A dumb question

[Bomb#20]

We're not going to lose the moon. The earth's Hill sphere is about three times bigger than the orbit the moon will have when it stops moving away, when the earth becomes tidally locked. The lion's share of the earth's original rotational angular momentum has already been transferred to the moon, so it hasn't got all that much further out to go.

The Hill Sphere isn't a hard limit. Beware the werewolves, Earth currently has two moons. The second one will soon be lost, though.

(I hope this link behaves--works for me, but it doesn't like it when the board tries to preview it.)

Radware Bot Manager Captcha

If I'm reading the diagram correctly, the second moon will be four million km away during the period when it's "captured" -- way outside the Hill sphere -- and will complete only a small fraction of a single orbit before it "escapes". I don't think horseshoe orbits are a good analogy for elliptical orbits.

Also, remember that there are two systems involved: Sun-Earth and Earth-Moon. Remember, everything locks eventually. Since the Earth-Sun lock is a year then the Earth-Moon lock is also a year--but a year is well outside our Hill Sphere. Given sufficient time the moon is lost.

I'm not following. Why would the Earth-Moon system become tidally locked to the Sun? Ignoring red-giant issues, the long-term projection of the three-body system is for the Earth-Moon system to lose angular momentum, with the Moon sinking closer and closer to the Earth, dropping below the Roche Limit, getting ripped apart by tidal forces, and becoming a ring system.

 

[Bomb#20]

We're not going to lose the moon. The earth's Hill sphere is about three times bigger than the orbit the moon will have when it stops moving away, when the earth becomes tidally locked. The lion's share of the earth's original rotational angular momentum has already been transferred to the moon, so it hasn't got all that much further out to go.

What will the orbital radius be for the moon when it stops moving away? How would you calculate that?

I didn't calculate it; I looked it up -- it will be about 1.4 times the current radius. But as I understand the reasoning, as the moon moves away it sucks angular momentum from the earth. So you just extrapolate that to the end. Currently the moon has about 80% of the angular momentum of the earth-moon system and the earth's daily rotation has the other 20%. So you use Kepler's laws to figure out how much further away the moon would need to be to have essentially all of it. The site I found said the month would be 47 days long at that point, which means the earth's rotational angular momentum will be 1/47 of its current level. I.e., the earth will have 0.4% of the angular momentum and the moon's orbit will have 99.6%. (The moon's own rotation will have something like 0.001%.) This whole process is estimated to take about 50 billion years.

 

[Bomb#20]

Also, remember that there are two systems involved: Sun-Earth and Earth-Moon. Remember, everything locks eventually. Since the Earth-Sun lock is a year then the Earth-Moon lock is also a year--but a year is well outside our Hill Sphere. Given sufficient time the moon is lost.

I'm not following. Why would the Earth-Moon system become tidally locked to the Sun? Ignoring red-giant issues, the long-term projection of the three-body system is for the Earth-Moon system to lose angular momentum, with the Moon sinking closer and closer to the Earth, dropping below the Roche Limit, getting ripped apart by tidal forces, and becoming a ring system.

Oh, wait. Are you saying everything locks eventually because everything loses angular momentum and you're assuming that means everything's rotation slows down? If so, that only applies to rigid bodies. When the Earth-Moon system loses angular momentum its rotation speeds up, because the Moon drops into a lower orbit, and lower orbits are faster.

 

[Loren Pechtel]

Once a tidal lock is established only a major outside disruption could end it. That will happen eventually, though. Any system not in a bidirectional tidal lock will slowly move towards lock--Earth isn't locked, thus the Earth is slowing down, transferring momentum to the moon. Eventually the gravitational binding of the moon to the Earth will cease to be the dominant force and it will wander off to orbit the sun instead. At the limit of the Hill Sphere the binding energy is zero and it will just wander off, in the real world this will never happen because as objects approach this limit they become more and more vulnerable to external forces and something is going to pull it away.

