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What could be the effects of erosion on a rocky Earth-sized planet on a universal time scale (in the order of $10^{40}$ years)? Let's assume that:

  • The source of sunlight is endless and almost constant, occasionally dipping in intensity causing global cooling. Generally it's sufficient to maintain complex life.
  • The planet is in a perfectly closed system, with no external interaction. There are no impacts, and all matter is perfectly confined within an 1.5 radius limit from the planet.
  • The polar caps on this planet are always frozen

I'm interested in the consequences at the geological level. Would landmasses still be present after such a long time? Is it possible to maintain some sort of mountains?

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    $\begingroup$ 10⁴⁰ years is about one thousand billion billion billion times greater than the age of this universe; 30 orders of magnitude! Nobody has any idea of what could happen of such long timespans. It may be that the universe itself will cease to exist. It may be that protons will decay. Nobody knows, and it's not particulary interesting because stars have lifetimes on the order of 10¹⁰ , so stuff which happens on timescales one thousand billion billion billion times greater than the lifetime of a star is not really a topic of urgent research. $\endgroup$
    – AlexP
    Jan 9, 2018 at 15:52
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    $\begingroup$ By that point, erosion will no longer be a factor, nor will there be anyone around to notice erosion or the lack thereof. Star formation will have ceased, planets will have either fallen into their stars or been flung from their star systems, and black holes dominate a cold, dark and lifeless universe. $\endgroup$ Jan 9, 2018 at 20:25

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1040 years is a very long timespan.

  • Very early on (around 1010 years), the radioactive elements providing the planet's internal heat will decay. Plate tectonics will cease, mountain-building will end, and the magnetic field will go away. Normally, the atmosphere would escape, but you've got a magic confinement field preventing this.
  • Over the next eyeblink (109 years or so), water-driven erosion will wash most mountains into the sea. You'll be left with saltwater marshes and intertidal zones covering most of the former landmasses. Mountains in non-polar areas with no rainfall will survive this: no rain, no freeze-thaw cycles, and protective beaches mean the primary erosion method is wind-driven, which is much slower.
  • By 1011 years, the last land masses will sink beneath the ocean, from a combination of wind-driven erosion and coastal erosion. Erosion essentially ends, with a lack of air-water-land interfaces for it to take place at.

At this point, other effects not normally seen take over. For example, gravity-driven creep will cause the surviving irregularities in the seabed to slowly flow into a spherical shape. Random dislocations of atoms will slowly sort the planet by geochemical affinity. By 1020 years or so, your planet will be a series of uniform concentric spheres: air on the outside (with the light source stirring it up by convection, this won't sort appreciably), a saltwater ocean with all soluble minerals at their maximum possible concentrations, a layer of mineral salts, a layer of chalcophile and lithophile minerals, and a core of siderophile elements.

On longer timescales, even more exotic effects take over. For example, if the proton is unstable, your planet will evaporate over the course of 1038 years or so into an expanding cloud of neutrinos and gamma rays.

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The main thing combatting erosion is active plate tectonics and volcanism.

Over the time scales you are discussing the radioactive heat sources from elements in the interior of the planet are all decayed and most of the original heat of formation is likely gone as well. So your planet is going to have nothing to raise new continents or make new rocks, the interior will be cold and unmoving.

A frozen core has a number of other effects, no molten core means no spinning metal, so no appreciable magnetic field so your magical constant light source should be tuned for light only as the planet will lack a defense against other charged particles normally emitted by a star.

Not sure how you are confining matter, but it would be necessary as the normal very long term course is for atmospheres to blow away due to solar wind and otherwise having the upper layers of the atmosphere reaching escape velocity. See atmospheric escape. This would be more prevalent for light elements (aka hydrogen) so water is going to eventually go away. Depending on the method of preventing the material escaping, you could still see a loss of water along with an accumulation of upper atmosphere hydrogen or other odd stratification of light elements not normally seen in earth like unconfined atmospheres.

Over very long timescales landmasses would tend to erode and wear down to an even level, which would be slightly below sea level if your planet somehow has an ocean after this long a time. So no mountains are very unlikely. Land masses may still be possible, depending on if your planets has tides. Large tides for any remaining water would be more likely to wear down any remaining land masses.

