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View Full Version : How far away would the orbit of the moon be if it had a mass equal to Earth.

CobaltBlue
2016-Jan-05, 05:48 PM
Assuming that the moon's density was high enough to create one Earth gravity, how far away from Earth would it have to continue safely revolving around the Earth?

antoniseb
2016-Jan-05, 06:44 PM
What do you mean by safely? Are you just asking how far away a 1 Earth mass would need to be to be the same as the Moon is now for tides?

CobaltBlue
2016-Jan-05, 06:48 PM
No, how far away would it need to be, (and also how fast would its orbit have to be) in order to maintain a distance where the two planets maintained a stable orbit with each other.

schlaugh
2016-Jan-05, 07:13 PM
You might try plugging values into the calculator linked below. Using one Earth mass for the moon but maintaining the current distance it looks like the tidal force increases substantially, maybe as much as 81 times of the current tidal effect if I am reading this correctly.

http://keisan.casio.com/exec/system/1360312100

ETA: Just saw your second post. The two objects would orbit around a common point called the barycenter (https://en.wikipedia.org/wiki/Barycenter), roughly halfway between the Earth and the moon in your example with each having one Earth mass. It would be stable but not sure for how long and what effects the Sun and other planets would have on disrupting such a system. Could be a very long time.

BigDon
2016-Jan-05, 08:38 PM
With Schlaugh's rather disconcerting input I, for one, vote against increasing the Moon's mass six-fold or so.

All in favor?

CobaltBlue
2016-Jan-05, 08:53 PM
What I'm trying to ask is this: Obviously if the moon were to suddenly reach a mass equal to Earths, then at their present distance and the moon's rate of revolution, they'd eventually crash into each other. How far out would you have to move the moon, so that wouldn't happen? I'm assuming that at that point the gravitational pull of the moon on the tides would remain the same since it is a greater distance from Earth now. If the moon's volume didn't change (only its mass and therefore density) it would obviously be smaller in the night sky and would shed less light at night. I'm just trying to find out how far out that would be- the pull of other planets on the system notwithstanding.

agingjb
2016-Jan-05, 10:13 PM
Back of the envelope (and welcoming correction): an Earth Earth double in a roughly circular mutual orbit would have a period of a month at a separation of 340,000 miles, about.

CobaltBlue
2016-Jan-05, 10:16 PM
Back of the envelope (and welcoming correction): an Earth Earth double in a roughly circular mutual orbit would have a period of a month at a separation of 340,000 miles.

I appreciate it. So we're talking almost half again the average distance. That actually helps me a lot.

schlaugh
2016-Jan-05, 10:25 PM
What I'm trying to ask is this: Obviously if the moon were to suddenly reach a mass equal to Earths, then at their present distance and the moon's rate of revolution, they'd eventually crash into each other. How far out would you have to move the moon, so that wouldn't happen? I'm assuming that at that point the gravitational pull of the moon on the tides would remain the same since it is a greater distance from Earth now. If the moon's volume didn't change (only its mass and therefore density) it would obviously be smaller in the night sky and would shed less light at night. I'm just trying to find out how far out that would be- the pull of other planets on the system notwithstanding.

(Interesting side issue: if two objects of equal mass orbit around a barycenter, then what are the respective Roche limits for each mass? Or does that even matter?)

I'm not sure that if the moon suddenly increased to 1 Earth mass that the two planets would crash into each other. What makes you think that? Certainly tidal locking would occur much sooner for the Earth since tidal forces would be sharply increased with a larger mass orbiting at the current, average distance of 384,400 km.

The calculator mentioned above should let you fiddle with the inputs to achieve the same tidal force but with varying degrees of mass and distance. What I come up with is a moon of 1 Earth mass would need to be a bit more than 4 times further away to have the same tidal force as it does today (assuming the calculator is accurate.) :)

ETA: That said, the calculator make no assumptions (and may not have to) on an orbit with a barycenter equally distant from both objects.

CobaltBlue
2016-Jan-05, 10:32 PM
(Interesting side issue: if two objects of equal mass orbit around a barycenter, then what are the respective Roche limits for each mass? Or does that even matter?)

I'm not sure that if the moon suddenly increased to 1 Earth mass that the two planets would crash into each other. What makes you think that? Certainly tidal locking would occur much sooner for the Earth since tidal forces would be sharply increased with a larger mass orbiting at the current, average distance of 384,400 km.

