...
where RTD = Round Trip Distance. Thus if If we know the RTD (e.g. by knowing the coordinates (latitude and longitudes longitude) of the source (monitoring host) and target (remote node) then we can obtain the RTD using the Haversine formula to calculate the great circle distance and double this to get the RTD. Note that the Haversine formula assumes the earth is a spheroid whereas it is an ellipsoid and this can rise to errors of a few tens of kilometers.
If we know the RTD and and destination) and have measured the min_RTT then we can derive Alpha as:
...
The approximations can mean that Alpha can be > 1. Besides the approximation of the speed of light in vaccum and the Haversine approximation mentioned above, there is the approximation that the speed of light in fibre is 0.66c. However if the refractive index of the fibre is 1.4 then the speed of light in the fibre is not 200,000km/sec but 214,000km/sec. For more on the refractive index see John E. Midwinter, “Optical Fibers for Transmission”, John Wiley & Sons, NY, 1979. There is it states:
For multimode and single mode step index fibers operating at wavelengths near 850 nm a typical cladding would have a refractive index of 1.518 and the core would have a refractive index of 1.538 which is 1.3% greater. The velocity of propagation in the multimode step index fiber would be near the speed of light (c) divided by 1.538.
For a refractive index of 1.538 then the velocity of light in the fibre = 0.65 650138 * c.