the spaceship will see the flash. It’s the moment that the people on the Spaceship will think the right lantern flash. It will still take a while before they see it. The light will go from (0, 3) to (1, 2).
- Find the time when the light from the rightmost flash reaches the spaceship:
- According to the people in the Aseroid, and
- According to the people in the Spaceship.
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