I believe if you don’t have a better idea than that proposed by authorities (e.g., NASA “engineers” in this case) , you should be honest with it anyway. And just say, “This is not a better idea, but your idea will possibly destroy billions of tax-payer dollars or maybe even hurt someone.”
In this particular case, I think I have a far better idea than relying on the GPS for position of space probes and The Gateway Space Station orbiting The Moon.
While in orbit around Earth, the GPS atomic cesium clocks are set to run +38,700 nanoseconds faster than similar ones on Earth.
Ge-Se = corrected time, where Ge is the general relativity correction of 45,900 nanosecond and Se is the special relativity time correction of -7,200 nanoseconds slower for speeding around Earth.
The earth’s approximate mass is = 597.2 × 10^22 kg
It is from the proximity of this massive object, Earth, that general relativity can be thought to function for us and our frame of reference, as opposed to the GPS satellites.
Earth is 81.28 time more massive than The Moon (Mm = 7.34767309 × 1022 kg)
In one-dimension, it is straight forward to see there will be different time-delays involved with Moon orbit.
For Earth and near-Earth orbit…
Se = 7,200 ns slower
Ge= 45,900 ns faster
Delay T = +38,700 ns faster on GPS corrected on GPS
BUT IN LUNAR ORBIT,
Gm = 45,900/81.277 = +565 ns
Delay T = Gm-Sm = -6,635 ns SLOWER on GPS corrected
Their is a sign change in time delay…
Again, this is only a simple one-dimensional representation of the tensor, guv – The Metric Tensor – or simply “The Metric”, which holds all info on spacetime and mass variation, curvature, and separates for us, future from past. In ALL four-dimensional calculations of the tensor, it may have both positive and negative reversals.
My better idea is to solve the 4-D Metric numerically, taking into account all topology on the lunar surface, and any known assymmtries under the surface, BEFORE making any pronouncement on how we can use GPS all the way into Lunar orbit. Or just have a separate LPS (Lunar Positioning System) in orbit around the Moon. Peace Out, NASA.