The calculator mentioned above should let you fiddle with the inputs to achieve the same tidal force but with varying degrees of mass and distance. What I come up with is a moon of 1 Earth mass would need to be a bit more than 4 times further away to have the same tidal force as it does today (assuming the calculator is accurate.) :)

Granted, my understanding of physics is somewhat limited, but the reason I believe that they would crash into each other if their speeds were not increased is that the closer two objects are and the greater their mass, the stronger the pull of gravity is upon them. If the moon were to suddenly increase its mass to equal the Earth's then the gravitational pull between them would overcome the centrifugal force of the moon trying to pull away and bring it crashing down. Hmmm.... four times the distance to to maintain the same tidal forces? That could create some problems for what I'm trying to do.

StupendousMan
2016-Jan-05, 11:22 PM
Obviously if the moon were to suddenly reach a mass equal to Earths, then at their present distance and the moon's rate of revolution, they'd eventually crash into each other.

Your "obvious" claim is false. Can you explain why you think they would crash into each other rather than continuing to orbit their common center of mass?

Perhaps you mean "after many trillions of years, the gravitational radiation would carry away enough angular momentum to cause the two objects to merge." If one ignores all other objects in the universe, yes, that is true. But I suspect you meant something else.

Jens
2016-Jan-05, 11:23 PM
What I'm trying to ask is this: Obviously if the moon were to suddenly reach a mass equal to Earths, then at their present distance and the moon's rate of revolution, they'd eventually crash into each other.

This might sound counter-intuitive but the answer is that no, they would not. If you have two bodies in orbit and you increase the mass of one, it will not put them into a death spiral. The orbit will simply find a new equilibrium. The only important thing is something called the Roche limit, which is when an object gets so close to another that the gravity on the near side is stronger than that on the far side, ripping it apart.

Jens
2016-Jan-05, 11:27 PM
Your "obvious" claim is false. Can you explain why you think they would crash into each other rather than continuing to orbit their common center of mass?

I don't think you need the hostility. I think it's a very common misconception that for example, if you slowed down the earth's orbital speed, it would spiral into the sun.

bknight
2016-Jan-06, 12:17 AM
No, how far away would it need to be, (and also how fast would its orbit have to be) in order to maintain a distance where the two planets maintained a stable orbit with each other.
You realize that the Moon is shifting away from the Earth by a few centimeters per year and it started out Much closer to the Earth after the initial impact and has been opening up the distance since that time.

CobaltBlue
2016-Jan-06, 12:19 AM
You realize that the Moon is shifting away from the Earth by a few centimeters per year and it started out Much closer to the Earth after the initial impact and has been opening up the distance since that time.

Yes, I'm aware of that fact. Now, I replied to the other points made about why I thought they would crash into each other, but the posts have not yet appeared.

slang
2016-Jan-06, 01:14 AM
Yes, I'm aware of that fact. Now, I replied to the other points made about why I thought they would crash into each other, but the posts have not yet appeared.

As of now there are no posts waiting to be approved in this thread.

CobaltBlue
2016-Jan-06, 01:15 AM
As of now there are no posts waiting to be approved in this thread.

See post number 10.

slang
2016-Jan-06, 01:38 AM
See post number 10.

I repeat, as of now there are no posts waiting to be approved in this thread. If your browser shows anything else, it's your browser that is suspect. Also, don't reply to moderators comments unless specifically asked for, see rule 17. Use report button, PM, or feedback. Thanks.

Grey
2016-Jan-06, 02:07 AM
Welcome to the board, CobaltBlue. As others have noted, there's no reason an Earth-mass moon couldn't orbit at the same distance as the present Moon. And even if you suddenly increased the mass of the Moon somehow, it would not crash into the Earth. The orbit would be different, but it would still be a stable orbit.

CobaltBlue
2016-Jan-06, 02:09 AM
Welcome to the board, CobaltBlue. As others have noted, there's no reason an Earth-mass moon couldn't orbit at the same distance as the present Moon. And even if you suddenly increased the mass of the Moon somehow, it would not crash into the Earth. The orbit would be different, but it would still be a stable orbit.

Thank you. It would seem that my considerations would have to be more for the tidal effects of each on the other. This is actually for a novel I'm working on, so I'm trying to get SOME things right about the astrophysics.

Ken G
2016-Jan-06, 02:10 AM
Granted, my understanding of physics is somewhat limited, but the reason I believe that they would crash into each other if their speeds were not increased is that the closer two objects are and the greater their mass, the stronger the pull of gravity is upon them.That is true, the gravitational force would increase, and the Moon would start to get closer.

