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Images like this enter image description here

and this

enter image description here

are common in sci-fi/fantasy settings, for the obvious "rule-of-cool" reasons. And while the 'rule-of-cool' is certainly worth using (in moderation) when appropriate, I can't help but wonder just how realistic are giant cracks in rocky planets?

Since that question, alone, is quite broad, here are some parameters to narrow it down:

  1. We'll assume a geologically dead ([relatively] cool, [mostly] solid core) planet, to avoid having all that liquid hot magma immediately flowing in to the crack and filling it in.

  2. Since "planet" generally indicates that it's big enough for its own gravity to make it (roughly) spherical over time, but also considering that this tendency will also work to close the crack, we'll go for a small-ish planet, let's say about 3400km radius (about the size of Mars)

  3. And to give ourselves the best chance for some semblance of realism, we'll keep the crack much smaller than those images. Let's say 7000km long (roughly a third of the circumference of the planet), and 1000km wide at its widest, and 1500km deep at its deepest.

  4. As for what the planet is made of, let's stick with the same elements in the same proportions as Earth.

  5. To make it a place where a story can take place, let's also give it an atmosphere and climate zones that can support human life.

  6. The atmosphere, together with earthlike composition, should also mean earthlike erosion takes place (though not necessarily at the same rates, due to the reduced gravity)

  7. To avoid too many erosion complications, lets also say that even though the planet would likely have massive bodies of water in order to have a similar atmosphere to Earth, let's assume the crack is entirely continental, does not intersect any oceans or seas, or any other significant bodies of water.

Is this crack a stable( >10,000 years ) geological formation? Or does gravity and erosion significantly(an order of magnitude) change its dimensions in a short( <10,000 years ) time?

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    $\begingroup$ lost in space has a planet with a big crack in it, and they have to stay within a valley inside it that formed a pocket of air because all the air on the surface fell into the crack or got blown away by what produced it. Naturally most of that water and atmosphere will fall into the crack so be prepared for either a very deep lagoon, a very deep ocean trench, or a lot of atmosphere, enough that it may have made the planet uninhabitable before the crack $\endgroup$ Apr 28 at 9:30
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    $\begingroup$ Because of the physical-temporal scale of humans, we tend to discern solid/liquid/gas as distinct states of matter. They are not in the truest sense. Just as a drop of water which had a valley or crack carved through it would soon snap back into spherical form, so too would a planet. For some value of "soon", at least. One split in half would discover gravity pulls the too pieces back together, and even if somehow they had cooled, the gravity will impart enough energy to weld them back together. $\endgroup$
    – John O
    Apr 28 at 13:34
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    $\begingroup$ Gravity will always force the body back into (mostly) a sphere beyond a certain size. See : What is the minimum mass required so that objects become spherical due to its own gravity? $\endgroup$
    – J...
    Apr 28 at 13:53
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    $\begingroup$ Maybe the Magratheans could make you one, but they are (mostly) sleeping. $\endgroup$ Apr 29 at 14:13
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    $\begingroup$ Keep in mind that many very large canyons have been known to form in surprisingly short time periods due to severe flooding. Because of this the quantity of erosive sources on the surface (wind, water, dust, seismic activity) could shorted the erosion time down to a year in extreme cases. Likely, if there is water on the surface, this crack would in a hundred years or so contain almost all of the water on the planet, essentially becoming a giant, very deep lake. $\endgroup$
    – Blue Dev
    Apr 29 at 19:39

10 Answers 10

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There is a crack in Mars called Valles Marineris. It is about as long as the contiguous USA.

A picture of Mars showing the US drawn over Valles Marineris

And here is a 3D rendering of it:

3D rendering of Valles Marineris

This rift is comparable to your specs in length and width, but not depth (only 7 km). 1500 km is a quarter of the way through Earth's surface to it's inner core. That would never be stable. So I think something like the Valles is the best you can do for a proper crack. Larger than this... maybe if you dried Earth's oceans and called the seafloor a crack. Would be mostly shallower than Valles Marinwris though.

Last time the Earth did get a crack the size you ask for was when it impacted against a Mars-sized planet a few billion years ago. Earth quickly (in geological terms) reformed itself into a mostly smooth shape.

