How can I correct for transit time?

Question

I know the exact time a radio telescope detected a transient event. I also know the exact location of the telescope, and the galactic coordinates (galactic longitude, latitude) and right ascension and declination of the beam pointing center.
I conjecture that the event was also observed by another receiver at another location. How can I correct for the time difference between the two locations (i.e. the event reached one observer earlier than the other due to that they are in different locations)? Currently, I’m taking the dot product of a vector between the known observer and the source, and a vector between the known observer and the potential observer, and dividing that by the speed of light. To obtain the vector between the observers, I calculate their ‘n-vectors’ ( https://www.movable-type.co.uk/scripts/latlong-vectors.html  ) and take the difference. However, I’m getting nonsensical delay values.

uhoh · Answer

This may be a partial answer depending on what you do or don't know how to do at the moment, and the level of accuracy you require. Feel free to add some feedback.
If you'd like to use (or learn to use) Python then you can solve this problem trivially using Skyfield!
It depends on the level of accuracy that you need. The time difference will be of the order of 20 milliseconds for a 6000 km difference in light-path distance for example, but in that time the Earth moves (in some direction) about 0.02 * $sqrt{GM/a}$ where GM is 1.327E+20 m^3/s^2 and $a$ is about 1.5E+11 meters, or about 600 meters.
If you don't want to worry about small corrections right now, just calculate the dot product between the normal vector pointing from the direction of the event and the vector drawn from the known observation site to the proposed site, that's the path length difference. Divide that by the speed of light to get the time difference.

How can I correct for transit time?

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