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It seems as if the 'lowest energy' state for the Earth is to not have any mountains and that given enough time, the oceans would erode all land. Essentially it's an argument like entropy. And I mean in the far future, once tectonic activity has ceased.

Is this the case, and if so how long might it take? If it is not the case, why not?

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    $\begingroup$ Related question. I also remember seeing somewhere that the sun will expand and evaporate all water before the heat that drives tectonic activity dissipates. In that case, the situation that you describe is not relevant since it will never happen. $\endgroup$
    – Gimelist
    May 17, 2015 at 0:16
  • $\begingroup$ It's not just a matter of erosion, but also re-balancing the uneven weight distribution of rock below the surface - which is why continents exist, the thicker continental crust floats on top of the heavier oceanic crust. The weight evens out. I don't know if it would ever balance out, certainly it would take hugely long time if it did. Granite is harder and lighter so it's good continental material. I don't think erosion would be sufficient to re-distribute the cooled mantle. mlms.loganschools.org/~mlowe/lowehome/DictionaryPictures/… $\endgroup$
    – userLTK
    May 17, 2015 at 22:40
  • $\begingroup$ According to this article, all land on Earth could erode in 2 Billion years. economictimes.indiatimes.com/magazines/panache/… $\endgroup$
    – Ryan
    Mar 30, 2022 at 18:48

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Continents are made up of different, lighter materials than oceans and both continents and oceans "float" on the mantle. Continents are also thicker than oceans so erosion does not only need to take care of the ~5 km which is above sea level but it should also erode away the continental root (which can be several 10's of kilometers until the continental crust is actually slightly thinner than oceanic crusts are today.

However tectonics is not the only source of topography which can easily be seen if we look at Mars where a hotspot has created an enormous mountain on a tectonically inactive planet.

So if you want to end up with a topography free planet you need to shut down all possible mantle plumes too.

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I would argue that plate tectonics is the major reason their is elevation on the surface of the earth. But let me be clear that the oceans are not the major eroders of land - running water on the land is (from rain and snow). You are correct to assume that as the earth cools, plate tectonics will subside and the rate of erosion will overcome the rate of uplift due to plate tectonics.

As for making estimates about how long it will take to do this, I would not wish to hazard a guess. Earth has been going strong for billions of years and it probably has a few billion more years left.

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    $\begingroup$ Nearly all the water that falls as some sort of precipitation originates as evaporation from the oceans. Without the oceans, there would be very little, if any, snow and rain. Erosion is enhanced by the dissolution of CO2 with H2O forming carbonic acid (H2C03). $\endgroup$
    – BillDOe
    Jul 4, 2015 at 5:15
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    $\begingroup$ I think you have missed my point. The question asks will the "ocean" erode all land. Oceans can only erode through wave action along the coasts. The evaporation of water has nothing to do with erosion on land. Precipitation and subsequent water runoff on land is the major reason the land erodes. This includes carrying sediment in suspension and dissolution in chemical weathering through water runoff. I suppose there is semantics involved here but most would not relate erosion by runoff directly to the ocean. $\endgroup$
    – see you
    Jul 4, 2015 at 21:29
  • $\begingroup$ This reminds me of when I read a children's book that mentioned river meanders being cut off and wondered if all the rivers in the world will become straight in enough millions of years. There's actually a river in North Vietnam that's just like what I imagined. It's so ludicrously straight. Check it out. $\endgroup$ Jul 4, 2015 at 22:49
  • $\begingroup$ @MarcDefant, No, I don't believe I missed your point. But I think making your statement, "...oceans are not the major eroders of land.." without also mentioning their rather important contribution to the source of precipitation, could cause uninformed readers to draw the wrong conclusion. $\endgroup$
    – BillDOe
    Jul 5, 2015 at 1:39
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Your question is partially flawed because it is not the oceans that erode continents. Instead it is the collective erosion known as denudation, the sum of all processes inclusing weathering, slope processes and fluvial processes that reduce topography on the continents.

The level to which these processes tend will be the ocean level, identified as the base level. That said a few processes may erode to levels below the base level. Deep weathering could possibly reache below this level but probably only to tens of metres. Glacial processes can definitely erode to kilometers below sea level but this is localised to valleys (probably following fracture zones in the bedrock) forming fjords that may be eroded down to 1 to 1.5 km below sea level.

To add to this general condition, we must consider that sea level fluctuates depending on the distribution of sea basins realtive to continents. New ocean floor is relatively high elevation when compared to older ocean floor due to density differences. Water can also be accumulated on land during cold periods which can cause sea levels to vary. Hence the sea level is far from constant through time.

An implication of the question is what will happen in the future. I will assume the earths interior will cool with time chaning the continental drifting. With slowing drifting mountain building will decrease so that denudation will likely be dominating. A problem here is that we probably need to consider loss of atmosphere and other issues that we do not know much about. There are indictions from Mars that water has been more abundant in teh past yet the topography on Mars is significant because the erosional processes have lost their poser as loss of water may have been critical.

So what will happen in the futiure depends on how tectonic and atmospheric processes change in the distant future due to changes or development in both the earth's interior and the atmosphere in terms of water content (water being a critical componete in both weathering of rocks abnd transport of material in topgraphic terrain).

To conclude, the question is much larger than can first be thought and we need to consider large time frames in which many of existing processes and systems will drastically change. So to provide a time frame is very difficult and essentially pointless.

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