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    $\begingroup$ agreed you can get a shallow scar but gravity induced pressure will force rock into any deep one, under millions of tones of pressure rock behaves like a plastic and will flow, you can only have shallows holes in planets. $\endgroup$
    – John
    Apr 28 at 0:33
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    $\begingroup$ Well --- if you can make it a bit (2x?) deeper, maybe it could represent the only breathable zone in an otherwise too-thin-air planet --- thing the difference between sea level and the top of Mt. Everest. Could be a very interesting setup (and with different climates in the zones oriented east-west versus north-south, maybe). $\endgroup$
    – Rmano
    Apr 28 at 11:54
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    $\begingroup$ "maybe if you dried Earth's oceans and called the seafloor a crack. Would be mostly shallower than Valles Marinwris" The Mariana Trench, on Earth, is 2550km long, 68km wide, and is over 10km deep at its deepest known point. $\endgroup$
    – J...
    Apr 28 at 13:52
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    $\begingroup$ @J... yeah but the average depth is like 4km. $\endgroup$ Apr 28 at 15:25
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    $\begingroup$ The question is, though, can a crack exist for a shorter time and if so, how long? Moreover, can such a crack, for that time, expose glowing material? $\endgroup$ Apr 28 at 19:05
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No, it couldn't be remotely stable, and erosion is not going to matter.

Even assuming the crack got formed by some very 'gentle' process that didn't destroy the planet outright, you’ve got to consider the scale of the pressures involved in a crack like that. The material making up the side of the crack has to support the weight of all the material above it. A quick google gives the breakdown pressure of stone at anywhere from tens to a couple hundred megapascals for the strongest types. On Earth, you exceed those pressures between 1 and 10km deep. That’s probably why we don’t have canyons deeper than that. Your crack is vastly deeper, so the walls of the crack have no chance of holding up.

How would that play out?

Your planet is a bit smaller than Earth but the same composition, so your surface gravity will be about half of Earth's. The gravity at the bottom of the crack will be a bit less than a third of a G. I'm too lazy to do the integration, so let's use a constant 0.4 G's for gravity in the crack.

Using that, the pressure forcing the walls together at any given point is just the weight of the stone above. Assuming a cubic meter of crack wall masses between 3000kg and 5500kg, then half-way down the crack the pressure will be between 9 billion and 16 billion pascals. At those pressures, the strength or stiffness of the walls themselves is a rounding error. The walls will flow under the stress, become molten due to frictional heating, and be forced together by the pressure as fast as they can move. The pressure is enough to accelerate the walls at 300,000 G's. I'm unsure if the speed of the walls is limited like Seismic P-waves or whether you can just apply Newton's laws, but the walls will cross that 500km gap in a fraction of a second either way. It will happen sooner deeper down where the pressure is greater and the separation smaller, so the crack will seal itself up like a zipper from bottom to top.

The violence of the impact as the walls snap together will be profound. The force will send a blast wave up towards the surface, ejecting a mass of molten rock out into space.

The volume of your crack is something like 1% of the volume of your planet if I’m picturing it correctly. That means that when it snaps closed, the radius of your planet has to shrink by 0.33%. That doesn't sound like much, but it comes to an 11km drop for the entire surface of the planet. Lots of kinetic energy released. So picture a wave several km high circling the planet at several km/s until all that energy gets converted to heat..

Needless to say, this is far worse than the meteor that killed the dinosaurs. Even if conditions were earthlike before the crack closed, they won't be afterwards.

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    $\begingroup$ What if the planet (at least its core) is cold and made out of silicon or diamond? Apparently silicon has a compressive strength of 3.2GPa which would be relatively close to your 9–16GPa pressure estimate. Diamond has 10–20GPa. $\endgroup$
    – Michael
    Apr 29 at 12:16
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    $\begingroup$ @Michael, a mono-crystalline diamond might be able to sustain such a crack, at least in the short term (random dislocations mean the crack is likely to flow closed in the long term). Silicon won't: a factor of 3-5 gap in strength still means a catastrophic collapse. $\endgroup$
    – Mark
    Apr 29 at 22:53
  • $\begingroup$ @Michael you're right about diamond holding up to the pressure - its density is low enough that the pressure would be near the lower end, but diamond has a tensile strength of only around 2 Gpa, so i would worry about tidal forces. $\endgroup$
    – Mothas
    May 1 at 3:50
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The volume of the hole is about 10,500,000,000 cubic kilometers. The density of Earth is about 5,518,000,000 tonnes per cubic kilometer. The mass of the hole was about 6$\cdot$1022 kg. As such, the surface gravity of each side of the hole from similar chunks of planet over the long edge is about 0.8 cm/s2. Over a thousand years around ten billion seconds pass. That's around 600,000 kilometers of acceleration.

It's probably stable over ten years. Over a hundred years a lot has probably collapsed in there. By a thousand years, the planet has probably smoothed over a lot. That's a lot of acceleration for the rocks to undergo.

