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If Earth had enough mass in its own rings, more than the weight of Earth:

  • What could it decrease the gravity to?
  • Would the atmosphere have more depth or be thinner?
  • What would the weather be like?

enter image description here

https://physics.stackexchange.com/questions/281828/if-earth-had-rings

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    $\begingroup$ What do you mean by "moon jump"???? $\endgroup$ – Camilo Rada Mar 5 '18 at 0:59
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    $\begingroup$ It's hard to tell what the question is. The title does not make sense and the pictures don't add anything at all. What did the answers on Physics leave out? $\endgroup$ – kwinkunks Mar 5 '18 at 1:02
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    $\begingroup$ Another very important thing you need to be doing Muze: giving credit sources for the photos. It's one thing to overlook when it's a vital part of a question, but when it's just to jazz it up, they really should be sources and be photos you can legally use. $\endgroup$ – JeopardyTempest Mar 5 '18 at 4:46
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    $\begingroup$ Also: text in pictures instead of in text is very bad idea as some people rely on screen reading softwares. $\endgroup$ – plannapus Mar 7 '18 at 9:45
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    $\begingroup$ @JeopardyTempest I took the other pics off and I photoshopped the 1 left. $\endgroup$ – Muze the good Troll. Mar 7 '18 at 17:22
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Rings wouldn't decrease the gravity much, but the exact amount would depend on the exact geometry of the rings. One reason is that the gravity of one side of the ring would partially cancel the attraction of the other side. In a similar fashion described by the Shell theorem demonstrated long ago by Newton and proving that if you are inside a shell of mass the gravity effects from one side cancel the other, therefore it would be no gravity inside the shell. However, in the case of a ring the forces only fully cancel at the very center. Nevertheless, partial cancellation of forces would make that the gravity of a "Earth's mass" ring would be much weaker than the one of an "Earth's mass" planet. For the rings to significantly reduce the acceleration of gravity on Earth's surface you would need super-massive rings (and note the rings with the mass of the Earth would fall in this category), something that is extremely unlikely, as such massive rings would coalesce into moons. In the case of Saturn's rings, they only have the equivalent to a 0.000005% of the mass of Saturn. If such super-massive rings coalesce into moons, those moons could be more massive than Earth's itself, so Earth would be orbiting the moons more than the other way around. More precisely you would have a chaotic multiple-body system, in which Earth would be just one of the bodies.

It is worth noting that even our moon doesn't have much of an effect in the acceleration of gravity despite the mass is fairly large (1.2% of Earth's mass) and it is all concentrated in one place (instead of distributed in a ring). The mass of the moon is 7.3e22 kg, which is for comparison about 2000 times more than the mass of Saturn's rings.

In the case of the moon for instance, your weight doesn't change at all in high or low tide. That's because the scale that measures your weight, and the ground under it are all suffering the same tidal effect than you, so the force your mass put on the scale is unaffected by the presence of the moon. And the same would be true for your hypothetical super-massive rings.

Regarding to your second question, for all the above, I doubt it would change significantly the thickness of the atmosphere.

Now, when it comes to weather it is a completely different story. The presence of the rings could strongly decrease the amount of solar radiation reaching the tropics, therefore it could change the whole global atmospheric circulation pattern, maybe the Hadley cell wouldn't form as we know it, changing the climates worldwide.

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    $\begingroup$ You also need to consider that the mass of a ring system is not all that great. Saturn's rings mass about as much as the small moon Mimas, which (even with the mass all collected in one lump) has a surface gravity less than 1% of Earth's. $\endgroup$ – jamesqf Mar 4 '18 at 19:24
  • $\begingroup$ This isn't strictly true, though. If you have a very massive ring just above the equator of a low mass sphere, the net gravitational force at the equator is upward. $\endgroup$ – Keith McClary Mar 18 '18 at 23:29
  • $\begingroup$ @KeithMcClary I disagree, inside massive rings there would be no effective gravity force (as long as you are in the plane of the rings). And if there is a central body, on the equator of it you would feel only the gravity of that body, therefore pointing downwards, no matter how massive are the rings. $\endgroup$ – Camilo Rada Mar 18 '18 at 23:41
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    $\begingroup$ " inside massive rings there would be no effective gravity force (as long as you are in the plane of the rings)" That argument depends on spherical symmetry, it doesn't work for a ring.See for example "Electric field of a charged ring" on this page. (The math is the same as for gravity.) $\endgroup$ – Keith McClary Mar 19 '18 at 0:00
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    $\begingroup$ That is discussed here. John Rennie's Answer assumes bodies orbiting each other (i.e., in free fall). $\endgroup$ – Keith McClary Mar 19 '18 at 1:27

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