How, and How Well will Juno measure the effects of frame dragging? (GR effect due to Jupiter's mass & rotation)

Question

This answer links to Spaceflight 101's One Week to Jupiter – NASA’s Juno Spacecraft en-route to Gas Giant after five-year Journey which says

Also, Juno will put Einstein’s General Theory of Relativity to the test by studying orbital frame dragging close to a massive body.

Question: How, and How Well will Juno measure the effects of frame dragging? What instruments and/or equipment will be used to detect frame dragging? Will it be a fairly precise quantitative determination, or more of a qualitative "yep, there's an effect" verification?

The biggest effect of Jupiter's rotation is the gravitational quadrupole or J2 moment caused by Jupiter's oblateness, which is a result of the rotation. It causes the apses of Juno's orbit to precess substantially. See Juno's original orbit around Jupiter - is this apsidal precession? If so, need expression.

above: a plot of Juno's original planned orbit. Because of a slow responding helium check valve, Juno actually was left in its higher orbit, but still experiences precession of the apses. Plot from here.

So the frame dragging would have to be separated from all other effects due to deviations of Jupiter's gravity field from a pure monopole. This sounds extremely difficult!

Answer 1

So the frame dragging would have to be separated from all other effects due to deviations of Jupiter's gravity field from a pure monopole.

It's much worse than that. Frame dragging is a rather small effect, even in a highly eccentric Jovian orbit with a low periapsis distance. Atmospheric drag, Jupiter's $J_2$ and $J_3$ are much greater perturbations on Juno's orbit than is frame dragging. One of the key purposes of the Juno Gravity Science experiment is to ferret out parameters such as the (classical) $J_2$ and $J_3$, along with other spherical harmonics, as these give deep insight into the nature of Jupiter's core. For example, it is now known that the neither the core of the Moon nor of Mars is frozen completely solid given observations of the orbits of satellites orbiting those bodies.

That said, getting those classical spherical harmonics coefficients more or less correct means that frame dragging (and atmospheric drag) need to be taken into account. This is not Juno's job. This gets at the key question,

Question: How, and How Well will Juno measure the effects of frame dragging?

Juno doesn't measure this. This is the job of systems on the Earth. Juno itself knows very little about its orbit. It knows instead that at certain times, it is commanded to rotate so that the only large bright object in view (aka Jupiter) becomes centered in its field of view, and that it must correct its rotation rate so that this large bright object remains centered in its field of view.

Juno's flight software doesn't know that it is orbiting that large bright object, let alone knowing that a simple monopole model does not fully describe that orbit. This knowledge instead is the purview of observational equipment and people on the surface of the Earth. It helps a lot that a key part of the Juno Gravity Science experiment includes equipment on Juno that enables systems / people on the Earth to measure Juno's range rate at the microns per second level.

Answer 2

Update

While @DavidHammen's answer is insightful and informative, I'll add to the mix by addressing specifically:

What instruments and/or equipment will be used to detect frame dragging?

From this JPL Juno press kit's Science overview:

To measure these tiny shifts, Juno’s telecommunication system is equipped with a radio transponder that operates in the X band, which are radio signals with a wavelength of three centimeters. The transponder detects signals sent from NASA’s Deep Space Network on Earth and immediately sends a signal in return. The small changes in the signal’s frequency tell us how much Juno has shifted due to variations in Jupiter’s gravity. For added accuracy, the telecommunication system also has a Ka- band translator system, which does a similar job, but at radio wavelengths of one centimeter. One of the antennas of NASA's Deep Space Network located in Goldstone, California, has been fitted to send and receive signals at both radio bands. An instrument called the Advanced Water Vapor Radiometer helps to isolate the signal from interference caused by Earth’s atmosphere.

JPL provided the Juno telecom system. The Italian Space Agency contributed the Ka-band translator system.

So it's two transmitters and two receivers plus a water vapor radiometer on the ground as well as two separate transponders on Juno using different bands that work together to try to overcome the challenges of measuring the tiny effects outlined in @DavidHammen's answer.

The idea is that signals in the two transponder bands will be delayed by different amounts by water vapor in the Earth's atmosphere, and by measuring the difference between the delays one can approximately subtract the effect of the water on the round-trip light time. Some GPS/GNSS systems apply two-frequency measurements to reduce GPS error due to water vapor, though there are other techniques they can use as well.

For more on this see:

• Would Adaptive Optics be Useful in Radio Astronomy?
• What is precipitable water vapor in millimeter-wave radioastronomy and how is it measured?

Original answer (and still helpful)

I'll just address the "How" part (leaving "How well") to @DavidHammen's answer.

There is no "frame dragging sensor" aboard Juno. As an orbiter of Jupiter, it's trajectory is the "sensor" and the trajectory is determined by various radiometric techniques based on delay-Doppler measurements from the Deep Space Network on Earth.

These can include both two-way (send a coded, stable frequency signal, receive the phase-coherent rebroadcast from the spacecraft, apply correlation to precisely determine the delay and the Doppler shift) and more complex methods. For more on that see @MarkAdler's answer to

• How does a three-way doppler shift measurement work?

For more on precision tracking in general, see @TomSpilker's answer to

• Spacecraft Navigation