The Earth is Getting Fatter
murk1e writes "The BBC News service has an article which reveals that the Earth is getting fatter. It is well known that the Earth is slightly wider at the equator than at the poles, it is less well known that for years, the Earth has been becoming more spherical. Now it appears that the trend has reversed, and the Earth is getting more obese (in the sense of shape change rather than changing mass). Perhaps the Earth should sue?"
That doesn't sound like Doppler-based measurement. It's simple laser ranging, though you've got to take the Doppler effect into account because of the relative motion of the Earth and the satellite.
The Earth is not a closed system, we receive most of our energy from the Sun, and a lot of energy is radiated off of our planet, as well.
Variations of entropy locally on Earth are not significant by comparison.