Klown Kar Planet: Last Days Before Tidal Lock

[Bizmuth]

Hi all;

Here's the sit: I'm writing a novel which involves colonization of other systems. I want to have a weirdo planet (thus the title) and I decided on a planet that doesn't quite complete a rotation. There's a thread here: https://www.physicsforums.com/threads/how-the-last-days-look-like-just-before-a-tidal-lock.790409/ that discusses it.

Anyway, the point is a planet close enough to its primary to be subject to eventual tidal locking. This planet will be mostly solid, and will have a significant mass inhomogeneity that will make it act like an unbalanced bicycle wheel. At some point, the rotation slows down until it can't quite make it around on the last day. After that, it will swing back and forth through 350 degrees or whatever, every "day".

So, two questions I'm interested in: 1) What would be a plausible range for the period of the swing, and how long would this state last until tidal forces finished locking the planet?

I don't need rigorous math proofs, this is fiction. Just something that won't make the reader want to throw the book at the wall.

 

[DaveC426913]

At some point, the rotation slows down until it can't quite make it around on the last day. After that, it will swing back and forth through 350 degrees or whatever, every "day".

Not sure I follow. It would swing back and forth through 10 degrees, not 350.

 

[Hornbein]

Hi all;

Here's the sit: I'm writing a novel which involves colonization of other systems. I want to have a weirdo planet (thus the title) and I decided on a planet that doesn't quite complete a rotation. There's a thread here: https://www.physicsforums.com/threads/how-the-last-days-look-like-just-before-a-tidal-lock.790409/ that discusses it.

Anyway, the point is a planet close enough to its primary to be subject to eventual tidal locking. This planet will be mostly solid, and will have a significant mass inhomogeneity that will make it act like an unbalanced bicycle wheel. At some point, the rotation slows down until it can't quite make it around on the last day. After that, it will swing back and forth through 350 degrees or whatever, every "day".

So, two questions I'm interested in: 1) What would be a plausible range for the period of the swing, and how long would this state last until tidal forces finished locking the planet?

I don't need rigorous math proofs, this is fiction. Just something that won't make the reader want to throw the book at the wall.

I doubt that this could happen but I think it is quite a clever idea, so go for it. If you want to be semi-realistic, then make the period quite long, like a millenium. If it could happen at all it would seem that it would go on for a very long time, like a million years.

 

[DaveC426913]

zThis planet will be mostly solid, and will have a significant mass inhomogeneity that will make it act like an unbalanced bicycle wheel. At some point, the rotation slows down until it can't quite make it around on the last day. After that, it will swing back and forth through 350 degrees or whatever, every "day".

Maybe it's just me, but I think you need to lay the order of events out more explicitly to ensure this makes sense.

At some point, tidal forces slow the planet until its day is almost as long as its year. It's revolving around the sun in, say, 7 million hours, but rotating on its axis in, say, 6,900,000 hours.

What next?

 

[Bizmuth]

Not sure I follow. It would swing back and forth through 10 degrees, not 350.

(I think it's important to re-stress that the planet is not homogenous. I'm assuming a significant off-center mass concentration. Otherwise this doesn't work.)

Actually, I think 350 (some amount slightly smaller than 360) is wrong. I think it might be some amount slightly smaller than 180. Possibly.

Understand that I'm viewing this intuitively, not from a rigorous math POV, but I visualize it like a satellite with a large boom, with a weight at the end. This uses simple orbital mechanics to ensure that the boom is always pointed toward the Earth. If you force a rotation on the satellite, and assume for the sake of argument that tidal braking would be effective, then the satellite would gradually slow and would eventually stop rotating with the boom once again pointing towards the Earth (could it stop with the boom pointing away from the Earth?). But it wouldn't stop with the boom perpendicular to the Earth, because that's not a stable orientation.

But I'm interested in the part just before it stops rotating. Before this point, the rotation would be uneven in that it would slow down and speed up depending on the orientation of the boom. Think of an unbalanced bicycle wheel. As it approaches a 90 degree attitude, it slows down, and as it crosses the 90 degree point it speeds up again. Eventually the satellite will be slowed down enough so that the boom isn't quite able to make it past the 90 degree point. It stops, then swings back, passing though the nadir, then makes it almost all the way up to 90 degrees again on the other side. Rinse, repeat. I can think of no mechanism or reason why it would just come to a stop at nadir without some period of swinging back and forth.

