Gravitational wave source triangulation

[member 656954]

In my new novel, Handwavium, renowned genius physics Professor Samuel Clements Silver has created a prototype gravitational wave radio. For plot purposes, the protagonist needs to use the signal to triangulate his location.

I know LIGO has three detectors and have seen reports of sources like black holes being locationally identified, so I'm assuming that the concept works. All the action happens on Earth, but...

1. Can you locate with two measurements? Or do you need three?
2. Would the location be exact, or is there locational fuzziness based on distance between source and receiver? Or distance between readings?

I've entirely fudged the engineering of the radio, as this snippet from the story illustrates, so am happy with impossibilium, this is not intended to be diamond hard science fiction:

He took his watch off. Johnson had not even looked at it, though if he had it was doubtful that he would have sensed anything special about it. Apart from that it looked very expensive. Placed onto the adapter, induction charging started the hour hand spinning, slowly at first, and then so rapidly that it blurred. Silver listened to the hum for a moment, face averted as he half expected it to fragment like so many of its predecessors had but the watch also worked as intended. The tip of the hour hand was doped with Wittenian, an island of stability, superheavy element that was just massive enough for useful gravitational waves as it deformed spacetime rotating at speed.

Any thoughts or observations are welcome

 

[Vanadium 50]

Well, a radio antenna tells you you are on a line, and a GW antenna tells us you are on one of two perpendicular lines. So if you have a station in St. Paul and another one in Nashville, and your signal is in Chicago, you know that your signal is in Chicago. Or Thunder Bay, Or Amarillo. Or Richmond.

In the words of Bob Newhart, " I've just been notified that the sub will be surfacing in a moment, and you will be gazing at the familiar skyline of New York City... or possibly Buenos Aires."

 

[member 656954]

Thanks @Vanadium 50, I'm going to have to plot that, but it seems from your example that three readings would be necessary to properly triangulate.

 

[Vanadium 50]

Well, maybe. Some solutions might be too far away. Others might be in unlikely places: on water, in a desert, etc. You may have other information - if you knew the source was in Canada, you could select Thunder Bay from the list. If the sender says "the sun is coming up now", you could pick a solution. Or, or, or...

It all depends on your story,

 

[member 656954]

It all depends on your story,

Thanks, @Vanadium 50, that's perfect. Multiple locations with another piece of information in the story that I've been trying to figure out what to do with works really well for the plot.

 

[stefan r]

I think you need three points to properly triangulate if you are using the timing of the wave's arrival. With something like radio signals on Earth you only need two detectors. However, that is because you can assume the source is on Earth's surface. In space two passive radio detectors could still "triangulate" but that would be the locus of all triangles that could create a signal with that timing. Radar works differently because it sweeps out a line.

Ligo detectors give some information from the arrangement of the legs. My impression is that they should be blind to a wave that effects both legs equally. All source located in the plane that bisects ligo's legs should be invisible.