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    $\begingroup$ I'm not sure what are "kilometers of motion", but I concur with your answer. Gravity would cause enormous pressure at the bottom of the fissure which no rock would be able to sustain. $\endgroup$
    – Alexander
    Apr 27 at 23:27
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    $\begingroup$ Earth rocks slowly flow at 10km down. On this smaller world they would be expected to flow at 30km down. $\endgroup$ Apr 28 at 3:56
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    $\begingroup$ I hate to be pedantic, but the mass of the hole is zero. The mass of the stuff that used to be where the hole was, however... $\endgroup$
    – JDL
    Apr 28 at 11:57
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    $\begingroup$ I don't understand the logic here. You seem to be calculating the surface gravity of a spherical body made from the material extracted from the hole, but why with a 5000km radius? That's larger than the planet itself. Even with a different calculation, I don't see the relevance - it's the gravity of the remaining planet that matters, not the gravity of the material that's not there anymore. And what is 100,000 km of acceleration supposed to mean? It's not like the walls of the canyon freely accelerate toward one another due to gravity. $\endgroup$ Apr 28 at 13:26
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    $\begingroup$ The units and quantities here are massively confusing and also probably irrelevant. Acceleration is not additive, not like this for sure. And "600,000 kilometers of acceleration" makes no sense physically. I'm not sure I understand what you mean, but if it's that the material would move this much, it's a huge logical leap least to say. I'm accelerating by 9.81m/s2 constantly, yet I feel pretty stable sitting at my computer. $\endgroup$
    – Neinstein
    Apr 28 at 15:38
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Hot Mess:

This is a tricky question to answer. The first big question is, "What caused the crack?" The likely sources of the damage will seriously affect how the crack looks and how it fills in. I'm assuming with a geologically stable planet that it's not plate tectonics. So the likely culprits are massive impacts (which would create deep craters, not rifts) or some kind of gravitational effect like a black hole making a close fly-by at great speed and creating a short differential gravity effect.

Most of the events that would cause such a rift will be BIG events. The effect is likely that the rock in the surrounding area will get very hot and liquefy from friction. Volcanoes are already created from the friction of continental plates rubbing against each other, and the Marianas trench, the effect of a subduction zone generating such volcanoes, only gets to a mere 11 km. So it's likely the disaster itself will largely fill itself in, or at least significantly affect it's shape.

Most of the disasters that would create such a hole would wipe out most life on the planet. While it's a little hard to deconstruct the Chicxulub event, the impact crater was something like 20 km deep, and that resulted in a mass-extinction event completely altering life and climate for the planet. That's just a TINY fraction of the 1500 km hole you're talking about. The atmosphere and oceans of the planet would likely be blown off by something able to do this kind of damage.

If the oceans didn't simply evaporate into space, they would likely start filling in the rift as they rained back to the surface. Side fissures of this hole would likely break into an ocean SOMEWHERE. This might actually be a good thing for your rift's survival, as the mass of the water will partly compensate for the shift in the mass of all that rock that's now missing. The water will apply pressure on the rock adjacent to it, help cool things, but also seep into the adjacent magma generated from the heat and create very volatile gassy eruptions. For your 10,000 years AT LEAST, the area will be a volcano-strewn wasteland.

The shape of your planet will possibly be warped by the causative event. While the appearance of the rift might seem to match your depths, the actuality might be that the surface has buckled sideways and the rift is really two huge, sinking mountain ranges with a deep fissure between them. Again, all this deformation is likely to generate a ton of heat and melt rock all over the place.

So in my opinion, you'll be able to spot the effects of this rift for millions of years, but the rift will most likely fill in with molten rock and water within a few decades as the bending and flexing of the planet destroys all life.

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    $\begingroup$ Honestly, I don't see how such a crack could really form outside of outright magitechnology, really. The kind of energy that could blow so much mass out of the planet (presumably on an escape velocity, since the rest of the planet seems spherical enough) is probably way more than is needed to melt the planet. And if you magically teleported the mass away, let's not forget the incredible pressure that was at the edges of the cut just an instant ego - all that matter would violently explode towards the now empty space. $\endgroup$
    – Luaan
    Apr 29 at 11:32
  • $\begingroup$ @Luaan Yeah, I kinda had to leave the cause open, since I couldn't come up with one that would be so specific, and mentioned the rocks would probably liquify. All the answers pretty much agree this scenario wouldn't work, Still, it's a fun question. Who doesn't love giant explosions and melting planets? $\endgroup$
    – DWKraus
    Apr 29 at 12:31
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Short answer:

I suggest you use a small, artifically shaped and terraformed mostly iron nickel world to have a crack which is very large absolutely and also relative to the size of the world.