Some Possibilities:

If you are providing some source of magical light and confining the atmosphere, maybe provide some source of heat to keep the interior of the planet molten.

To a limited degree biological activity can also raise landmasses. Like coral growth in the ocean, or building up a soil layer from biological sources. I think the best these could do is hills, but it's better than an eroded flat plain.

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  • $\begingroup$ Could there still be huge plateaus at the poles, effectively higher than every landmass? Anyway I'm considering some sort of biological activity to raise portions of land, because every source of energy in this setting must be high in the sky for plot reasons. $\endgroup$ Jan 9, 2018 at 15:45
  • $\begingroup$ Potentially if your poles stay frozen there could be plateaus covered in ice sheets like Antarctica at the poles, but that is kind of random and up to where the continents are when tectonic motion stops. $\endgroup$
    – Josh King
    Jan 9, 2018 at 15:52
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    $\begingroup$ That could be a neat effect, if the ocean is shallow enough and the tidal forces have a strong enough pull, that there are always two separated oceans constantly circling the globe. It might make more sense for the whole planet to have become tidal locked in that time, though $\endgroup$
    – phflack
    Jan 9, 2018 at 17:49
  • $\begingroup$ I would think glaciers would wear down poles below sea level, rather than have plateaus. $\endgroup$
    – user25818
    Jan 9, 2018 at 21:35
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The current age of the universe is around 13 x 109 years.

The thing with powers of ten is that a small change in exponents may mean a very big change in the actual value you have. 1040 years is around 31 orders of magnitude greater than 109.

That planet would have experienced the age of the universe as we know it approximately 1031 times. That is approximately 10,000,000,000,000,000,000,000,000,000,000 universe ages, or 10,000,000,000,000,000,000,000,000,000,000,000,000,000 years.

The actual name for that expletively huge age is "ten duodecillions years".

Most elements will have decayed into oxygen, nitrogen or carbon, which would all end up having escaped into space (Earth loses tons of atmosphere every year). Some elements will decay into stable sulfur or some other heavier-than-oxygen element, which can be solid, but if it associates with ligher elements (such as hydrogen sulfide), it will become gaseous and eventually escape into space too.

Long lived elements like Potassium (half-life: 1.3 billion years) and even Uranium (half life: 4.9 billion years) would all be depleted.

It is very likely that your planet's mass has mostly turned into gases at some point, which then escaped into space. The remaining mass was not enough to hold it all together and its parts were spread throughout the universe over the eons. The alternative is to have it frozen to close to absolute zero throughout all that time, so that the lighter elements stay solid and don't escape the planet. In this case, your planet is a big ball of amorphous ices. This icy mass will eventually flow over itself like water, and over the eons this will make your planet one of the most round things in the universe. Consider Uranus, which is also made of ices (it used to be called a gas giant, but nowadays it is more correctly considered an ice giant).

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Mountains are formed by tectonic processes

Erosion works fast enough that if new mountains were not being formed all the time, all mountains would have been destroyed in the last billion years.

For example, the Appalachian mountains in the Eastern US were built by the Acadian orogeny, roughly 350 million years ago. After such a time, what is left is some low rugged hills, rarely over 1.5 km high. Since the Appalachians once looked like the Rockies and Alps, given another 350 million years, there won't be anything left.

Fortunately, the Earth's tectonic motion is constantly throwing up new mountains. When the Appalachians were born, India was still fused with Africa as part of the southern supercontinent Gondwana. But then, India was split by tectonic forces and thrust at a (for a continent) great speed into the much larger plate of Asia, creating new mountains that are about as high as mountains can get, the Himalayas.

So to answer your question, assuming that the world is endlessly tectonically active, then the world will continue looking the way it does, with mountain ranges being thrust up as fast as they are worn down.

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You are talking a huge amount of time passing. On these timescales, the atmosphere will escape in the blink of an eye. What will happen next is interesting: with no atmospheric pressure, any solid will slowly evaporate (or rather, sublimate). This will form a very tenuous atmosphere, which will escape into space through the same mechanism as the original answer. Over time, the planet itself will evaporate. This is a form of erosion that does not happen over normal stellar timescales, but will be the dominant one in the long term until there is no planet left.

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