Lunar gravity question

Here's something I've been wondering: is it possible for a celestial object the size of our moon to have gravity that's equal to or otherwise almost indistinguishable from Earth's (1 g)? Like, is there some material out there that is dense enough to accomplish this if it served as the moon's core?

The reason I ask this is because I've been pondering a story where a major part of the setting hinges on how the moon of the planet the characters live on (which is otherwise exactly like our own Earth 20 Minutes into the Future) is inexplicably inhabitable. It's got equivalent gravity, a breathable atmosphere, hospitable flora and fauna, and it's not tidally-locked...all while being the exact same size as our moon and being the same distance away from its home planet as the moon is from Earth. It flies in the face of the laws of the universe (which is again, the same as real world physics) and everyone knows this - how the moon is able to flout them is the biggest mystery of the setting. So I'm just trying to cover all my bases here and see if the aspect of its Earth-like gravity can be ruled out as being implausible too, and if not that's cool.

edited 14th Oct '15 8:54:32 PM by ComicX6

Gravity is a matter of density, not volume, which is why black holes are no bigger then the stars they used to be but are well, black. Hypothetically if your moon was packed densely enough then it could have the gravity of jupiter if you wanted it to. The issue of course is that simply saying 'oh the moon is hyper dense' solves the issue and there is no mystery like what you wanted.

BUT: and it's a big stinky but, increasing the gravity of your moon has massive ramification for the earth. Our moon gravitational pull on the earth is what causes our tides, crank the moons gravity up and not only our tides would go nuts, our molten core would as well creating volcanoes and earthquakes as it pulled our lava around like iron chasing a magnet. This kind of gravitational squeezing, albet much stronger, is in fact a likely hypothesis for why IO is a real life example of a Lethal Lava Land and of course the same goes for your inhabited moon.

Unless you want a lot of geological activity and hyper tides, your best bet is a gravity maguffen to make your moon habitual.

Is it necessary to have it the exactly the same distance from the planet? You could easily solve the gravity issues by having the "new moon" be three times denser than our moon, and have it ~1.7 (sqrt(3)) times farther away(which is minuscule on any kind of astronomic scale).

edited 14th Oct '15 11:36:16 PM by Sharur

Okay, there's some limitations on what your super-moon's core could be made of. The most dense stable element we know of is Osmium. Compressed the way Earth's core is, that still wouldn't be enough to give it equivalent mass. So you're looking at either something exotic (a chunk of neutron star?) or...unstable transuranics. And what happens when you compress those? :P.

Actually, this moon's mean density would be 20.3 g/cm³, and osmium, iridium and platinum (all stable) are over that. On the other hand, such a large concentration of post-iron element(s) is at best highly improbable.

The fact that the moon is not tidally locked suggests that it is very recent. This "moon" looks like it must be an artificial construct.

edited 15th Oct '15 5:15:16 AM by Aetol

If it's artificial it might as well have a solid uranium core used for power generation. Assuming it doesn't explode.

It could also be spinning very fast. Rotation speed can increase the "pull" of surface gravity. (But also exacerbate the different levels of tidal forces at altitude.)

Actually I was thinking of some sort of mysterious artifact, not a purpose-built space station. Like the planet in the "Random Access Memorabilia" arc of Schlock Mercenary.

Actually the centrifugal force would decrease the gravitational pull, since people would be on the outside of the surface. Besides, anything that size would dislocate before the centrifugal force had any significant effect.

Depending on how you plan to solve the mystery, the implausibility of the moon's gravity might be something you need to retain.

The other thing would be a counter-force on the other side of the planet, that limits the effects of the moon's presence on the planet. My physics-fu isn't what it used to be, so I don't know if this would actually work at all - does anyone else?

I actually second that notion: something's causing it to be a lot more dense than it should be, but what it is, is central to the story.

Yeah, the point is that it's supposed to be implausible. Some sort of Sufficiently Advanced Alien MacGuffin is exactly what I envision to be the culprit, but I don't want the characters to really start out at that conclusion since they're trying to look at it from a hard science perspective instead of giving serious consideration to something "silly" like aliens.

Thanks for all the input; I actually hadn't considered the tidal effects that this super-dense moon would create for its home planet if it were following proper physics, but it's obvious now that I consider it. I've also been pondering the ramifications of having an inhabitable moon would have on a world like ours; I'd imagine for one that space programs would be much more robust than they are in reality with a second, albeit much smaller Earth being a literal light-second away.

Point of order. Black holes aren't the same size as (what's left of) their parent stars, they're much, much smaller. A courtesy of The Other Wiki a solar mass black hold would have a Scwarzchild Radius/event horizon of about 300 metres.

The short answer: Yes, it's possible. All you need is a dense enough material.

The slightly longer answer: We can calculate the required density of the material. In this case we know the radius and the acceleration so we can solve for mass with the formula M = AR²/G which gives us 4.43*10²³kg, then for density with the formula D = 3M/4πR³ which gives us a density of 20.18 (as compared to water). A ball the size of the Moon with that average density will feel to someone on the surface the same as standing on the Earth, as far as gravitational acceleration is concerned.

The even longer answer: It's actually not that easy to find materials 20.18 times as dense as water. Lead is about 11.34 times as dense and even gold is only 19.32 times. Solid platinum, iridium or osmium would all be sufficiently dense to produce the desired gravity, but although all have stable isotopes and occur naturally in significant quantities, one would not expect to find an entire planetary object the size of the Moon made almost purely of any of them (or any combination of them), unless someone built it artificially. You get a bit of an edge by virtue of gravitational compression, which might bring gold up to the required density, but gold has the same problem of availability and purity.

Other thoughts:

Merely having surface gravity equal to that of the Earth is not necessarily enough for habitability. Remember that this is still a smaller and lighter object than the Earth, and its gravity field drops more quickly with additional altitude above its surface. So it still isn't as good at holding onto an atmosphere over long periods of time (i.e. millions of years) as the Earth is. Also, if it lacks a natural magnetic field, that lets in charged particle radiation from its star, which tends to erode the atmosphere as well. It should be able to hold onto a breathable atmosphere for some thousands or perhaps even millions of years, but after getting to a similar age as the Earth itself (about 4.5 billion years) it would likely have been stripped down to near-vacuum.

Also, with about six times the mass of our Moon and at the same distance, this theoretical object would raise tides on its parent planet about six times higher than what we experience right now. This would have pretty substantial effects on the planet's coastal regions. If the object were rotating at a similar rate to the planet, any large water bodies on it would also experience significant tides from the planet's gravity, probably exceeding the height of the tides on the planet itself.

EDIT: About 3 kilometers, actually. You're off by a factor of ten.

edited 15th Oct '15 3:27:31 PM by Meklar

You can up the weirdness and avoid the giant tides problem in one fell swoop by taking your cue from the Schlock Mercenary story I mentioned, where the planet's gravity sharply drops from "almost as strong as earth" to "what it should be for something this small" a few hundreds kilometers above the surface. In this case the characters knew about the physics that could create such an effect, but it seems people in your setting wouldn't.

edited 15th Oct '15 4:46:43 PM by Aetol

Oisri finds its way out of the Schlockiverse?