So, additional question: Is an orientation with the boom pointed straight away from the Earth stable? Or would it spontaneously flip? If stable, then Klown Kar planet will only swing through 180 less a bit. If not stable, then KKP would swing through 360 less a bit.

 

[DaveC426913]

Understand that I'm viewing this intuitively, not from a rigorous math POV,

As am I.

Before this point, the rotation would be uneven in that it would slow down and speed up depending on the orientation of the boom.

I am not sure this is true. it takes a LOT of energy to slow down and speed up the rotation of a planet's rotation. I don't think this can occur over the year time frame you're proposing, let alone happened cyclically.

I can think of no mechanism or reason why it would just come to a stop at nadir without some period of swinging back and forth.

The reason why a bicycle wheel would bob before stopping is because its inertia (keeping it rotating) is large compared to gravity (trying to stop it). In the case of a planet, over a much longer time period, I think the tidal force from the sun is larger than the planet's rotational inertia. Once it reaches tidal lock, it's not going to over rotate.

I am not certain, but my gut tells me so.

 

[newjerseyrunner]

Also, you'll have a difficult time constructing a lopsided planet. It certainly couldn't form that way, a planets like hydrostatic equilibrium. Your planet might have to be very small in order to have a lopsided shape. I'm not sure how you could make a large planet be so off-center. The moon is denser on the side that faces the earth, but not by much, and we're a pretty big gravity well considering how close the early moon was to the planet.

 

[Bizmuth]

Once it reaches tidal lock, it's not going to over rotate.

Right, but it won't have reached tidal lock yet. Look at it this way. Assuming tidal braking is linear, then if you start at time A with a rotation X, and you know that the planet will be slowed at Y milliseconds per year, you can calculate the date Z when it becomes locked. Given a homogenous sphere, it's pretty straightforward. But given a non-homogenous sphere (which brings back the satellite-boom metaphor), at some point before Z the planet is going to be rotating pretty slowly. As with the bicycle wheel, the slower the rotation, the more pronounced the effect of an unbalance will be. The big unknown, of course, is the magnitude of the inhomogeneity compared to the mass of the planet.
If the ratio is too low, of course, the slowing down approaching the 90 and 270 points will be detectable only with sensitive instruments and might never stop a rotation "short", so to speak. But if the ratio is high enough, it might.
Fortunately, I'm writing fiction, so the ratio is high enough because I say so . But you confirm my thought that if it did work out, it wouldn't be anything like a 36 hour period or anything like that. (I initially came up with a period of 1.43 days, but then realized I was using the entire planet's mass in the pendulum period calculation)
I'm still a little out to lunch about whether such a behavior would be based on a 180 or 360 degree (less a bit) swing. If 180, there would be a small slice of the planet that would never see the sun. Hmmm.

Anyway, I'm quite prepared to be beaten up over this. The planet doesn't get introduced in detail until book 2, and I have a more prosaic alternative available. And if anyone has a weirder idea than this, I'm all ears.

 

[Bizmuth]

Also, you'll have a difficult time constructing a lopsided planet. It certainly couldn't form that way, a planets like hydrostatic equilibrium. Your planet might have to be very small in order to have a lopsided shape. I'm not sure how you could make a large planet be so off-center. The moon is denser on the side that faces the earth, but not by much, and we're a pretty big gravity well considering how close the early moon was to the planet.

Also, the interior has to be solid or nearly so, or the inhomogeneity would just sink to the center.

Of course, our heroes can speculate all they want, but they won't know for sure what happened. For whatever reason, there will be a large mass concentration at one point on the planet, not too far below surface level. Keeping it as near the surface as possible keeps it away from the still-fluid core and means maximum moment-arm for the pendulum effect.

If the planet was still rotating fairly quickly, it might actually be a prolate spheroid rotating on its minor axis. However, by this point, I think it'll be generally spherical.

 

[DaveC426913]

Of course, our heroes can speculate all they want, but they won't know for sure what happened.

True, but you as the writer have no such luxury. You must know.

