Question for any physicists out there. If the theory can be tested with just a 1 kg mass on Earth, could the fluctuation in mass of GPS satellites also be detectable from their timing data?
I'm a physicist but not an expert in this field, but my guess would be the answer a comprehensive "no".
The way satellites orbit is incredibly well described by Newtonian mechanics and there the impact of their mass on the shape/timing of the orbit is by changing the center of mass of the combined satellite-earth system. That is you only get measurable effects if the fluctuation in the mass are big enough compared to the mass of the earth.
The way satellites orbit is incredibly well described by Newtonian mechanics and there the impact of their mass on the shape/timing of the orbit is by changing the center of mass of the combined satellite-earth system. That is you only get measurable effects if the fluctuation in the mass are big enough compared to the mass of the earth.