We're not going to lose the moon. The earth's Hill sphere is about three times bigger than the orbit the moon will have when it stops moving away, when the earth becomes tidally locked. The lion's share of the earth's original rotational angular momentum has already been transferred to the moon, so it hasn't got all that much further out to go.

What will the orbital radius be for the moon when it stops moving away? How would you calculate that?

It will stop when the Sun-Earth-Moon system is locked. Thus the moon would have an orbit of one year (although with the sun shedding mass over time that will be more than our current year.) I didn't need to do anything more than this as I know the maximum orbital period of something around Earth is under a year.

Wikipedia says our Hill Sphere is 1.4714Mkm.
OmniCalculator says that the orbital period at that altitude is 206.93 days. If we look at half the Hill Sphere (the highest number I'm finding for what might be stable on geological scales) it's down to 73.63 days.

It would be pretty hard to hold onto the moon through any sort of ejection event. However, I see a possible survival scenario: If we don't fall in when the sun goes red giant it might lose half it's mass by the time it settles down as a white dwarf. That would cause Earth to wander off--gentle, not an ejection event. That would remove the sun from the picture and make the Earth much more able to hold onto the moon.

 

[Loren Pechtel]

We're not going to lose the moon. The earth's Hill sphere is about three times bigger than the orbit the moon will have when it stops moving away, when the earth becomes tidally locked. The lion's share of the earth's original rotational angular momentum has already been transferred to the moon, so it hasn't got all that much further out to go.

The Hill Sphere isn't a hard limit. Beware the werewolves, Earth currently has two moons. The second one will soon be lost, though.

(I hope this link behaves--works for me, but it doesn't like it when the board tries to preview it.)

Radware Bot Manager Captcha

If I'm reading the diagram correctly, the second moon will be four million km away during the period when it's "captured" -- way outside the Hill sphere -- and will complete only a small fraction of a single orbit before it "escapes". I don't think horseshoe orbits are a good analogy for elliptical orbits.

Yeah, the point was that in the real world it's fuzzy.

Also, remember that there are two systems involved: Sun-Earth and Earth-Moon. Remember, everything locks eventually. Since the Earth-Sun lock is a year then the Earth-Moon lock is also a year--but a year is well outside our Hill Sphere. Given sufficient time the moon is lost.

I'm not following. Why would the Earth-Moon system become tidally locked to the Sun? Ignoring red-giant issues, the long-term projection of the three-body system is for the Earth-Moon system to lose angular momentum, with the Moon sinking closer and closer to the Earth, dropping below the Roche Limit, getting ripped apart by tidal forces, and becoming a ring system.

If the Earth-moon system becomes doubly locked the sun is still in the game trying to lock the Earth. Thus the process does not stop at the double lock point.

 

[bilby]

If the Earth-moon system becomes doubly locked the sun is still in the game trying to lock the Earth.

Surely the Sun is trying to lock the Earth-Moon system, not just the Earth. Solar tides affect both Earth and Moon, and presumably also affect the way these two bodies orbit each other - The Moon's orbit around the Earth (or rather the two's orbit around their barycentre) is a rotation that is subject to solar tides, but in a more complex fashion because their orbital rotation is flexible - the Moon is not (yet) physically linked to the Earth (because NASA hasn't got a long enough pole).

 

[Jokodo]

We're not going to lose the moon. The earth's Hill sphere is about three times bigger than the orbit the moon will have when it stops moving away, when the earth becomes tidally locked. The lion's share of the earth's original rotational angular momentum has already been transferred to the moon, so it hasn't got all that much further out to go.

What will the orbital radius be for the moon when it stops moving away? How would you calculate that?