 

[Hornbein]

Also, the interior has to be solid or nearly so, or the inhomogeneity would just sink to the center.

Of course, our heroes can speculate all they want, but they won't know for sure what happened. For whatever reason, there will be a large mass concentration at one point on the planet, not too far below surface level. Keeping it as near the surface as possible keeps it away from the still-fluid core and means maximum moment-arm for the pendulum effect.

If the planet was still rotating fairly quickly, it might actually be a prolate spheroid rotating on its minor axis. However, by this point, I think it'll be generally spherical.

The inhomogeneity WILL sink to the center. It would have to be a foreign body that by some very strange chance collided at low speed. The collision would have to be recent enough that it hasn't sunk to the center, but not so recent that everything is too hot ie. molten. It would have to be of heavy metals in order to be denser than the rest of the planet.

 

[newjerseyrunner]

Does this lopsidedness have to be natural? An artificial gravity device dropped on the planet by an alien species in the distant past could cause your weird planet. Mining on a planetary scale could as well.

 

[DaveC426913]

Does this lopsidedness have to be natural? An artificial gravity device dropped on the planet by an alien species in the distant past could cause your weird planet.

Kind of takes the fun out of an emergent scenario though. Once you introduce advanced gravity control, it might as well just make the planet move in figure-8's or spell out 'Eat at Joes'.

Mining on a planetary scale could as well.

Heh. I like this idea.
When our slag heap outsizes our planet, it's time to move on.

 

[Hornbein]

The inhomogeneity WILL sink to the center. It would have to be a foreign body that by some very strange chance collided at low speed. The collision would have to be recent enough that it hasn't sunk to the center, but not so recent that everything is too hot ie. molten. It would have to be of heavy metals in order to be denser than the rest of the planet.

One more thing: the planet's core would have to be stone like Venus, not heavy metal iron like Earth. Otherwise the inhomogeneity could not be denser than the core.

 

[Bizmuth]

Does this lopsidedness have to be natural? An artificial gravity device dropped on the planet by an alien species in the distant past could cause your weird planet. Mining on a planetary scale could as well.

I've actually got an alien species in the book that does drive-by mining. However, what they leave behind isn't generally colonisable.

 

[Bizmuth]

One more thing: the planet's core would have to be stone like Venus, not heavy metal iron like Earth. Otherwise the inhomogeneity could not be denser than the core.

Does Venus not have a metal core? I was under the impression that Venus has had some fairly recent volcanism, so it should at least still be molten.

You brought up a thought with this comment. The planet has to be non-homogenous in order for a pendulum effect to be possible, but the mass concentration doesn't have to be heavier than average. A large concentration of low-mass material on one side would automatically shift the center of mass. It also wouldn't tend to sink to the center, another plus. I think it would create sufficient non-uniformity to give tidal forces something to latch onto, to create the pendulum effect.

Alternatively, a large concentration of basaltic rock on one side of the planet, with an equivalent concentration of granitic on the other side (maybe a Pangea?) would create an imbalance. Would have to be one helluva continent, though. OTOH, having the imbalance right at the surface, and reinforced antipodally, would maximize the effect.

I'm just spitballing, now.

 

[newjerseyrunner]

Just to be clear, I'm pretty sure Venus's core is molten iron, just like Earths (am I wrong?) I was under the impression that the interior of Venus is very similar to Earth, I think you're confused by the fact that it has a minimal magnetic field. A hot molten iron core doesn't make a magnetic field by itself, it has to be spinning. Venus spins VEEEEERRRY slowly.

I could see a Type II civilization extracting huge chunks of a solid planet in order to build megastructures nearby. I imagine them just taking trillions of tons of material all at once and leaving a planet shaped like a this kind of clown car.

 

[Hornbein]

Does Venus not have a metal core? I was under the impression that Venus has had some fairly recent volcanism, so it should at least still be molten.

You brought up a thought with this comment. The planet has to be non-homogenous in order for a pendulum effect to be possible, but the mass concentration doesn't have to be heavier than average. A large concentration of low-mass material on one side would automatically shift the center of mass. It also wouldn't tend to sink to the center, another plus. I think it would create sufficient non-uniformity to give tidal forces something to latch onto, to create the pendulum effect.