Long Answer:

Part One of Three: The Difficulty of Using a Natural Planet.

according to the question:

We'll assume a geologically dead ([relatively] cool, [mostly] solid core) planet, to avoid having all that liquid hot magma immediately flowing in to the crack and filling it in.

and:

Since "planet" generally indicates that it's big enough for its own gravity to make it (roughly) spherical over time, but also considering that this tendency will also work to close the crack, we'll go for a small-ish planet, let's say about 3400km radius (about the size of Mars)

And:

As for what the planet is made of, let's stick with the same elements in the same proportions as Earth.

And:

To make it a place where a story can take place, let's also give it an atmosphere and climate zones that can support human life.

And:

The atmosphere, together with earthlike composition, should also mean earthlike erosion takes place (though not necessarily at the same rates, due to the reduced gravity)

Are all those factors consistent with scientific possibilities? Are all those factors consistent with each other?

Take the breathable atmosphere. On Earth photosynthetic lifeforms gradually evolved and began to produce an oxygen rich atmosphere. On Earth in took about four billion (4,000,000,000) years for an oxygen rich atmosphere breathable for humans to be formed. If the planet is going to lose all its atmosphere in three billion years, or three million years, or 518,283,492 years, or 105 years, or any other length of time shorter than the billions of years it will take to produce a breathable atmosphere, the planet will never produce a breathable atmosphere and will never be habitable for humans or for other lifeforms that need oxygen.

A number of factors influence what type of atmosphere a planet has, including what type of atmosphere it oriignally forms. For example, having a strong magnetic field to deflect charged particles in the stellar wind from the planet will protect its atmosphere from being gradually lost as the stellar wind knocks them away.

But the most important factor in how long a planet retains its atmosphere is its escape velocity. The escape velocity of a planet and its surface gravity change with the mass, volume, and density of a planet. As the surface gravity increases, the escape velocity also increases, though not at the same rate. There are different formulas for calculating a world's surface gravity and its escape velocity.

According to Habitable Planets for Man, Stephen H. Dole, 1964, https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf on pages 34 to 35, a rough formula to calculate the time it takes for a planetary atmosphere to be reduced to 1/e, or 1/2.718, or 0.368, of its original amount, shows that it depends strongly on the ratio between the sescape velocity of the planet divided by the root-mean-square velocity of the molecules in centimeters per second. The higher the temperatures of the molecules, the higher their root-mean-square velocity, and the faster they escape.

Table 5 on page 35 show that where the ratio is one or two, the molecules will escape so fast that the planetary atmosphere will be reduced to 0.368 of its orginal amount in zero seconds. If the ratio is three, it will take a few weeks. If the ratio is four, it will take several thousand years. If the ratio is five, it will take about a hundred million years, and if the ratio is six, it will take infinite time.

On page 36 Dole mentions that gases escape from the Earth high in the atmosphere, in the exosphere, and the temperature there is much higher than the surface temperature on Earth, about 1000 to 2000 degrees K.

On page 54 Dole says:

However, if we take as a rough approximation that maximum exosphere temperatures as low as 1000 K are not incompatable with the required surface conditions of a habitable planet, then the escape velocity of the smallest planet capable of retaining atomic oxygen may be as low as 6.25 kilometes per second (5 x 1.25). Going back to figure 9, this may be seen to correspond with a planet having a mass of 0.195 Earth mass, aradis of 0.63 earth radius, and a surface gavity of 0.49 g.

Such a planet would lose more than half of its atmosphere every hundred million years, and would have to replace atmosphere fby various processes to retain it for billions of years to produce an oxygen rich atmosphere. And of course if it turns out to be necessary for the maximum exopshere temperatures to be closer to 2000 K for the surface temperature to be high enough, the planet would lose atmosphere even faster.

A radius of 0.63 that of Earth's radius of about 6,371 kilometers would be a radius of about 4,013.73 kilometers, which is about 1.18 times the radius, and thus would have about 1.643 times the volume of, your specified planet with a radius of about 3,400 kilometers.

I note that Dole believed that a planet with 0.195 Earth's mass and a radius of 0.63 Earth's radius would be capable of retaining an oxygen rich atmosphere, but doubted that such a small planet could produce an oxygen rich atmosphere. Dole made two separate calculations of the minimum mass necessary for a planet to produce an oxygen rich atmosphere. One calculation indicated a minimum mass of 0.25 Earth, another a minimum mass of 0.57 Earth mass. Dole rather arbitarily selected 0.4 Earth mass as the minimum mass of a planet capable of producing an oxygen rich atmosphere. Such a planet would have 0.78 the radius of Eerth (4,969.38 kilometers) and a surface gravity of g. It would exceed your 3,400 kilometer planet by 1.461 times, and its volume by 3.118 times.