I didn't calculate it; I looked it up -- it will be about 1.4 times the current radius. But as I understand the reasoning, as the moon moves away it sucks angular momentum from the earth. So you just extrapolate that to the end. Currently the moon has about 80% of the angular momentum of the earth-moon system and the earth's daily rotation has the other 20%. So you use Kepler's laws to figure out how much further away the moon would need to be to have essentially all of it. The site I found said the month would be 47 days long at that point, which means the earth's rotational angular momentum will be 1/47 of its current level. I.e., the earth will have 0.4% of the angular momentum and the moon's orbit will have 99.6%. (The moon's own rotation will have something like 0.001%.) This whole process is estimated to take about 50 billion years.

I didn't check the math, but an interesting side note: we can calculate the distance at earth and moon will be when they achieve mutual tidal locking with much better precision than the time it will take to get there. While the total energy that had to dissipate to the moon for this to happen is a constant, the rate at which it dissipates depends on coincidences life the current arrangement of continents: the more they conspire to create barriers against the movement of the tides, the more the tides show down the earth's rotation.

 

[bilby]

the more they conspire to create barriers against the movement of the tides, the more the tides show down the earth's rotation.

I knew it was all a big conspiracy!

It's the Isthmus of Panama that's behind all of this. The whole thing is so hush-hush, you can't even find out from Google who currently holds the office of Isthmus in the Panamanian regime.

Hang on, brb, just going to check what this black helicopter is doing outsi

 

[Loren Pechtel]

If the Earth-moon system becomes doubly locked the sun is still in the game trying to lock the Earth.

Surely the Sun is trying to lock the Earth-Moon system, not just the Earth. Solar tides affect both Earth and Moon, and presumably also affect the way these two bodies orbit each other - The Moon's orbit around the Earth (or rather the two's orbit around their barycentre) is a rotation that is subject to solar tides, but in a more complex fashion because their orbital rotation is flexible - the Moon is not (yet) physically linked to the Earth (because NASA hasn't got a long enough pole).

That's my point--once the Earth-Moon system becomes fully locked the sun is still messing with things. The only truly stable state is when both pairs are locked--but that results in loss to the Hill Sphere.

 

[bilby]

If the Earth-moon system becomes doubly locked the sun is still in the game trying to lock the Earth.

Surely the Sun is trying to lock the Earth-Moon system, not just the Earth. Solar tides affect both Earth and Moon, and presumably also affect the way these two bodies orbit each other - The Moon's orbit around the Earth (or rather the two's orbit around their barycentre) is a rotation that is subject to solar tides, but in a more complex fashion because their orbital rotation is flexible - the Moon is not (yet) physically linked to the Earth (because NASA hasn't got a long enough pole).

That's my point--once the Earth-Moon system becomes fully locked the sun is still messing with things. The only truly stable state is when both pairs are locked--but that results in loss to the Hill Sphere.

But there is no "both pairs"; There are three bodies, and so three possible pairings.

 

[Gospel]

Don't listen to bibly. It's a clone. The real bibly is on a black helicopter en route to Isthmus HQ.

 

[Jokodo]

the more they conspire to create barriers against the movement of the tides, the more the tides show down the earth's rotation.

I knew it was all a big conspiracy!

It's the Isthmus of Panama that's behind all of this. The whole thing is so hush-hush, you can't even find out from Google who currently holds the office of Isthmus in the Panamanian regime.

Hang on, brb, just going to check what this black helicopter is doing outsi

Incidentally, we indeed live in a time of unusually high tidal breaking, with plenty of landmasses near the equator where they get in the way of the tidal bulge. That some of the landmasses that block the equator extend way south and north only makes things worse.

 

[steve_bank]

I first heard this about a North Africa underground lake that was found and is beg pupped over long distances.

All the pumpedd water that ends up in the oceans is increasing sea levels.

