Core Conundrum: Newsletter Challenge (March 2018)

You could measure the weight of the lander on the planet and calculate the resulting MoI (moment of inertia)difference by the effect on the gravitational acceleration anomaly as a function of latitude with line-of-sight rf signal...

The signal from the spacecraft received from inside the planet's gravitational field will be shifted down in frequency (gravitational redshift).

The more often used exact equation for gravitational redshift applies to the case outside a non-rotating, uncharged mass which is spherically symmetric. The equation is:

• G is the gravitational constant,
• M is the mass of the object creating the gravitational field,
• R is the radial coordinate of the point of emission (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate),
• r is the radial coordinate of the observer (in the formula, this observer is at an infinitely large distance), and
• c is the speed of light.

https://en.wikipedia.org/wiki/Gravitational_redshift

1. Assuming that the core is metallic and

2. That the rock outside of the core is non-metallic and

3. Assuming the planet rotates on its axis with the axis not oriented toward the Earth and

4. That the radio equipment on the spacecraft can emit a broad range of frequencies and

5. That the receiving stations on Earth can detect the radio signals from the spacecraft over a wide db signal range.

Then, the size and makeup of the core can be determined by measuring the change in signal intensity over a range of wavelengths, as the spacecraft rotates around the core as the planet itself rotates. The (metallic) core blocks signals that are passed by non-metallic rock.

1.-Approach the exoplanet in a low orbit coplanar with Earth. The radio signal emitted by the spacecraft will vanish around half of the total time. Same for signals emitted from Earth detected in spacecraft. Knowing the spacecraft velocity the diameter of exoplanet can be determined, hence its size (assumed spherical).

2.-At landing, either measuring the necessary thrust exerted to land smoothly or the redshift the planet mass can be deduced.

By broadcasting Down into the planet assuming there is a surface to land on. As the planet rotates and/or orbits it's sun, the signal characteristics will change. By setting a base line with a starting frequency and a full orbit/rotation or two, the transmitter can then sweep up and down it's bandwidth over several rotations, and the variance can be measured and evaluated by radio telescope.

Using the "Red Shift" methodology elucidated in prior posts you can determine the gravitational field. THEN you can take that field and by using integrated gravity blocks, (think 3d pixels) and various material densities can "stack" and arrange them in a computer model to (extraterrestrial) geophysically map the subsurface. We did this back in the mid-1970's with salt domes on the Texas Gulf Coast. (Oh the joys of FortranIV, forklift sized card decks, paper outputs, and waiting all night for the monster Univac to run your model only to find out that on that a one character typo on card 1039 caused the program to loop and the operators to kick you out of process).

To make this work, you need to make a lot of assumptions.

Is it a rocky? Is there a metallic core? Gaseous? Is it platinum or solid rubber lovingly crafted by those Magrathean planetary engineers? Any of them could generate the same gravity field and be indistinguishable from a gravity field alone.