# How can I correct for transit time?

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.

• It's hard to tell right now exactly what level of detail you need, but I've added an answer. Please feel free to add more details or explain what else you'll be needing! – uhoh Jul 2 at 7:14
• Rather than asking essentially the same question twice or even thrice!, it's better to explain more clearly the first time exactly what you need. If you needed more detail you should have mentioned it right here rather than accepting my self-proclaimed "partial answer" and then re-asking. In Stack Exchange we try to avoid answer fragmentation by not spreading answers out over several posts or different sites. – uhoh Jul 14 at 9:55

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.