Rampant Groundwater Pumping Has Changed the Tilt of Earth's Axis

Human depletion of groundwater has shifted the global distribution of water so much that the North Pole has drifted by more than four centimeters per year

www.scientificamerican.com

Rampant Groundwater Pumping Has Changed the Tilt of Earth’s Axis

Human depletion of groundwater has shifted the global distribution of water so much that the North Pole has drifted by more than four centimeters per year

https://www.cnn.com/2023/06/26/world/pumping-groundwater-earth-axis-shifting-scn/index.html

Groundwater provides drinking water for people and livestock, and it helps with crop irrigation when rain is scarce. However, the new research shows that persistent groundwater extraction over more than a decade shifted the axis on which our planet rotates, tipping it over to the east at a rate of about 1.7 inches (4.3 centimeters) per year.

Humans pump so much groundwater that Earth’s axis has shifted, study finds

“Earth’s rotational pole actually changes a lot,” said lead study author Ki-Weon Seo, a professor in the department of Earth science education at Seoul National University in South Korea, in a news release. “Our study shows that among climate-related causes, the redistribution of groundwater actually has the largest impact on the drift of the rotational pole.”

 

[Loren Pechtel]

If the Earth-moon system becomes doubly locked the sun is still in the game trying to lock the Earth.

Surely the Sun is trying to lock the Earth-Moon system, not just the Earth. Solar tides affect both Earth and Moon, and presumably also affect the way these two bodies orbit each other - The Moon's orbit around the Earth (or rather the two's orbit around their barycentre) is a rotation that is subject to solar tides, but in a more complex fashion because their orbital rotation is flexible - the Moon is not (yet) physically linked to the Earth (because NASA hasn't got a long enough pole).

That's my point--once the Earth-Moon system becomes fully locked the sun is still messing with things. The only truly stable state is when both pairs are locked--but that results in loss to the Hill Sphere.

But there is no "both pairs"; There are three bodies, and so three possible pairings.

But how could the moon lock to both Earth and the Sun?

 

[Jokodo]

If the Earth-moon system becomes doubly locked the sun is still in the game trying to lock the Earth.

Surely the Sun is trying to lock the Earth-Moon system, not just the Earth. Solar tides affect both Earth and Moon, and presumably also affect the way these two bodies orbit each other - The Moon's orbit around the Earth (or rather the two's orbit around their barycentre) is a rotation that is subject to solar tides, but in a more complex fashion because their orbital rotation is flexible - the Moon is not (yet) physically linked to the Earth (because NASA hasn't got a long enough pole).

That's my point--once the Earth-Moon system becomes fully locked the sun is still messing with things. The only truly stable state is when both pairs are locked--but that results in loss to the Hill Sphere.

But there is no "both pairs"; There are three bodies, and so three possible pairings.

But how could the moon lock to both Earth and the Sun?

In the Lagrange point?

 

[Shadowy Man]

If the Earth-moon system becomes doubly locked the sun is still in the game trying to lock the Earth.

Surely the Sun is trying to lock the Earth-Moon system, not just the Earth. Solar tides affect both Earth and Moon, and presumably also affect the way these two bodies orbit each other - The Moon's orbit around the Earth (or rather the two's orbit around their barycentre) is a rotation that is subject to solar tides, but in a more complex fashion because their orbital rotation is flexible - the Moon is not (yet) physically linked to the Earth (because NASA hasn't got a long enough pole).

That's my point--once the Earth-Moon system becomes fully locked the sun is still messing with things. The only truly stable state is when both pairs are locked--but that results in loss to the Hill Sphere.

But there is no "both pairs"; There are three bodies, and so three possible pairings.

But how could the moon lock to both Earth and the Sun?

In the Lagrange point?

Which one? The closest ones to the Moon are unstable.

 

[Loren Pechtel]

If the Earth-moon system becomes doubly locked the sun is still in the game trying to lock the Earth.

Surely the Sun is trying to lock the Earth-Moon system, not just the Earth. Solar tides affect both Earth and Moon, and presumably also affect the way these two bodies orbit each other - The Moon's orbit around the Earth (or rather the two's orbit around their barycentre) is a rotation that is subject to solar tides, but in a more complex fashion because their orbital rotation is flexible - the Moon is not (yet) physically linked to the Earth (because NASA hasn't got a long enough pole).

