Remind me again how gravity works?

[AndrewL]

In the case of the Earth, the gravity actually increases slightly till you get to the mantle, then decreases linearly till you reach the core. This is because the density of the Earth is not constant, and the effect of getting closer to the denser core is greater than the effect of not feeling the gravity from the layers above you for the first part of the descent.

I would expect this to be even more true of Jupiter.

[chrisk]

basks in the validation of fellow physics Dopers

[Trinopus]

@chrisk

Did Newton solve it for the case where the density of the planet was constant, or for all possible cases?

Well, for all possible cases where the density is evenly spread out. i.e., if you have a huge concentration of density in India, and a huge region of very light mineral formations in Mexico, then the shell itself is asymmetric. Someone very deep below India would feel a net upward pull, while someone deep below Mexico would feel a net downward pull.

But if the shells themselves (think in terms of calculus, where the shells can be made arbitrarily thin, like an ideal onion) are symmetric, then any collection or sum of them will follow Newton’s rules.

Take a spherical volume centered around the planet Earth, but with equal radius to the commonly accepted radius of Jupiter. Release a low-density gas into this volume, (and use a force-field if necessary to keep it from drifting away) and call this volume the planet Super-Earth.

As you ‘descend’ through Super-Earth to the solid surface, will the pull of gravity increase or decrease? I say, in this case, it will increase, because the effect of the sparse gas in the layers you are descending past is small enough to be outweighed by the fact that you are approaching closer to a dense core, and the effect of gravity from that core, (ie, the solid planet Earth as we know it,) will grow stronger as you approach.

Would you agree with me so far?

Ah! It took me a while to visualize this, but, yes, I quite agree. All that Newton said was that you disregard the shells above you. Since, in your model, they aren’t doing much anyway, then, yeah, gravity would increase as you fall through this vast extended “super atmosphere” toward the surface of the “real earth.”

In that case, is there anything that prevents the same effect from manifesting as we descend through the Jovian atmosphere? I suspect that we don’t know density of the different layers of Jupiter to be certain.

(And yes, I’m pleased that I got an opportunity to use ‘Consider:’ after you’d referenced Ringworld )

Ah! again! Okay, you got me: I dunno. The density almost certainly does increase toward the center of Jupiter (or as Pogo would say Jupister.) But, as you descend and disregard larger and larger external shells of matter, what remains is smaller and smaller, and thus has less and less pull.

In your model of a Super-Earth, the gradation of density is extreme. In Jupiter, it may be sufficiently gradual as not to produce the effect of increasing gravitational pull.

(I’m almost good enough at math to answer the question, if someone could present a function of Jupiter’s density as a function of distance from its center. I just did some Googling and didn’t find it.)

ETA: Oops! Missed AndrewL’s post. Right! Sorry! Yes!

[eschereal]

@chrisk

Take a spherical volume centered around the planet Earth, but with equal radius to the commonly accepted radius of Jupiter. Release a low-density gas into this volume, (and use a force-field if necessary to keep it from drifting away) and call this volume the planet Super-Earth.

This is a really weird and fascinating thing to envision. You realize that almost half of your super-atmosphere would be above the altitude for geosynchronous orbits? A layer of gas that would be both rotating with the earth and orbiting it, and above that, not rotating because orbital speed is too slow. Imagine the crazy weather patterns such an atmosphere would have. I guess it helps explain why the gas giants have rather short day lengths.