If the moon were to suddenly increase its mass to equal the Earth's then the gravitational pull between them would overcome the centrifugal force of the moon trying to pull away and bring it crashing down. The first part of that is true-- the second part is not. Gravity being stronger than the centrifugal force only means that the Moon will begin to fall in, but it won't keep falling in. It's similar to what would happen if you slowed the Moon down to, say, half its current speed. Either way, the Moon starts to fall in, but instead of crashing down on the Earth, it simply goes into an elliptical orbit. agingjb assumed you were requiring a circular orbit with the same period in his calculation, but if you are only asking if the Moon will hit the Earth, then we are allowing elliptical orbits. The Earth is a pretty small target-- the Moon would still miss the Earth even if you increased its mass to the mass of the Earth. Interestingly, the orbit of two distant bodies is always an ellipse, so even if the Moon started to fall in at first, it would later return to its same distance, only to start falling in again and again.

tony873004
2016-Jan-06, 02:35 AM
On January 21, 2016, the Moon will suddenly become as massive as Earth in this simulation:
http://orbitsimulator.com/gravitySimulatorCloud/simulations/1452046717314_MoonGainsMass.html
Press the Play button [>] on the Time Step interface to begin.

Ken G
2016-Jan-06, 02:55 AM
Nothing like a simulation to show what happens! But I think you should make one point-- the simulation seems designed to fix the center of mass, so when you change the Moon mass, there is a sudden shift in the location of both Earth and Moon in your simulation. That does not correspond to any actual movement of those planets, relative to the Sun, it's just a coordinate effect. This kind of masks the fact that the Moon will return to its present distance from Earth-- the orbit does not get uniformly much tighter, it's tighter at perigee but not apogee-- if it looks otherwise it must be a kind of illusion from how the center of mass shifts.

By the way, your simulation prior to the mass change is the first visceral image I've seen of how much the separation between Earth and Moon varies. It really gives me the feel of a much ricketier orbit than I usually imagine!

schlaugh
2016-Jan-06, 03:04 AM
On January 21, 2016, the Moon will suddenly become as massive as Earth in this simulation:
http://orbitsimulator.com/gravitySimulatorCloud/simulations/1452046717314_MoonGainsMass.html
Press the Play button [>] on the Time Step interface to begin.

Not a good day to be on planet Earth. (Nicely done, thank you.)

tony873004
2016-Jan-06, 03:04 AM
... This kind of masks the fact that the Moon will return to its present distance from Earth-- the orbit does not get uniformly much tighter, it's tighter at perigee but not apogee-- if it looks otherwise it must be a kind of illusion from how the center of mass shifts...
Uncheck the "barycenter" option on the Frame A interface. Then the camera locks on the Earth rather than the barycenter.

John Mendenhall
2016-Jan-06, 03:48 AM
That is true, the gravitational force would increase, and the Moon would start to get closer.

(snip)

You might want to recheck tjis idea, Ken . . .:doh:

Regards, John M.

tony873004
2016-Jan-06, 03:54 AM
For a different visualization, on the Frame A interface, use the (-) button under the word Zoom to zoom out to 2000. Then select "Moon" instead of "Camera A" from the dropdown list.

John Mendenhall
2016-Jan-06, 03:59 AM
With Schlaugh's rather disconcerting input I, for one, vote against increasing the Moon's mass six-fold or so.

All in favor?

Figures are a little off, BigD.

Regards, John M.

John Mendenhall
2016-Jan-06, 04:07 AM
You might want to recheck tjis idea, Ken . . .:doh:

Regards, John M.

Never mind, your next post cleared it up. Sorry.

John Mendenhall
2016-Jan-06, 04:13 AM
I don't think you need the hostility. I think it's a very common misconception that for example, if you slowed down the earth's orbital speed, it would spiral into the sun.

A single small reduction results in a new closer orbit, not a death spiral.

schlaugh
2016-Jan-06, 04:20 AM
Figures are a little off, BigD.

Regards, John M.

I'm not surprised. :)

But can you elaborate? I was using that calculator which may or not be accurate but the values seemed to verify after running them through Excel.

If the mass was increased to one Em and the distance increased to 4x current then the tidal force was almost the same as in the current state model.