Part two: Designing a Terraformed World With a Huge Crack.

But the situation is not that bleak for your 3.400 kilometer radius planet having a breathable oxygen atosphere.

Posssibly an advanced civilization terraformed the planet to have an artificial oxygen rich atmosphere. A planet with 0.195 times the mass of Earth could retain 0.368 of the atmosphere it was given for about 100 million years if the exopshere temperature was only 1000 k, which might be long enough to seem worth while to the advanced civilization.

Dole says on page 36 the main source heating the exosphere gases of Earth is far ultraviolet radiation from the Sun. If the star is a cooler star than the Sun, it might prodcue much less far ultraviolet radiaiton and the exosphere temperature could be 1000 K or less while the planet's surface was heated up to be warm enough by the star.

Or maybe the advanced civilization would build fusion generators to heat up the surface of the planet while the exosphere was heated up only by radiation from the star.

Of course your planet would be a lot smaller than Dole's 0.195 Earth mass planet.

A planet with a radius of about 3,400 kilometers would have about 0.5337 the radius of Earth, 0.2848 the surface area, and about 0.1520167 the volume. Thus if it had The same overall density as Earth it owuld have 0.1520167 the mass of Earth.

According to this online calculator https://philip-p-ide.uk/doku.php/blog/articles/software/surface_gravity_calc your planet would have 0.53 g surface gravity.

According to this escape velocity calculator https://www.calctool.org/CALC/phys/astronomy/escape_velocity

It would have an escape velocity of 5.97092 kilometers per second.

Giving your planet 0.17 the mass of Earth, it would have an escape velocity of 6.31423 kilometers per second, a little more than the 6.25 which Dole considered to be the minimum for retaining an atmosphere. It would have an overall density about 1.0156 that of Earth. And it would have a surface gravity of 0.6 g.

So basically a planet capable of having an oxygen rich atmosphere, even one produced artificially, would have a surface gravity at least about 0.5 times that of Earth. The lesser surface gravity would help a bit in retaining the crack for long periods, but would not be a very big help.

Suppose that the hypothetical advanced civilization that terraforms the planet doesn't count on the escape velocity of the planet to retain the artifical atmosphere, but builds a roof (possibly suported by air pressure) around the entire planet to retain the atmosphere. Presumably there would be giant airlocks in the roof to let spaceships land and take off.

A shellworld13 is any of several types of hypothetical megastructures:

One of which is:

An inflated canopy holding high pressure air around an otherwise airless world to create a breathable atmosphere.4 The pressure of the contained air supports the weight of the shell.

https://en.wikipedia.org/wiki/Shellworld

Asteroid 16 Psyche is about 278 by 272 by 164 kilometers, so its largest dimenision is 1.69 times its smallest dimension, and its "highest" surface point is about 57 kilometers above its "lowest" surface point as measured from the center of mass.

Several possible origins have been proposed for Psyche. The earliest of these was that Psyche is an exposed metallic core resulting from a collision that stripped away the crust and mantle of an originally larger differentiated parent body some 500 kilometers in diameter.[11] Other versions of this include the idea that it was not the result of a single large collision but multiple (more than three) relatively slow sideswipe collisions with bodies of comparable or larger size.[34] However, this idea has fallen out of recent favor as mass and density estimates are inconsistent with a remnant core.[8]

https://en.wikipedia.org/wiki/16_Psyche#Origin

But even if Psyche is not the remnant nickel iron core of a dwarf planet shattered by collisions it is theoretically possible for such remnant iron nickel cores to remain after collisons shatter their larger parent bodies.

Such metallic asteroids could get many times much larger than 16 Psyche before their gravity became strong enough to force them into spherical shapes, sepecially since an iron nickel core would be much stronger than stone.

So I can easily believe that an iron nickel alloy object could get large enough to have a radius of 100 kilometers or larger before it was pulled into a spheroid by its gravity and reached what is called hydrostatic equilibrium.

