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Topic: Ghost ships (Read 9064 times) |
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rmsgrey
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Re: Ghost ships
« Reply #25 on: Aug 18th, 2004, 4:50am » |
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The captain of H can observe the real-space motion of the other ships as they pass through his. Knowing that, he knows the direction of the line connecting the four ships (which in real-space sweeps at a constant speed in a constant direction) and so can easily avoid accelerating along that line.
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mike_uk
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I just stumbled across this page,
Is it not possible to suggest that as the two ships f and g have already collided 3 times
which means that they have collided with every other ship as you can't collide with your self.
so f has hit e , g, h
g has hit e, f , h
as both f and g hit h as their last collision it would suggest to me that e is not on a collision course with h and that if it ever does cross the path of h it will either cross its path before or after it. and that the captain of h needs to do nothing as there is no chance of e hitting him.
thats just my interpretation of this
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rmsgrey
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Re: Ghost ships
« Reply #27 on: Nov 10th, 2004, 6:21am » |
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Lets look at a special case:
Assume H is sitting still. Call the point where E and F collide X, where E and G collide Y and where F and G collide Z. Since F collided with both E and H, F must be moving along the line that connects X and H. Similarly, G must be moving along the line connecting Y and H. Since F and G both pass through Z, it must be on the lines XH and YH. Since both lines have 2 points in common, they must be the same line. Finally, since XYZH is a straight line, and E is moving along the line XY (which is the same line), E must be heading either directly towards or directly away from H.
Now, if H isn't sitting still, but instead moving at constant velocity, then the same thing applies. If you imagine plotting the ships' positions on a series of transparent charts, then laying the charts on top of each other so that H's positions sit directly above each other, then, by the arguments above, the other ships' courses will form a single dotted line passing through H's "position"
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Hippo
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Re: Ghost ships
« Reply #28 on: Dec 17th, 2007, 1:52am » |
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Sorry I didn't read the whole thread.
The proof with coplanarity is nice, but it seemed to me noone noticed that the ghost ships are sailing on Earth - a ball. Not on a plane.
I didn't thing about it so far, but it seemed to me that this little difference can play an important role.
Does not the method actualy proof they will not colide when doing nothig?
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JiNbOtAk
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Re: Ghost ships
« Reply #29 on: Dec 17th, 2007, 4:08am » |
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on Dec 17th, 2007, 1:52am, Hippo wrote:| Sorry The proof with coplanarity is nice, but it seemed to me noone noticed that the ghost ships are sailing on Earth - a ball. Not on a plane. |
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If the distance between the ships are relatively small, it wouldn't matter, rite ? After all, we approximate flat surfaces all the time, when it should be a ball.
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