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Earth's mass is about 1E+25 kg, the Sun about 2E+30 kg, and the Moon is only around 7E+22. Lunar orbit has well known problems with mascons and while the earth still has perturbations due to mascons, they are seemingly more benign (addtl).

Lunar mascon example.

Example of a large mascon on the moon.

Would the Sun's be even less noticeable provided we didn't burn up upon approach? What is the maximum density of a naturally occurring mascon and would it be enough to be noticeable on something with a mass as large as Jupiter? Or what is the biggest planet required for a mascon of maximum elemental density to not be noticeable?

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    $\begingroup$ Somewhere in either Space or Astronomy SE there is a discussion about density variations in gas giants due either to weather or induced by the gravity of large moons, and the effects of those density variations on the orbits of said moons. It may be in a Q&A or have taken place in comments, and I have a hunch one participant was @DavidHammen. Those might be thought of as "dynamic mascons", rather than static mascons in solid planets. I'll continue to search for that. $\endgroup$ – uhoh Nov 1 '18 at 23:03
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    $\begingroup$ @uhoh Luciano Iess and Christopher Mankovich are working on papers concerning wave features in Saturn's rings, seen by Cassini, that arise from density perturbations due to planetary normal mode oscillations. These would be, as you call them, "dynamic mascons", the planetary versions of the oscillations that allow us to do helioseismology. It turns out Saturn's rings are very sensitive seismometers for periodic oscillations! $\endgroup$ – Tom Spilker Nov 2 '18 at 6:51
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    $\begingroup$ @TomSpilker that sounds really interesting! I wonder if that's what I'm thinking of, do you remember if we discussed that kind of thing in comments here? Also, I remember reading several years ago about a spectroscopic Doppler? measurement of Jupiter, from terrestrial telescopes, looking at "planeto-seismology", and early discussions of doing it for Saturn as well (not necessarily for the effects from satellites, but I can't remember). Looking for that now, it's been a while. $\endgroup$ – uhoh Nov 2 '18 at 7:49
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    $\begingroup$ @TomSpilker JOVIAL! :D www-n.oca.eu/jovial2016/Kick-off_Avril2016/Monday/… last slide $\endgroup$ – uhoh Nov 2 '18 at 7:58
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    $\begingroup$ @uhoh That linked presentation is interesting. I know Tristan Guillot but I didn't know he was proposing this planetary seismology observatory network. $\endgroup$ – Tom Spilker Nov 3 '18 at 2:42
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@Fred is correct with his answer, but there are interesting ramifications—and qualifications—to add.

As long as you can generate a higher-density region of unconstrained excess mass, there is no limit to how big a planet can be and still have mascons that significantly perturb orbits. When I say "higher-density", I mean a density higher than the typical material that's at the same distance from the center of the planet. And when I say "excess mass", I mean the mass difference between the mascon and the same volume of material with the same density as the "typical material".

You can have huge density concentrations in a planet's core, but because that's pretty close to spherically symmetrical (as regards the gravity field geometry beyond the planet's surface) it doesn't affect orbits as much as mascons near the planet's surface. The mascon has to be something that really perturbs spherical symmetry. That's why @Fred correctly states that if a big planet had a bunch of evenly distributed mascons they wouldn't have much effect. That even distribution better approximates spherical symmetry than one big, hulking blob of a mascon.

But physics gets in the way of that "unconstrained excess mass". The bigger a planet gets, the larger the magnitude of its gravitational acceleration, and the larger (in terms of total mass) a mascon has to be to make a significant perturbation to the planet's potential field. [The vector gradient of the scalar potential field gives the gravitational acceleration] A large mass in a strong gravity field produces a large force—weight—on the material supporting it from below. If the gravity is strong enough, and the mass large enough, the pressure due to the mass's weight is larger than the strength of the supporting material beneath it, so the material deforms (flows plastically)...and the mascon sinks!

This actually happens on Earth. When geologic forces produce a pile of rock more than ~9 km high (more than that if it is partially buoyed by ocean water), the pressure at the bottom of the pile is greater than the strength of solid rock (even igneous rock, like granite or basalt, which yields the 9 km figure; weaker rocks reduce that figure), and the rock flows plastically, and the pile shrinks. The Hawaiian Islands are a good example. Volcanic activity builds piles nearly 10 km high (from the ocean floor) and they immediately start sinking into the basaltic crust below. Slowly, yes, but sinking nonetheless. Bathymetry shows the distortion of the crust around the islands.

