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 Originally Posted by oskar
How do they go from seeing some particles move to pinpointing the exact place and distance of the double blackhole system?
We don't know the exact place of the event. We know the distance (more or less) and an area of the sky in which it most likely occurred - kind of a long arching crescent shape in the southern sky near the large magellanic cloud.
Basically, it's not too dissimilar to radar. One radar can tell you the distance, but that still leaves you with a circle around you where it could be anywhere on that circle, since all of those locations are the same distance. However, introduce a second radar station which identifies the same event, and you have 2 overlapping circles, one from each radar station. So you've narrowed it down to only 2 locations. With a third station, you can pinpoint the exact location because its circle will only intersect one of the two points created by the other 2 circles.
They were able to determine the size of the 3 black holes from the data - parents were 29 and 36 solar masses, the daughter is 62 solar masses - as well as the distance. This is done by matching up the predictions made by Einstein's Field Equations about this kind of event to the actual observations. My guess is that the 2 observatories both measured the distance and the discrepancy in their timing has left us with a kind of wedge shaped piece of the sky which is where our "radar circles" overlap. It's noteworthy that our 2 "stations" are really close together compared to the distance of the signal. So the circles are very nearly identical and their crossing is like 2 nearly parallel lines with only a very slight angle between them. This is why we've narrowed it down to a wedge shape, but not an exact location.
Originally Posted by oskar
And what would such an event mean for a solar system that was, let's say only 1 million light years away from that thing?
As far as the gravitational waves are concerned, practically nothing. We're not talking about any kind of visibly noticeable effects. What LIGO detected was a change in lengths of about 1/1000 the diameter of a proton over 4 km. That's equivalent to measuring the distance from the sun to it's nearest starry neighbor to within about 1/2 the diameter of a hair.
In general, being close to a black hole is pretty dangerous, especially so if that black hole has an accretion disk. They tend to emit a lot of high energy particles and rays which are quite destructive to ... well, atoms - aka all the things.
I honestly don't know how close you would need to have been to have seen any noticeable effects.
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