Scientists use pairs of satellites to map the small variations in Earth's gravitational field. It is possible to see groundwater depletion and changes in distribution of glacial ice, among many things.
The primary challenge in determining the mass of Earth is actually measuring the gravitational constant, G, itself. Everything else involved is known at much higher precision. The product of G and Earth's mass is known to two parts in a billion, but the uncertainty in G is ~22 parts per million.
LISA is primarily sensitive to time-varying gravitational gradients on timescales of a fraction of a minute to a few hours and won't be terribly useful for determining the orbits of objects in our solar system. (but it is very, very cool).
or maybe that upcoming space laser interferometer (LISA) since it has to figure precisely how all mass is affecting its position?
I love the history of figuring the circumference of the earth, imagine getting it right within 2% in 240 BC
(then Columbus effing it up by 25%)
https://en.wikipedia.org/wiki/Earth%27s_circumference#Histor...