How will "InSight's onboard communications gear perform a radio-science experiment to shed further light on Mars' innards?" (Space.com)

Question

The Space.com article How NASA Mars Lander's 'Steampunk' Claw Will Work (Video) says:

InSight's mission aims to provide a detailed look at Mars' interior structure and composition. The lander carries two primary science instruments — a burrowing heat probe called the Heat Flow and Physical Properties Package (HP3) and the Seismic Experiment for Interior Structure (SEIS), a suite of super-precise seismometers. (InSight will also use its onboard communications gear to perform a radio-science experiment that should shed further light on Mars' innards.)

Question: Just how exactly will InSight's onboard communications gear perform a radio-science experiment to shed further light on Mars' innards?

A few GHz won't penetrate very far into the planet at all, so the experiment must be quite subtle, and therefore pretty cool, and use some planetary effects on upwards-propagating signals from the lander to a passing orbiter, or to Earth, or so I suppose. Is the effect related to some plasma, or is it inertial perhaps (tiny displacements or rotation shifts)?

Answer 1

From the surface operations website about the Radio science experiment (RISE):

RISE is a silent worker. Its job is to stay on the lander deck and trade X-band radio signals back and forth with Earth for an hour or so each day. It must do this for about two years in order to detect subtle, slow changes in Mars's wobble. Watching for small changes in the signals as seen on Earth will help answer questions about the nature of Mars' core. RISE will be the first instrument to start collecting science data for InSight, likely on the very day that InSight lands on Mars.

So the RISE operations are about nutation, precession and moment of inertia measurments of Mars as a physical body. Estimates of the moment of inertia and thus the mass distribution inside of Mars exist since the Viking era, but no precise measurments have been performed since then.

In order to measure those quantities one has to determine differential positions of Insight vs. MRO or Mars Odyssey. Insight needs those relays anyway in order to communicate with Earth, so their positions are also known to a high degree of precision.