Leaving the distance as is but increasing only the mass seemed to show an 81 fold increase in tidal force. I agree that number doesn't seem to make sense but the moon is only 0.12 the mass of the Earth so an eighty-fold increase in its mass should yield a significant increase in tidal force.

John Mendenhall
2016-Jan-06, 04:25 AM
An aside: a 3-body system with one dominant body (earth1, earth2, sun) with the earths orbiting each other is unstable and one of the earths will be ejected. Yes, I looked it up.

And my favorite: :doh:

Jens
2016-Jan-06, 04:30 AM
Not a good day to be on planet Earth. (Nicely done, thank you.)

I'm not sure why anything would be different from our perspective. Would we even notice? Or is it that the tides would grow and we'd have to move away from the oceans?

tony873004
2016-Jan-06, 04:31 AM
An aside: a 3-body system with one dominant body (earth1, earth2, sun) with the earths orbiting each other is unstable and one of the earths will be ejected. Yes, I looked it up.

And my favorite: :doh:

Do you have a link? I've never heard this and I would be surprised if it were true.

Jens
2016-Jan-06, 04:31 AM
On January 21, 2016, the Moon will suddenly become as massive as Earth in this simulation:
http://orbitsimulator.com/gravitySimulatorCloud/simulations/1452046717314_MoonGainsMass.html
Press the Play button [>] on the Time Step interface to begin.

That is great.

schlaugh
2016-Jan-06, 04:56 AM
I'm not sure why anything would be different from our perspective. Would we even notice? Or is it that the tides would grow and we'd have to move away from the oceans?

I was thinking mostly of tides. Initially i thought that the new barycenter would have a large effect but now I'm not so sure. Would the change be noticeable on earth?

Ken G
2016-Jan-06, 05:40 AM
Uncheck the "barycenter" option on the Frame A interface. Then the camera locks on the Earth rather than the barycenter.That'll do it!

Ken G
2016-Jan-06, 05:51 AM
I was thinking mostly of tides. Initially i thought that the new barycenter would have a large effect but now I'm not so sure. Would the change be noticeable on earth?
The amazing thing about gravity is you can never feel it, except for its tidal effects-- that's the equivalence principle. So increasing the mass of the Moon could only affect Earth by its tidal influences, meaning, the difference in the changes in the force between different locations. So I don't think the effects would be particularly severe if you did the increase slowly, and didn't live on the Bay of Fundy or some such place, but if you did it all of a sudden, that might have the effect of some kind of tidal shock. Maybe tidal waves and earthquakes?

Fiery Phoenix
2016-Jan-06, 07:26 AM
Why wouldn't a substantial reduction in orbital velocity cause an orbiting body to crash into its primary? I was always under the impression that speed is what keeps stuff in orbit, and that planets don't fall into the Sun because they're moving fast enough along their orbital paths (but not fast enough to actually escape the Sun's gravity).

It's about midnight and I'm not thinking very clearly, so apologies if I'm mixing things up here.

Jens
2016-Jan-06, 08:57 AM
Why wouldn't a substantial reduction in orbital velocity cause an orbiting body to crash into its primary? I was always under the impression that speed is what keeps stuff in orbit, and that planets don't fall into the Sun because they're moving fast enough along their orbital paths (but not fast enough to actually escape the Sun's gravity).

It's about midnight and I'm not thinking very clearly, so apologies if I'm mixing things up here.

Well it depends on how substantial the reduction is. If you reduce it to zero, then yes it will crash into the primary. But if you think about it (and as the simulation demonstrated), suppose that the moon was suddenly slowed by half. It would still be moving horizontally relative to the earth, so what would happen is, it would start falling faster, but it's still moving forward so it wouldn't strike the earth, but rather go flying by rather quickly, and then go far to the other side, and then come back rather quickly, but still it would miss the edge of the earth because it's still got that horizontal velocity.

Jeff Root
2016-Jan-06, 09:57 AM
By the way, your simulation prior to the mass change is the first
visceral image I've seen of how much the separation between
Earth and Moon varies. It really gives me the feel of a much
ricketier orbit than I usually imagine!
It isn't as visceral as an animation, but it *is* to scale:

http://www.freemars.org/jeff/planets/Luna/Luna.htm

The mean distance between Earth and Luna is shown in the top
diagram and by the middle dot in the similar diagram at mid-page.
The three pictures of eclipses above that diagram unfortunately
(or by less than perfectly thought out design) look like they are
supposed to correspond to the three positions of the Moon, but
they don't quite, and weren't intended to. Done prior to 2003.

