I think the Sagnac effect only occurs when the signal travels in a loop which has some area. Around the orbit of the Earth is a huge loop, so it should show the Sagnac effect.

From one country to another, and back again along the same path is a loop that doesn't enclose any area, so it should show no Sagnac effect. Even all round the Earth's orbit and back along the same path should show no Sagnac effect.

Do you dispute that a loop enclosing an area is required for the Sagnac effect? I only know this from Wikipedia and some odd websites, so I might be wrong. But I'd like to understand where 90ns comes from. There's no value in somebody claiming its the Sagnac effect without showing their calculations, maybe that person just guessed?? Also your 2000ns prediction disagrees with Wikipedia because you used the Earth's radius instead of the loop's radius, and assumed a circular loop when it was flat.

If you don't agree with me, please show what your references say for your Sagnac equation and explain how I or Wikipedia is wrong.