Alternatively, a large concentration of basaltic rock on one side of the planet, with an equivalent concentration of granitic on the other side (maybe a Pangea?) would create an imbalance. Would have to be one helluva continent, though. OTOH, having the imbalance right at the surface, and reinforced antipodally, would maximize the effect.

I'm just spitballing, now.

Venus has a stone core, and no magnetic field. Stone doesn't conduct EM. The Moon is stone too.

By heavier you mean denser.

Planets of sufficient mass have powerful forces making them (almost) round. But change in shape tends to be slow. Did you know that Canada is still rebounding from the weight of glaciers that melted away 10,000 years ago?

But planets also have powerful forces that would make a large dense mass sink to the center. Basaltic/granitic sounds good. If the denser mass were spread out thin and flat it wouldn't sink. The planet would change shape until it was balanced, but it would take quite a long while.

 

[Hornbein]

Whoops, I guess I was wrong about Venus. That's what I get for trusting informal communications. The Moon is stone though, so a stone planet seems possible.

By heavier you mean denser.

Planets of sufficient mass have powerful forces making them (almost) round. But change in shape tends to be slow. Did you know that Canada is still rebounding from the weight of glaciers that melted away 10,000 years ago?

But planets also have powerful forces that would make a large dense mass sink to the center. Basaltic/granitic sounds good. If the denser mass were spread out thin and flat it wouldn't sink. The planet would change shape until it was balanced, but it would take quite a long while, especially if it were solid.

 

[Artribution]

I'm really dying to know why you want these details. I mean, it would be practically impossible to live on the surface anyway, right?

 

[newjerseyrunner]

I'm really dying to know why you want these details. I mean, it would be practically impossible to live on the surface anyway, right?

Why?

The moon has iron in it too, the difference is that it wasn't liquid long enough for it to all end up at the core. In fact, the side that faces Earth is denser than the far side because of tidal forces on it.

You're going to have to have fairly low mass in order for the planet to retain it's strange shape for very long, but also require an atmosphere to keep your life forms going. That atmosphere requires protection from the star, or it'll be blown off. What if instead of a planet, you make this a large moon instead. Instead of being tidally locked to the star, it's locked to the planet. The planet's magnetic field could protect it.

 

[Bizmuth]

I'm really dying to know why you want these details. I mean, it would be practically impossible to live on the surface anyway, right?

Why?

Edit: Newjerseyrunner beat me to it. NJR, that's a nice idea. I don't have to make a final decision until I'm into final edits, and I'm not saying that much in book 1 anyway. Bottom line, I want to make the planet habitable from an ecological point of view, but weird. Moon of super-earth might do it.

 

[Artribution]

Well, I was thinking that if it had an atmosphere, the weather effects alone be severe to catastrophic. But maybe I'm not considering how slow its rotation would already be and how long a day cycle you're thinking of.

 

[Bizmuth]

Well, I was thinking that if it had an atmosphere, the weather effects alone be severe to catastrophic. But maybe I'm not considering how slow its rotation would already be and how long a day cycle you're thinking of.

The planet would have to be getting about the same amount of solar energy as Earth, because it has to be habitable. There've been articles on weather patterns and such for tidally locked planets that indicate they'd still be habitable. Seems the old saw about atmosphere freezing on the dark side is unlikely. Something with a slow swing (or full rotation) wouldn't necessarily have more wild weather-- at least I can't think of any reason for it.

 

[Artribution]

Well, if the atmosphere on the cold side isn't freezing solid, and the hot side is receiving the same amount of warming as the Earth, and the temperature in the 'habitable' zone is tolerable and stable, then there must be a sufficient rate of heat transfer (from hot-side to cold-side and back again) to subject the habitable zone to perpetual surface wind speeds in the neighborhood of a category-5 hurricane, right?

And the surface wind would always be blowing from cold-side to hot-side, because the warmer air currents from hot-side to cold-side would be at higher altitude.

 

[Bizmuth]

Well, if the atmosphere on the cold side isn't freezing solid, and the hot side is receiving the same amount of warming as the Earth, and the temperature in the 'habitable' band is tolerable and stable, then there has to be a sufficient rate of heat transfer (from hot-side to cold-side and back again) to subject the habitable zone to perpetual surface wind speeds in the neighborhood of a category-5 hurricane, right?