-- Jeff, in Minneapolis

Ken G
2016-Jan-06, 10:36 AM
Yes, the scale is useful to see. It is always helpful to explaining why eclipses are so rare!

slang
2016-Jan-06, 10:58 AM
Thank you. It would seem that my considerations would have to be more for the tidal effects of each on the other. This is actually for a novel I'm working on, so I'm trying to get SOME things right about the astrophysics.

quote-bumping as this post was approved a little late and the thread has moved on. :)

CobaltBlue
2016-Jan-06, 12:56 PM
Thank you for the simulation.

Grey
2016-Jan-06, 08:20 PM
Thank you. It would seem that my considerations would have to be more for the tidal effects of each on the other. This is actually for a novel I'm working on, so I'm trying to get SOME things right about the astrophysics.So, for the tides, two things to note. One is that, as others have mentioned, increasing the Moon's mass to the Earth's (a factor of about 80) also increases the size of tides by a factor of 80. That's enormous. Worse, if you look at the simulation, and imagining the Moon suddenly gaining that mass somehow, the orbit becomes more highly elliptical, and perigee is now something like three times closer. Tides scale linearly with mass, but by the inverse cube of the distance, so being three times closer means another factor of 27 for the size of tides. So instead of having a tide on the order of a meter difference, you'd have a pair of 2,000+ meter waves circling the Earth every day. Could make life rough for people on the coastline, or even pretty far inland.

CobaltBlue
2016-Jan-06, 08:25 PM
So, for the tides, two things to note. One is that, as others have mentioned, increasing the Moon's mass to the Earth's (a factor of about 80) also increases the size of tides by a factor of 80. That's enormous. Worse, if you look at the simulation, and imagining the Moon suddenly gaining that mass somehow, the orbit becomes more highly elliptical, and perigee is now something like three times closer. Tides scale linearly with mass, but by the inverse cube of the distance, so being three times closer means another factor of 27 for the size of tides. So instead of having a tide on the order of a meter difference, you'd have a pair of 200+ meter waves circling the Earth every day. Could make life rough for people on the coastline, or even pretty far inland.

Yes, I'm starting to realize this. I'm exploring other concepts, including a rotating space station. I need about 4 million square miles of internal surface. The problem I ran into there, was that to generate 1g of gravity on a ring that was 4,000 miles by 1000 miles, I was having to spin the poor souls at a rate of a little more than one rotation an hour. The idea is to have the Earth visible, and that would be visually, shall we say nauseating.

schlaugh
2016-Jan-06, 08:47 PM
John Varley's Titan (https://en.wikipedia.org/wiki/Gaea_trilogy)series did just that but the "station" was actually a torus and enclosed. The diameter was 1300 km and also rotated about once an hour but with less apparent gravity (about 1/3 Earth gravity IIRC). But in that case nothing on the outside was visible from within.

Watching the Earth move around a circle in an hour's time doesn't seem that it would be all that dizzying. Does viewing the minute hand on a watch cause unease?

CobaltBlue
2016-Jan-06, 08:59 PM
John Varley's Titan (https://en.wikipedia.org/wiki/Gaea_trilogy)series did just that but the "station" was actually a torus and enclosed. The diameter was 1300 km and also rotated about once an hour. But in that case nothing on the outside was visible from within.

Watching the Earth move around a circle in an hour's time doesn't seem that it would be all that dizzying. Does viewing the minute hand on a watch cause unease?
You may have a point there. The idea is that the Earth which has been struck by an asteroid is visible as a reminder to those on the space station that they can't go home yet. The station itself is a wheel shape (not rounded at the edges like a torus that is 1000 miles wide and 4000 miles in circumference (giving it a surface area slightly larger than the United States. It would need to spin at one revolution approximately every 50 minutes to maintain 1g gravity. If it was put in the L5 position and set "rolling" around the solar system with a slow axial spin to represent night and day (haven't done the math on how that spin would affect gravity) it might work.
Thanks for the input.

Ken G
2016-Jan-06, 09:29 PM
I hadn't realized the effects would pile up that much, it does seem like the tides would indeed be pretty nasty, though it's a big continent-- so it might just make people steer clear of beaches, sun, and surfing!

Grey
2016-Jan-07, 11:31 AM
I hadn't realized the effects would pile up that much, it does seem like the tides would indeed be pretty nasty, though it's a big continent-- so it might just make people steer clear of beaches, sun, and surfing!Yes, and I mistyped above. When you multiply 80 by 27, that gives you 2,000+ meters, not 200+ meters. Even Denver isn't high enough to be safe.