That's my point--once the Earth-Moon system becomes fully locked the sun is still messing with things. The only truly stable state is when both pairs are locked--but that results in loss to the Hill Sphere.

But there is no "both pairs"; There are three bodies, and so three possible pairings.

But how could the moon lock to both Earth and the Sun?

In the Lagrange point?

The Earth-Moon distance is determined entirely by the Earth and Moon. However, the location of the Lagrange points are determined by the Earth-Sun relationships. Thus I see no reason to think there's any relationship between them. It's moot, anyway, as both L1 and L2 are energy hills--flat, but unstable. And they're outside our Hill Sphere.

 

[Bomb#20]

We're not going to lose the moon. The earth's Hill sphere is about three times bigger than the orbit the moon will have when it stops moving away, when the earth becomes tidally locked. The lion's share of the earth's original rotational angular momentum has already been transferred to the moon, so it hasn't got all that much further out to go.

... Also, remember that there are two systems involved: Sun-Earth and Earth-Moon. Remember, everything locks eventually. Since the Earth-Sun lock is a year then the Earth-Moon lock is also a year--but a year is well outside our Hill Sphere. Given sufficient time the moon is lost.

I'm not following. Why would the Earth-Moon system become tidally locked to the Sun? Ignoring red-giant issues, the long-term projection of the three-body system is for the Earth-Moon system to lose angular momentum, with the Moon sinking closer and closer to the Earth, dropping below the Roche Limit, getting ripped apart by tidal forces, and becoming a ring system.

If the Earth-moon system becomes doubly locked the sun is still in the game trying to lock the Earth. Thus the process does not stop at the double lock point.

Sure, the sun is still trying to lock the Earth; but that would mean going from its (projected) 47-day rotational period to 365 days. I.e., the sun will be trying to slow the earth. To whatever extent it succeeds, that means from the moon's point of view the earth will start to have retrograde rotation. So the direction of the torque on the earth from lunar tides will be reversed. So the earth's rotation will start sucking angular momentum back out of the moon's orbit, causing the moon to start sinking back toward the earth. The process does not stop at the double lock point, but the direction of the effect reverses.

 

[Loren Pechtel]

We're not going to lose the moon. The earth's Hill sphere is about three times bigger than the orbit the moon will have when it stops moving away, when the earth becomes tidally locked. The lion's share of the earth's original rotational angular momentum has already been transferred to the moon, so it hasn't got all that much further out to go.

... Also, remember that there are two systems involved: Sun-Earth and Earth-Moon. Remember, everything locks eventually. Since the Earth-Sun lock is a year then the Earth-Moon lock is also a year--but a year is well outside our Hill Sphere. Given sufficient time the moon is lost.

I'm not following. Why would the Earth-Moon system become tidally locked to the Sun? Ignoring red-giant issues, the long-term projection of the three-body system is for the Earth-Moon system to lose angular momentum, with the Moon sinking closer and closer to the Earth, dropping below the Roche Limit, getting ripped apart by tidal forces, and becoming a ring system.

If the Earth-moon system becomes doubly locked the sun is still in the game trying to lock the Earth. Thus the process does not stop at the double lock point.

Sure, the sun is still trying to lock the Earth; but that would mean going from its (projected) 47-day rotational period to 365 days. I.e., the sun will be trying to slow the earth. To whatever extent it succeeds, that means from the moon's point of view the earth will start to have retrograde rotation. So the direction of the torque on the earth from lunar tides will be reversed. So the earth's rotation will start sucking angular momentum back out of the moon's orbit, causing the moon to start sinking back toward the earth. The process does not stop at the double lock point, but the direction of the effect reverses.

I think you're right. And that probably means the moon eventually comes down.