Previous page : Space-Time diagrams / Minkowski diagrams
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 Asteroid, and
- According to the people in the Spaceship.
- At what distance will the right flash be according to the people in the spaceship?
- Find this by using the movable point.
- Find this by using suitable calculations.
Position 3: Here, the origin of the two systems overlaps, and it is also when the two lanterns will flash according to the people on the asteroid. For the people on the spaceship, it is the time the left lantern flashes. According to the people on the asteroid, the lantern flashes at the same time; however, according to the people on the Spaceship, the right lamp flashed first, then the left. The flashes will be observed in another order, though. As we saw earlier, the light from the right flash will reach the people on the spaceship at the time 1.73 – according to them. Note, though, that even if the lantern at the right will flash before the flash from left, as seen from the spaceship, the people on the spaceship will not have any knowledge of the future that the people on the Asteroid cannot have. The light cone, indicated by the red lines, will, at the origin, be the same for the asteroid as for the spaceship.
- How long is the asteroid, according to the people in the Spaceship?
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