CobaltBlue
2016-Jan-07, 12:48 PM
I do appreciate everyone's input here. It's been very helpful.

Ken G
2016-Jan-07, 06:07 PM
Yes, and I mistyped above. When you multiply 80 by 27, that gives you 2,000+ meters, not 200+ meters. Even Denver isn't high enough to be safe.It's not clear the height of the tide will scale like that-- I believe the height of the bulge in the middle of the ocean is much smaller, the height at the beach has to do with effects similar to why waves rise up at the shore.

Grey
2016-Jan-07, 10:04 PM
It's not clear the height of the tide will scale like that-- I believe the height of the bulge in the middle of the ocean is much smaller, the height at the beach has to do with effects similar to why waves rise up at the shore.Actually, that one meter figure is roughly the size of the tidal bulge in the middle of the ocean. It's true that the height on the beach depends not just on the height of the bulge, but also on the shape of the land affecting the currents and so forth. But the net effect of that is often to increase the height differential with the changing tide (the famous Bay of Fundy often has a tidal differential of 10 to 12 meters), and waves do usually increase in height as they move to shallower water. So I think it's a realistic expectation that if Earth had a twin with an orbit that brought it to within 80,000 miles regularly, you'd actually get literally continent-scouring tidal waves (and the continents themselves wouldn't last). Heck, the average deformation of the land due to lunar tides is about 30 cm, so you'd also get some pretty impressive earthquakes and vulcanism. Of course, that kind of tidal stress would also mean that on a fairly short time scale (well, short geologically speaking, anyway), Earth and its twin would reach mutual tidal lock.

Grey
2016-Jan-07, 10:05 PM
I do appreciate everyone's input here. It's been very helpful.Glad we could be of help. It's always fun to take random speculation and run wild with it! ;)

Ken G
2016-Jan-07, 11:33 PM
Actually, that one meter figure is roughly the size of the tidal bulge in the middle of the ocean. This is actually a statistic that is a little hard to pin down. I have heard that in the middle of the ocean, the effect is smaller than normally thought. Also, the site http://home.hiwaay.net/~krcool/Astro/moon/moontides/ states "Offshore, in the deep ocean, the difference in tides is usually less than 1.6 feet." If correct, that would actually be a factor of 4 reduction in a bulge height of 1 meter, so it starts to matter even in estimates. Perhaps this is another way of saying a typical bulge height is about 1/4 the maximum possible in the "point" of the "football".

A more significant issue, in regard to threats to Denver CO, is the timescale for the ocean to get there. The Earth rotates completely through a bulge in about 6 hours, of course, so there is only a threat to regions close enough to the coast that a tidal surge can get there in 6 hours. I'm sure a tidal surge could move pretty fast, but it seems like destinations a thousand miles from the ocean should be fairly safe, no matter how high the tidal bulge is, due to all the friction the water will experience trying to get there. In fact, even without continents at all, I wonder what is the largest size of tidal bulges that the oceans could support, given that the bulge only has a few hours to fill? I suspect if the Moon had the mass of the Earth, the oceans would not reach their equipotential shape, and we'd have very dynamical oceans instead. Might be an issue for circumnavigation, or maybe the ships could use those tidal currents to their advantage. Just stay well away from the shore, unless you really know what you are doing! In any event, we can agree that coasts would be ripped to shreds, and just how far inland the effects would be felt is a tricky issue. The tidal waves would be Interstellar-like, though, that much seems sure!

Grey
2016-Jan-08, 01:27 AM
I got the one meter figure from these (http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit4/tides.html) two (https://www.lhup.edu/~dsimanek/scenario/tides.htm) sites. I agree that the height of the tidal bulge might not scale linearly with the force, this was all a seat of the pants estimate. My guess, though, is that the issue of the water being able to move quickly enough would not be a huge issue; it would certainly have some effect, but note that the difference between the tidal bulge of the ocean, and the Earth itself is just a factor of 3-ish. So at these scales, even the speed of rock deforming is on the same order of magnitude as water, more or less.