Solar System objects more massive than 1021 kilograms (one yottagram [Yg]) are known or expected to be approximately spherical. Astronomical bodies relax into rounded shapes (spheroids), achieving hydrostatic equilibrium, when their own gravity is sufficient to overcome the structural strength of their material. It was believed that the cutoff for round objects is somewhere between 100 km and 200 km in radius if they have a large amount of ice in their makeup;1 however, later studies revealed that icy satellites as large as Iapetus (1,470 kilometers in diameter) are not in hydrostatic equilibrium at this time,2 and a 2019 assessment suggests that many TNOs in the size range of 400–1000 kilometers may not even be fully solid bodies, much less gravitationally rounded.3 Objects that are ellipsoids due to their own gravity are here generally referred to as being "round", whether or not they are actually in equilibrium today, while objects that are clearly not ellipsoidal are referred to as being "irregular".

https://en.wikipedia.org/wiki/List_of_Solar_System_objects_by_size

So I will rather arbitarily assume that an iron nickel alloy asteroid, made of stronger material than ices or stones, could be between 100 kilometers and 2,000 kilometers in radius before its gravity pulled it into a spheroidal shape.

So possibly the hypothetical super advanced society in the story finds a large irregular iron nickel asteroid and sculpts it into an almost spheriodal shape, except for a large crack in it, selling the excess metals, puts a transparent shell around it, gives it atmosphere, dirt, water, plant and animal life, and creats a tiny habitable world that has a giant crack or scar, like a really really grand canyon, as a tourist attraction. The crack may be large enough to be very impressive when seen from ships in outer space and should be very impressive as seen from the ground.

An spherical iron nickel body in that size range (after being sculpted into shape) would have from 0.0156951 to 0.3139224 the radius of Earth, and thus would have from 0.0002463 to 0.0985472 times the surface area, and from 0.0000038 to 0.0309361 the volume of Earth. If it was made of material with the same overall density as the Earth, it would have 0.0000038 to 0.0309361 the mass of Earth.

But the overall density of Earth is 5.514 grams per cubic centimeter, while pure iron nickel meteorites similar in composition to this hypothetical world have densities of 7.9 grams per cubic centimeter, 1.4327167 times as great.

A 2,000 kilometer radius iron nickel world would have about 0.3139224 the radius of Earth and about 0.0443226 Earth's mass. It would have a surface gravity of 0.45 g and an escape velocity of 4.20371 kilometers per second.

A 100 kilometer radius iron nickel world would have about 0.0156951 the radius of Earth and about 0.0000054 Earth's mass. It would have a surface gravity of 0.02 g and an escape velocity of 0.207507 kilometers per second.

The 2,000 kilometer radius iron nickel world would have almost sufficient escape velocity to retain an atmosphere naturally, but its surface gravity would not low emough to help a lot in making the crack last long. The 100 kilometer radius world would have a surface gravity low enough to make the iron nickel walls of the great crack last for a long time. And the smaller size of the world would mean that a equally sized crack would appear much larger relative to the radius of the world.

So my recomendation for a world with a really spectacular and relatively permanent crack would be an iron nickel asteroid sculpted into the shape of a spheriod with a very large crack, and terraformed with an artifical atmosphere held in by a transparent air supported roof over the entire little planet.

People who can do materials strength calculations may be able to calculate the maximum height and angle of incline of the scar for a world with a specific surface gravity.

Part Three: Other Problems With a Natural Planet

There are other problems with your requested natural planet with a crack. Your request for simular materials to Earth is inconsistent with the iron nickel world which would be best for artificially sculpting into a spheroid with a giant crack.

An advanced society could sculpt an irregular stony little world into a spheroid with a giant crack. but the weaker strength of stone would result in a smaller and less spectacular crack for a world with the same surface gravity.

In recent decades scientists have done a lot of speculating and calculating about the conditions necessary for life on other worlds. Note that unlike Dole, most scientists consider the general case of habitability for liquid water using lifeforms in general, instead of humans and other lifeforms with the same requirments as humans in particular. Many worlds which they consider habitable for some hypothetical lifeforms would be deadly to humans.

Once such paper is "Exomoon habitability constrained by illumination and tidal heating", by Rene Heller and Roy Barnes, 2013. They dscuss the mass ranges of potentially habitable worlds on pages 3 & 4:

A minimum mass of an exomoon is required to drive a magnetic shield on a billion-year timescale (Ms ≳ 0.1M!, Tachinami et al. 2011); to sustain a substantial, long-lived atmosphere (Ms ≳ 0.12M!, Williams et al. 1997; Kaltenegger 2000); and to drive tectonic activity (Ms ≳ 0.23M!, Williams et al. 1997), which is necessary to maintain plate tectonics and to support the carbon-silicate cycle. Weak internal dynamos have been detected in Mercury and Ganymede (Kivelson et al. 1996; Gurnett et al. 1996), suggesting that satellite masses > 0.25M! will be adequate for considerations of exomoon habitability. This lower limit, however, is not a fixed number. Further sources of energy – such as radiogenic and tidal heating, and the effect of a moon’s composition and structure – can alter our limit in either direction. An upper mass limit is given by the fact that increasing mass leads to high pressures in the moon’s interior, which will increase the mantle viscosity and depress heat transfer throughout the mantle as well as in the core. Above a critical mass, the dynamo is strongly suppressed and becomes too weak to generate a magnetic field or sustain plate tectonics. This maximum mass can be placed around 2M! (Gaidos et al. 2010; Noack & Breuer 2011; Stamenkovi% et al. 2011). Summing up these conditions, we expect approximately Earth-mass moons to be habitable, and these objects could be detectable with the newly started Hunt for Exomoons with Kepler (HEK) project (Kipping et al. 2012).

https://arxiv.org/vc/arxiv/papers/1209/1209.5323v2.pdf

Note that an internal dynamo is considered necessary for a magnetic field to help protect the atmosphere and for plate tectonics.

Your desire for a geologically dead planet with little liquid magma, to maintain the crack, would probably result in a planet without a magnetic field or plate tectonics, and so it would not remain naturally habitable for a very long period geologically. Of course, if such a geologically dead planet was terraformed by an advanced society, as I suggested, they could keep it habitable for thousands or maybe millions of years, which might be long enough for their needs and for the events in a story.

Conclusion:

For the reasons given above, I suggest that the most spectacular possible crack in a habitable world would not be in a naturally habitable world but in a rather small iron nickel world artifically sculpted into a spheriodal shape with abig crack, and with an artificial atmosphere kept in by a roof over the whole world.

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No, by definition.

People still debate if Pluto deserves to be called a planet or not. The current definition has three elements:

  • In orbit around the sun.
  • Large/massive enough to reach a hydrostatic equilibrium, a roundish shape.
  • Has cleared the orbit of other objects (the Pluto sticking point).

So if it is able to retain a serious crack, and not just a few wrinkles on the surface like Mars, it is too small to be called a planet or even a dwarf planet. It would be a lesser object.

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    $\begingroup$ I think this is missing the point because there is no mention of time frame. A planet with such a crack will return to a hydrostatic equilibrium and close the crack eventually. But the question is whether this would happen on a time scale of days, years, millenia or millions of years (which is still very fast on astronomical time scales). $\endgroup$
    – quarague
    Apr 28 at 19:34
  • $\begingroup$ The flip side of the definition is that is a planet-like object is small enough, it won't have enough gravity to force it to become spherical, and you don't have to be much smaller than Pluto to get to that point. It may not technically be a planet, but it could still be quite large. $\endgroup$
    – ohwilleke
    Apr 28 at 22:55
  • $\begingroup$ @quarague, if the upper image from the OP applies, it would have to be borderline towards not being a planet. $\endgroup$
    – o.m.
    Apr 29 at 4:13
  • $\begingroup$ @quarague Minutes, and it's only that long because the speed of material movement is limited by the speed of sound. $\endgroup$
    – ZOMVID-21
    Apr 30 at 7:59
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No, it is not stable.

It's hard to account for everything that would effect such a scenario, but just to name a few things that would happen, first, all of the liquid water on the planet would try to fill the gap. Oceans would drain into the chasm even as magma tried to drain out of it.

This would only add to what I think would be the real undoing of an event like this - the imbalance. Think about the momentum of the planet, the speed of its spin. A cut into the planet like this would change the distribution of weight across the planet drastically enough to change the rotation, the eccentricity, and probably lots of other stuff. The atmosphere would go haywire.

Of course, this period of chaos would probably not last very long in geologic terms. In the 10,000 year window you're suggesting, the planet would stabilize. But I cannot imagine that the stable version of the planet would not have filled at least most of that chasm with something. My best guess - the part of the planet that was cut, being less heavy, spins up to become the new pole, all the water that rushed to fill it freezes over, and the new, stable planet just has one giant icecap, no liquid water, no life, and no atmosphere.

In summary, I do not believe that a visible chasm could exist on a stable system. Planets are round for a reason.

