"Earth’s Roche limit, the distance from the Earth where its tides could break another object apart"
It's a very common error. This limit is for an object "held together by gravity alone"! The moon is not held together by gravity alone - the dust on the surface is, but the rocks in the center are all fused together.
Additionally since they assume the moon will continue to have a synchronized orbit (the same side always faces us) it won't feel the tides in the same way. It would feel some constant stretching, but not the severe flexing caused by rotation.
The closer side would fall "down" and the far side would fall "up". Only the center would be in free fall. I suspect the moon could survive that - but I'm not sure.
If not, it would spread out into rings.
There's other errors too: In a situation like this the Earth would also synchronize it's orbit. A day would speed up and the moon pushed higher until the two matched. This would stop the flood, burn scenario in the article.
If the moon was orbiting the earth faster than the Earth's rotation, then the effects of tides would increase the Earth's rotation and decrease the moon's orbital velocity. This would result in the moon descending.
Why are the rocks in the centre "fused together"? Gravity. What other force is there that makes the Moon spherical and holds it together?
The point you make about the tidally-locked orbit doesn't hold. Tidal forces are there whether or not the object is tidally locked. The tidal forces would be high enough to rip the Moon apart if it's as close to the Earth as in this article.
The Roche limit can be derived for rigid bodies (like the Moon) or liquid bodies. The one for rigid bodies is closer to the central body than the one for liquid bodies.
> Why are the rocks in the centre "fused together"? Gravity.
That's what fused them in the first place but they hold together on their own now. Like an asteroid - it's a big rock, gravity is not the force holding it together.
Unlike the earth which has a liquid core, as far as I know the moon is a single solid chunk of rock. So the Roche limit is not an accurate measure - you need to take into account the tensile strength of rock.
> The point you make about the tidally-locked orbit doesn't hold. Tidal forces are there whether or not the object is tidally locked.
You misunderstood me. In a rotating body the tide would cause the object to flex on every rotation, given enough time it would surely break apart from material fatigue.
But in a tidally locked body the force is applied once (a stretching force) and stays that way, so there is no fatigue - either it's strong enough or it's not.
The friction of the tidal forces would generate enourmous amonts of heat, and that energy would be taken from the rotation of the earth and moon, causing both the moon and earth to be locked into synchronous rotation. At least if the moon did not fall down on earth as it probbaly would if going this low. This would cause the moon to stay in a fixed spot in the sky. Since the area under the moon would be in shadow from it most or all of the time, this would be an extra region with polar climate, that could bind up large portion of the earths water as ice, making the earth a lot dryer elsewhere. That is provided that the water did not boil away in the process of locking the rotation.
The Moon is tidally locked to us, be we are not locked to it. Because the Earth rotates faster than the Moon orbits, tidal interaction between the two trades Earth's rate for the Moon's orbital velocity. The Earth is slowing down (and if this process continued long enough, would become tidally locked to the Moon) while the Moon is getting further and further away.
If the Moon were in LEO this process would be reversed; the Moon would be spinning up the Earth while losing orbital velocity.
> If the Moon were in LEO this process would be reversed; the Moon would be spinning up the Earth while losing orbital velocity.
The situation is not reversible like that. Angular momentum is linear, but energy is to the power of two.
So there is more energy than momentum here. You loose energy from fictional heating on the tides and energy as the rotation of the earth "pushes" the moon away.
But if you reverse it than as the moon slows down, it goes lower, but as it does so it orbits even faster than before, meaning it would have to speed up the Earth even more.
So rather than having extra energy (i.e. heat) you don't have enough, so instead of tidally locking to the Earth, the moon just gets faster and faster and then crashes.
Conservation of momentum is why the moons orbit increases as the earth slows down dispite taking more energy. If your speeding up the earths rotation you get energy from the lower orbit and angular momentum from the same place.
Though to be really accurate you need to talk about the center of mass of the earth moon system ect.
Given that that new polar region would get way less sun than either of the existing poles, the icebergs below it might grow a lot higher than they do at the (ant)arctic.
Of course, there are way too many unknowns here. Icebergs will collapse under their own weight at some height, but gravity from the moon would somewhat counteract that. I also wonder what weather patterns would look like, whether stalactites could form on the moon, etc.
Maybe, we could get ice to connect earth and moon before the moon fell down to earth.
1) Its interesting to contemplate a "death star" the size of the moon but of immensely lower density. Could be handy! All the cool aesthetics and applications with none of the planet killing tidal effects.
2) I think the alternative earth dwellers would have some interesting gravitational slingshot opportunities, given something that heavy and that low. Perhaps an interesting multigenerational mega-engineering project would be placing a giant spherical ball of lead in high-ish earth orbit for interplanetary vehicles to slingshot around, not necessarily moon size but a serious chunk of metal. Perhaps a large asteroid or two could be refined down to solid metal (to allow close approach to the center of mass)
3) The ham radio moon-bounce people would be excited to hear it'll take little more than a HT to bounce a VHF signal off the moon, although the multipath might make it impossible to do more than CW and the short orbital duration makes it nearly as annoying to operate as a low orbit satellite. None the less the effect on the ionosphere would be very interesting to look at / think about. Multipath in general might be a very serious problem for radio communication on a planet like this.