Ken G
2016-Jan-08, 04:55 AM
I got the one meter figure from these (http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit4/tides.html) two (https://www.lhup.edu/~dsimanek/scenario/tides.htm) sites.Yes, those are the kind of vague numbers one can find on the internet: "about 1 meter" and "no more than 1 meter." It's odd they don't just calculate the height of the point of the football equipotential! But I think the main thing is, even if the point rises up 1 meter, most of the ocean never rotates through the point, so most of the ocean levels don't vary as much as that. I don't know that the 0.8 foot rise estimate as a typical peak rise is correct though, it's just the estimate I've seen with the most significant figures!

My guess, though, is that the issue of the water being able to move quickly enough would not be a huge issue; it would certainly have some effect, but note that the difference between the tidal bulge of the ocean, and the Earth itself is just a factor of 3-ish. So at these scales, even the speed of rock deforming is on the same order of magnitude as water, more or less.Ah, but I wonder how much of that is that the rock simply expands as the weight is lifted off it a little, rather than having to flow from place to place. Even in the oceans, some of the rise must be due to expansion of water rather than flows, though we know from the tidal currents that there is a lot of flowing going on. But to get far inland, we know the water really has to travel there-- I'm not sure how far the tidal surge would have time to flow up the Mississippi river, for example. It's a long way in 6 hours! Here's a description of a tiny section of river that gets up (so they say) to about 70 miles per hour, but it's not sustained over any great distance, though of course the scale of a 2000 foot water bulge is not equalled anywhere. It's hard to estimate the fastest sustained water flow you could have on a crazy planet like that, and no doubt the erosive effects would be awesome and the landscape of a continent would be rather rapidly changing. Come to think of it, I don't know why we haven't seen a sci fi rendition of a huge tidal surge, not caused by black holes a la Interstellar.

Noclevername
2016-Jan-08, 04:24 PM
Actually, that one meter figure is roughly the size of the tidal bulge in the middle of the ocean. It's true that the height on the beach depends not just on the height of the bulge, but also on the shape of the land affecting the currents and so forth. But the net effect of that is often to increase the height differential with the changing tide (the famous Bay of Fundy often has a tidal differential of 10 to 12 meters), and waves do usually increase in height as they move to shallower water. So I think it's a realistic expectation that if Earth had a twin with an orbit that brought it to within 80,000 miles regularly, you'd actually get literally continent-scouring tidal waves (and the continents themselves wouldn't last). Heck, the average deformation of the land due to lunar tides is about 30 cm, so you'd also get some pretty impressive earthquakes and vulcanism. Of course, that kind of tidal stress would also mean that on a fairly short time scale (well, short geologically speaking, anyway), Earth and its twin would reach mutual tidal lock.

Would that tide locking diminish the more drastic surface effects? And could the mutual orbit eventually become less eccentric if it lasts long enough?

Come to think of it, I don't know why we haven't seen a sci fi rendition of a huge tidal surge, not caused by black holes a la Interstellar.

King David's Spaceship, Jerry Pournelle, 1980. As told from a sailors' viewpoint.

Ken G
2016-Jan-08, 04:26 PM
Would that tide locking diminish the more drastic surface effects? And could the mutual orbit eventually become less eccentric if it lasts long enough?
Yes, tidal locking will circularize the orbits eventually, and then there would be no tidal changes at all.

King David's Spaceship, Jerry Pournelle, 1980. As told from a sailors' viewpoint.I should have known that no new idea is possible in science fiction!

Noclevername
2016-Jan-08, 04:49 PM
Thanks!

Grey
2016-Jan-09, 03:35 PM
Yes, those are the kind of vague numbers one can find on the internet: "about 1 meter" and "no more than 1 meter." It's odd they don't just calculate the height of the point of the football equipotential!You're right (although I think the sites I saw were more concerned with what the actual level rise is, as opposed to the theoretical one). Still, I figured someone must have done the hard work already, and with a little searching, I was able to find this (https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&ved=0ahUKEwjlmoXNgZ3KAhXKGh4KHW1-B3QQFggvMAI&url=http%3A%2F%2Fwww.cambridge.org%2Fus%2Fdownload _file%2F188298%2F&usg=AFQjCNEzJ4DtD4ITXQ7-mvYxoMltkFrLwA&sig2=jdarJUfz9KrQ6ZYaO6dGRw) very nice paper (It's a PDF). I went through it, and I don't see any issues (other than a small typographical error that doesn't affect their results). The author works out the theoretical equipotential surface as a result of the lunar tides; you can see the result down in equation 20. (This is where the small error is. The paper says Earth is m2 and the Moon is m1, even though you can see in Figure 4 that it's the other way around. I checked the calculation just afterword, and the author puts the masses in the right way, so it really was just a mistake in labeling in that sentence). This ends up giving a figure close to half a meter (0.54 m, if you're calculating the difference between high and low), so that would give us a kilometer high wave, rather than two kilometers. This also confirms my suspicion that the expected tidal distortion does vary linearly with the actual tidal force (i.e., linearly with the mass of the source, and inverse cube of the separation).