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  • $\begingroup$ Why "all liquid water try to fill the gap" ? that depends on geography and lakes/seas/oceans located elsewhere. It also depends on the tides. When there is no moon, a lot of water won't ever reach the rupture, when the water is evenly distributed over the planet. $\endgroup$
    – Goodies
    Apr 28 at 14:37
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    $\begingroup$ Given the scale of both the chasm and the amount of time, I don't think these considerations affect the overall pull of such a dramatic hole. Winds would be drawn down into the hole, bringing clouds with them. Even if there were bodies of water somehow isolated from the hole, they would evaporate over time into the atmosphere, and then not be refilled as, instead, rain clouds are continually drawn towards the chasm and the emptying ocean beds directly around it. Even if the chasm was somehow entirely landlocked (highly unlikely given its size), this would happen within 10000 years. $\endgroup$
    – Bluejoy
    Apr 28 at 15:10
  • $\begingroup$ See opening.. the collision takes place between two solid objects (there are no tectonic plates, the mantle and kernel are solid) and the collision takes place where there is no water. How should all water on the planet wind up in the hole ? Also take into account you'd have a considerable mountain range on either side of the crack. $\endgroup$
    – Goodies
    Apr 28 at 20:14
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    $\begingroup$ @Goodies A collision between such massive solid objects would quickly change them into massive liquid objects. The energy has to go somewhere. $\endgroup$
    – Luaan
    Apr 29 at 11:36
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Just have to start calculating pressure, gravity differences of $1500$ km depth. Pressure alone guarantees interesting things happening rapidly.

With density same as earth radius $3500$ km, mass would be about $.15$ of earth/ $9\times 10^{23}$ kg. Surface gravity $g \approx 5$.

A crack $1500$ km deep would be very unstable. As in, expect radical changes to depth over the next 24 hours. The pressures will cause plastic deformation of the rock. Within minutes along the bottom rock would melt to magma due to frictional heating. Massive devastating quakes magnitude 10+ would happen as rock moved. Since the planet is solid/hard/brittle it will ring like a bell causing the quakes to have global devastation.

Very uncertain as to final depth, but depth closer to max of 1Km would be reasonable. With low weathering and minimal plate tectonics the scar would last geological time frames ie billions of years. But the crack would collapse, close in order of days to weeks. Settling and after shocks for months and years afterword.

Basing timelines on: xkcd what if: bowling ball the size of earth

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Even Creating a "Crack" is Impossible

Let alone finding a way to make it stable.

The Chicxulub impact created a geographic feature roughly 20km deep and 200km around. The kinetic energy that Chicxulub imparted to the Earth was enough to cause hundreds of square kilometers of rock to melt and flow as a liquid. The impact created a mountain larger than Everest, which then immediately collapsed -- because it was still mostly liquid.

Even a magically efficient process designed just to create a massive Crack Feature over the course of a few minutes, the waste heat from that process would be enough to melt vast qualities of rock.

Violently creating a geographic feature that is orders of magnitude larger than Chicxulub would leave behind a vast field of glowing hot liquid rock, and would never meaningfully form a rift / crack in the first place.

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It's easy to calculate the maximum permanent depth of a local, steep-walled crack in the planet: $Depth=strength/(density*gravity)$.

Hydrostatic pressure in the rock at the crack's bottom can be determined as $P=gravity*density*depth$. Rock below this point is susceptible to flow to fill the bottom of the crack. Slope can locally reduce the pressure by a factor of 1/cos(slope). However, for very shallow slopes, the bottom will be forced up by static pressure, so it's limited to about doubling the depth, temporarily.

Rock properties can be found e.g. here: https://www.oocities.org/unforbidden_geology/rock_properties.htm . Volcanic rocks such as basalt or diabase can have a compressive strength of up to 350 MPa at a minimum density of $2700 kg/m^{3}$.

For Earth, maximum permanent depth is per this formula $D=350*10^{6}/(2700*9.8) = 13.2 km$. For a 30-degree sloped crack, it improves to $13.2*cos(30)=26.4 km$. Much shallower slopes can increase this further.

If the crack was created by something other than an impact, it's possible to do better. Luna has a smaller gravity and has its surface composed of silica. If molten, silica can form quartz glass with a strength of up to 1100 MPa.

A world with Moon's gravity, which is definitely a planet, could potentially have a crack as deep as $D=1.1*10^{9}/(2650*1.6) = 260km$. Note that this would require something to actually melt through a very large amount of material to fuse silica into quartz. Then it would have to solidify before settling.

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  • $\begingroup$ Where do the "10^6" and "10^9" come from in your example calculations? $\endgroup$
    – Harthag
    May 10 at 16:20
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    $\begingroup$ @Harthag These are MPa and GPa material strengths. MPa = 10^6, GPa=10^9 $\endgroup$
    – ZOMVID-21
    May 10 at 19:38
  • $\begingroup$ Broken link? Typo? I get a 404 "not found" error when attempting to use it. $\endgroup$
    – Harthag
    May 12 at 16:02

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