And the surface winds would always be blowing in one direction - from cold side to hot side - because the warmer air currents from hot side to cold side would be at higher altitude.

You're right about the path of the air. It rises at the point of Solar high noon, travels to the dark side at high altitude, then gradually falls as it cools, forcing the cold air towards the warm side. But there's no reason to assign a particular windspeed. It could in principal be anything from light summer zephyr to apocalyptic. Also, the wind force would be strongest around the "high noon" point as everything funneled together, and weakest in the twilight zone because the air movement would be distributed around the full circumference of the planet.

Interestingly, with a wind cycle like that, I can see the high noon point being a monumentally large mountain from constant depositing of windblown dust. Hmm. The nightside would get scoured down to bare rock, the day side would be gradually built up. Water would run downhill to the nightside, where it would be picked up by the winds, so storms would be constantly blowing in, dumping mostly in the twilight area and dissipating before they got too far into day side.

Of course, all of this is for a tidally locked planet. If it has a pendulum motion, this pattern would be completely broken up.

 

[Artribution]

On Earth, weather (and wind speed) is generated by global variations in temperature. The global atmospheric temperature range of a tidally locked planet (or one nearly so) would be comparatively extreme, so it would generate comparatively extreme winds, and they'd be more or less continuous, wouldn't they?

 

[newjerseyrunner]

I agree, that's another reason why it might be better to have it locked to a planet instead. Tidally locked planets will expose one side to extreme heat and the other side to extreme cold. Your only habitable zone in a planet like that is near the dividing line, and you'd have constantly hurricane strength winds.

 

[Hornbein]

You're right about the path of the air. It rises at the point of Solar high noon, travels to the dark side at high altitude, then gradually falls as it cools, forcing the cold air towards the warm side. But there's no reason to assign a particular windspeed. It could in principal be anything from light summer zephyr to apocalyptic. Also, the wind force would be strongest around the "high noon" point as everything funneled together, and weakest in the twilight zone because the air movement would be distributed around the full circumference of the planet.

Interestingly, with a wind cycle like that, I can see the high noon point being a monumentally large mountain from constant depositing of windblown dust. Hmm. The nightside would get scoured down to bare rock, the day side would be gradually built up. Water would run downhill to the nightside, where it would be picked up by the winds, so storms would be constantly blowing in, dumping mostly in the twilight area and dissipating before they got too far into day side.

Of course, all of this is for a tidally locked planet. If it has a pendulum motion, this pattern would be completely broken up.

I think most of the atmosphere would be static most of the time. The Coriolis force is very weak, so there is nothing to keep the air moving. It would reach an equilibrium and pretty much stay there. There could be a chaotic region near the borderline. Maybe like the williwas of Patagonia, or tornadoes might be common.

Air also has a strong tendency to form channels. It doesn't move equally over a strong area. If a mass of air wants to get from one place to another, it forms a sort of river. I used to live near the ocean, and two small parallel "rivers" of moving air would form over the ocean, in the same place every day there was any wind. You could tell by the ripples in the water.

---

By the way, if you've got an ocean it is all going to flow to the area of the dense mass. Isaac Newton figured that out long ago: the force of gravity had to be pretty much the same everywhere on the surface of earth, or water would flow until it WAS the same. Indeed, rock will flow until it is the same, though much more slowly. The atmosphere will also be thicker over the dense mass.

 

[Artribution]

I think most of the atmosphere would be static most of the time. The Coriolis force is very weak, so there is nothing to keep the air moving.

Temperature differences would keep the air moving. If one side of the planet is perpetually heated and the other side is perpetually cooled, there will have to be perpetual wind, because the atmospheric heat has to circulate.

I'm not sure how to consider the formation of specific currents. It would depend on geography.

A water cycle circulating between the two hemispheres would act as another form of heat transfer, meaning more rain and less wind, if you want, but I think you'd still have very high wind in any case.

Interestingly, with a wind cycle like that, I can see the high noon point being a monumentally large mountain from constant depositing of windblown dust. Hmm. The nightside would get scoured down to bare rock, the day side would be gradually built up. Water would run downhill to the nightside, where it would be picked up by the winds, so storms would be constantly blowing in, dumping mostly in the twilight area and dissipating before they got too far into day side.