Looking at Wikipedia (https://en.wikipedia.org/wiki/Tide), I was able to find a figure that helps estimate the propagation delay. Down in the section on amplitude and cycle time, it mentions that, in the absence of land, a long wavelength surface wave would take about 30 hours to go halfway around the Earth (as opposed to the ~12.5 hour semidiurnal period for the tides), so there is some amount of delay. It's interesting to note that the size of the actual tides is very nearly the same as the equipotential surface (at least for the real, relatively small tides), so in the open ocean at least, the tidal distortion of the water seems not particularly limited by wave speed or material elasticity or anything. You're certainly right that this would be different travelling over land. For smaller waves, what usually happens is that the wave slows down and gains height as it travels to shallower areas, or over land, so I assume something similar would happen, but I'm not sure what height it would reach, or how far it would make it, but my guess is that it would be a pretty long ways. In the long term, I expect that net result would be to erode the continents entirely, and my guess is that would happen faster than the inevitable tidal locking.

It does seem like it might make a cool science fiction scenario. But since it should be relatively short-lived on planetary time scales, something would have to happen to set it up. I'm not sure how you could get two planets in this kind of situation without the event that does that having its own dramatic effects.

Ken G
2016-Jan-09, 07:48 PM
This ends up giving a figure close to half a meter (0.54 m, if you're calculating the difference between high and low), so that would give us a kilometer high wave, rather than two kilometers. Half a kilometer, right? We can only count half the difference between high and low. And then there's the problem that most places don't rotate through the peaks of the bulges, so it might be more characteristically half that again. Not that a 1/4 kilometer rise above sea level wouldn't be something awesomely destructive!
This also confirms my suspicion that the expected tidal distortion does vary linearly with the actual tidal force (i.e., linearly with the mass of the source, and inverse cube of the separation).The height the equipotential is linear in the mass, because it's a small perturbation. But I was talking about the fact that the ocean might not reach the equipotential if it doesn't have enough time. That could be a problem in the open ocean, I don't know, but it seems like it would very likely be a big problem for water that has to spill over continents-- they very likely might not have enough time to fill the equipotential.

Looking at Wikipedia (https://en.wikipedia.org/wiki/Tide), I was able to find a figure that helps estimate the propagation delay. Down in the section on amplitude and cycle time, it mentions that, in the absence of land, a long wavelength surface wave would take about 30 hours to go halfway around the Earth (as opposed to the ~12.5 hour semidiurnal period for the tides), so there is some amount of delay.Yes, I thought tidal wave speeds in the open ocean might be a way to estimate that, and indeed it does seem to be longer than the time needed to fill the bulges. So maybe the bulges only half fill, or some such thing, but even that is in the open ocean-- on land, there would seem to be a lot more drag, I would expect the timescale to be even longer for water spilling across land.

It's interesting to note that the size of the actual tides is very nearly the same as the equipotential surface (at least for the real, relatively small tides), so in the open ocean at least, the tidal distortion of the water seems not particularly limited by wave speed or material elasticity or anything.I suspect that may have more to do with an amplification by the shallowing of the water near the shore. There are a lot of important resonant timescales that have to do with size scales for coastline variations. Tides vary a lot from place to place, not just the Bay of Fundy. My guess is, there are wave speeds that apply in shallow water that are much slower than the open-ocean result, so you get local effects monkeying with the global results a fair amount. But I agree that the bulge size does seem to provide a kind of benchmark expectation to start looking for local deviations to.
In the long term, I expect that net result would be to erode the continents entirely, and my guess is that would happen faster than the inevitable tidal locking.Yes, if the planet was always in that condition, it would seem like it would be hard to get continents at all-- the processes that create variations in crust height would seem like they would happen more slowly than the prodigious rate that tidal sloshing would wear them down! You might end up with a rather flat ocean floor. Maybe you could get continents like Antartica-- where the tidal currents are minimized at the poles that don't move through equipotential changes. But yeah, pretty soon it gets tidally locked, and that's the end of that.