I have always wondered about the Moon in geo-synchronous orbit. Over the ocean it could create a water mountain that didn't move. And geo-synch is nicely outside the Roche limit :-)
I wonder how that would have effected migration of humans across the planet, and how their various cultures adapted and formed. Some would see the Moon every day and night, others might only see part of the moon on the horizon. Others might only have distant stories of ancestors who saw the Moon and left it, or stories of the Moon leaving them. Others might forget about it entirely...
I imagine some cultures might resist moving away from where they could see the Moon. The omnipresent Moon might become a sort of god to those that lived under it, such that they would fear traveling so far away from it that it left. Maybe others would fear the perpetually darker nights.
This seems like it could be the premise of a science fiction story, perhaps similar to Asimov's Nightfall.
It would certainly be trivial to make a diagram of el/az of certain craters or mountain peaks referenced to earth magnetic north so as to make chronometers and such for determining longitude irrelevant. No need for precision chronometers would have some subsequent effects on the industrial revolution etc. Of course on the other side of the planet they'd need such "high tech" instruments as chronometers so in sci fi mode, the high tech far siders would likely end up conquering the near siders via higher technology.
A geostationary moon, if tidally locked to present the same face to the earth all the time, would certainly be a convenient termination point for a space elevator. So rather than a space elevator dumping you off in space, you'd be dropped off on the moon. Of course some genius will start transferring the earth's biosphere, oxygen, carbon, etc to the moon and just dumping it there to terraform it. Obviously (?) you can't just run a garden hose to the moon and suck on the moon end and expect a flow rate, although it is sci-fi so maybe if you pressurized the earth side up to something approximately ridiculous, you'd be able to squirt water across to the geosync moon. I would not want to be in charge of that project...
More likely, and perhaps even more fun, would be a moon that was almost in geosynchronous orbit. What would be the effect on civilization and the biosphere if instead of 1 meter tides with a 12 hr period we had 100 meter tides with a 100 year period?
The area of deflection would likely be very large and gravity would still be normal to the surface of the water, so no, you probably wouldn't be able to tell. You might perhaps notice the horizon being closer.
In orbit only the center of mass of the object is in free fall.
Anything farther away is falling "up" and anything closer is falling "down". So the water would fall "down" (i.e. toward the moon).
But since there is plenty of gravity on earth this would mean the water is effectively just lighter. And water on the other side of the Earth is heaver, and would flow to the lighter area until the lighter side was tall enough (i.e. had enough extra water) to balance that out.
Inside the Roche limit[0], the Moon would begin to disintegrate (depending on its relative strength compared to the disruptive forces) and the Earth would end up with rings.
As far as I remember, the ISS orbits low enough that it requires regular rocket boosts to maintain its orbit against drag from the last bits of the atmosphere. So if the moon orbited there, I'm guessing it would have fallen back to the Earth within a few hundred years or so.
My guess is that tidal forces (speeding up Earth's rotation, but slowing down the moon (the opposite of what happens in this reality)) would dominate over atmospheric drag.
How much atmospheric drag affects a spacecraft in LEO is a complex problem, being a function of the spacecraft's mass, surface area, orientation, etc. However the moon is dense enough that it would probably be fairly content to barrel through the sparse atmosphere for quite some time.
The volume to surface area of the moon is massively greater than the ISS, and only a tiny amount of the surface area is actually exposed to the atmosphere. If the Issue can last for months without a boost, I figure the effect of the moon on the moon would be neglible on much longer timescales.
It's not. It's not bright enough to see through backscatter in the atmosphere. Go look at the fullish moon on a sunny day and you'll see the same effect.
would the moon be able to orbit at its current angular speed / period as it does currently if it was closer and still maintain a constant distance?
i would think it would need to orbit much faster because the gravitational pull would be several fold larger. proportionally if it orbits at 27 days currently, it would need to orbit at (238,000 / (2160/2 + 260)) = 177.6x faster...and that's if gravity effects were linear, which they arent...they're inverse square.
"Earth’s Roche limit, the distance from the Earth where its tides could break another object apart"
It's a very common error. This limit is for an object "held together by gravity alone"! The moon is not held together by gravity alone - the dust on the surface is, but the rocks in the center are all fused together.
Additionally since they assume the moon will continue to have a synchronized orbit (the same side always faces us) it won't feel the tides in the same way. It would feel some constant stretching, but not the severe flexing caused by rotation.
The closer side would fall "down" and the far side would fall "up". Only the center would be in free fall. I suspect the moon could survive that - but I'm not sure.
If not, it would spread out into rings.
There's other errors too: In a situation like this the Earth would also synchronize it's orbit. A day would speed up and the moon pushed higher until the two matched. This would stop the flood, burn scenario in the article.