Now imagine even stronger gravity (maybe much stronger!), large density contrast, and larger mascon total volume, large enough to make a significant perturbation in the gravity field of a really large planet. That mascon sinks, until the material around it is only a bit less dense than the mascon itself, and the surrounding material's strength can support the mascon's buoyed weight. If that's deep enough that it's in the planet's aesthenosphere (temperature high enough that the material flows relatively easily under large stresses) then the surrounding material has essentially no bearing strength and the sinking continues until the surrounding material is just as dense as the mascon ("isostatic equilibrium", just deeper than the term is usually applied). At that point it ceases to be a mascon!

The precise size of a planet whose gravity is so large that it cannot support any kind of significant mascon (without isostatic disequilibrium sinking it) depends hugely on the materials the planet is made of. But I suspect that a Jupiter-sized planet made of silicate minerals and metals instead of mostly hydrogen and helium isn't going to support much of a mascon!

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    $\begingroup$ Even mascons caused by thick icefields of the last ice age did sink. Some areas of Europe are still rising again without the huge burden of ice. $\endgroup$ – Uwe Nov 2 '18 at 8:55
  • $\begingroup$ Thanks-- that's an awesome answer, I was wondering about gas giants and such as well like Jupiter! Would a mascon of gas probably act the same way, getting pulled deeper into the atmosphere (and likely into a dense liquid state or solid state joining the core)? This is a great explanation as to why large masses tense to become spherical! $\endgroup$ – Magic Octopus Urn Nov 2 '18 at 12:36
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    $\begingroup$ @Uwe Exactly! In geology that's called "isostatic rebound". It's happening in North America too, with some interesting consequences. The ice extended southward to roughly 40° S (depending on the location) and was thicker as you went north. The thicker ice pressed the crust downward more. Now that the ice is gone, the crust is slowly rebounding, more in the north than in the south. The Great Lakes are slowly inching their way southward! This has caused some flooding and erosion problems on south shores. $\endgroup$ – Tom Spilker Nov 2 '18 at 19:49
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    $\begingroup$ @MagicOctopusUrn Yes, you're exactly right. Aside from the "dynamic mascons", where the increased density is due to dynamic pressure increases, a gaseous "mascon" could be denser than its surroundings for a couple of reasons. One is that it is simply colder—"cold air sinks". That cold mascon indeed would sink, until one or more of multiple mechanisms warms it: tubulent mixing with the surroundings, adiabatic heating due to the pressure increase as it sinks, radiative heating from the surroundings, etc. Or it can be denser due to its composition: on, say, Jupiter, a parcel of "air"... $\endgroup$ – Tom Spilker Nov 2 '18 at 19:56
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    $\begingroup$ @MagicOctopusUrn ...with a larger water vapor or ammonia vapor content will be denser than its surroundings and will sink, until it gets deep enough that the new surrounding air has just as much heavy stuff in it. It probably wouldn't get so deep that you get to the core, or even to the metallic (fluid) hydrogen state. As it goes down, it eventually gets to levels where the water content is so high that the former mascon is no longer a mascon, and it just floats there. Even farther down the air is really hot and contains vapors of silicate minerals (!) that make it a lot denser. $\endgroup$ – Tom Spilker Nov 2 '18 at 20:01
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I think you may be looking at the issue too simplistically.

Mass concentrations are a function of differences in material density. The overall effect of mascons will be determined by their size, distribution, the number of mascons regions and the difference in density between the mascons and the rest of the planet.

Considering extremes, if a planet of large mass had numerous small mascons, fairly evenly distributed, the overall effect may not be troublesome. But if the same planet had one very large mascon with a significant density difference to the rest of the planet the effect of the mascon will noticeable.

As to the density of mascons, that is determined by the mineral composition of the mascon. If it is composed of silica the density will be 1.54 tonnes per cubic metre, but if it is hematite (high grade iron ore) it will be 5.15 tonnes per cubic metres and for basalt it will be 3.01 tonnes per cubic metre.

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