I really like that visual. Mountain of dust, or maybe mountain of storms.

Also, because the prevailing winds at the surface will be coming from the cold side and at high speed, the dessicated wastes of the hot side might not necessarily be all that hot at the surface, at least for the part closer to the twilight zone. The sun would always be shining but you'd always have a very cool breeze.

This is starting to sound like a nice planet, actually.

 

[Max Hofbauer]

Our moon is a naturally ocurring lopsided body. That must mean that the center of gravity is outside the center of geometry. The only way I can imagine such a mass distribution, requires a basically solid interior. Otherwise the material would be subjected to a slow flow, creating heat and dampening the movement. It would also mean that any bodies presenting a slight off-axis (geometrical axis, that is) rotation MUST have a solid interior and MUST have been tidally locked to another body at some point of their existence. The most probable kind of movement will not be the classical (linear) pendular action, but rather like a pendulum describing circles. You can ifigure it like the movement of a precessing top (without accounting for the spin itself), a wobbling movement. Don´t picture it as a stop-n-go movement, like a bicicle wheel. For more clarity you can make a conceptual model, using a ball with some excentric inner weight. From the surface of such an world, the sun would be discribing circles in the sky if the observer is in the center of the sun-facing side, and arches if the observer moves to the "twilight-zone". By the way; the twilight zone will probabely be best to live in, a ring-shaped area, trapped between too hot and too cold. Check the kind of movement in this video on lunar libration:
https://commons.wikimedia.org/wiki/...Lunar_libration_with_phase_Oct_2007_450px.gif
The other possible movement would be pendular in nature, featuring a stop-n-go kind of motion (like a swinging bike wheel). It will probabely be much slower. There would be two distinct, crescent-shaped, habitable zones (on meridians 180 and -180), stretching from "pole to pole", but not quite connecting...

 

[votingmachine]

You might be able to hand wave some mass imbalance with snow and water. Water would tidally flow towards the sun side. Snow could fall on the opposite side. As it rotates one way, the snow melts and cools the incoming ocean. The far side of the ocean is receding, and fresh snow is falling on the newly exposed ground. It requires a deep ocean (past tectonic weirdness as the planetary stress went crazy) that faces inward. Otherwise the planet would be relatively evenly distributed mass-wise, but with a bulging water mass, opposite a low density snow ... with enough hand waving it might sound plausible.

Or maybe a volcanic weird assymmetry ...

 

[votingmachine]

I thought of another possible way to make it work. Use the North Pole / South Pole wobble as the movement (axial precession), instead of the movement along the rotational axis of the poles. So hypothesize a planet that like Earth had rotation, and a wobble, where the Northern and Southern Hemispheres get differing day length. Then the rotation stops but not the wobble.

To see what I am getting at, look at the bottom graphic showing a wobbling Earth at the bottom. Make it a bit more extreme, and you've got your dynamics, although the axis of rotation is now a bit different.
http://www.windows2universe.org/earth/climate/sun_radiation_at_earth.html

It is again a bit of a hand waving explanation, but it might be possible to throw in some water tides to help create a mass assymettry.

There is a table of Solar system axial tilts here:
https://en.wikipedia.org/wiki/Axial_tilt

A big tilt, with a tidal lock of the side facing the sun ... that seems to work, although it takes a full year for the "day" cycle of movement to occur.

 

[Bizmuth]

Some interesting thoughts coming out of this. Another thought for a weird planet would be one that is a moon of a jovian primary, in a polar orbit (but not tidally locked). Such a planet would have one pole facing the sun for part of the year, then sunrises and sunsets, then the other pole. During the polar summers, the sun would describe a circle around the zenith, which would get larger and larger (and more tilted as you move away from the planet's pole), until it starts dipping below the horizon. Kind of like what the arctic gets on Earth, except much more extreme (At summer solstice, at the pole, the sun would be directly overhead). But during the "winter", the jovian primary would supply a lot of light. It would be an interesting annual cycle.

 

[Artribution]

A friend points out that if you have less sunlight, that means less heat transfer and therefore less wind. So a little further from the sun, the planet we were talking about could have perpetual monsoons instead of perpetual hurricane winds, if you wanted it to.