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I am interested in the growth of plants on different planets. I have read on this site that a 100-pound person will weigh 38 pounds on Mars. Therefore, the ratio of acceleration due to gravity ($g$) on Mars to that on Earth is 0.38.

Now, from the conservation of kinetic and potential energy, we know that $$(1/2)m*v^2 = mgh -\text{Equation 1}$$ where $m$ is the mass of the body, $v$ is the initial velocity of the body which is thrown vertically upwards and $h$ is the maximum height that the body would rise and then start falling down

Assume that a water particle at the plant's root has same energy on Mars as on Earth, and this could allow us to write the following:

Maximum height that water can travel on an Earth plant = $h_\rm{Earth}$ = $v^2/2g_\rm{Earth}$ — Equation 2

Maximum height that water can go on a Mars plant = $h_\rm{Mars}$ = $v^2/2g_\rm{Mars}$ — Equation 3

Divide Eqn (3) by Eqn (2), giving

$$h_\rm{Mars}/h_\rm{Earth} = g_\rm{Earth}/g_\rm{Mars} = 1/0.38 \approx 2.5$$

I understand that a plant uses the process of osmosis to transfer nutrients. I would appreciate your comments/corrections to my analysis.

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    $\begingroup$ Is this question specific to Palm trees, or trees? Palms are a somewhat atypical plant that have a fixed starting diameter and then grow fronds upwards, meaning on earth they tend to height limited by mechanical strength rather than flow upwards. Might also be helpful to clarify if this plant is growing indoors under earth normal pressure and light, or somehow outside in near vacuum and cold. $\endgroup$
    – GremlinWranger
    Commented Sep 29 at 1:44
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    $\begingroup$ There are multiple things wrong with this question. Tree roots do not shoot water upward. The leaves instead pull water upward via water evaporating from the leaves, thereby creating negative pressure. Water slowly climbs from the roots to the leaves via capillary action rather than a magical pump in the roots. $\endgroup$
    – David Hammen
    Commented Sep 29 at 6:35
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    $\begingroup$ My question was for plants in general; not specific to Palm tree. I understand that there is no pump in the plant's root system. Woody's answer is very helpful. Thanks to all members. $\endgroup$
    – SGH
    Commented Sep 29 at 21:28

2 Answers 2

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Answer: No

Plants use osmotic pressure to transport water and nutrients, but this is not what determines the height limit for terrestrial plants.

Transport of water in vascular plants is largely due to turgor pressure (similar to osmotic pressure). See https://nph.onlinelibrary.wiley.com/doi/10.1111/nph.18683 for a detailed discussion.

Turgor pressure is generated because solutes are more concentrated inside plant cells than outside the cells' membrane. Osmotic pressure drives water into the cells, creating turgor pressure which pushes the flexible semi-permeable cell membrane against the rigid cell wall. It is this turgor pressure which pushes water up the vascular channels to the top of plants and also provides pressure for roots to separate rocks. Pressure of up to 2.0Mpa (290psi or 670ft of water) can be generated https://en.wikipedia.org/wiki/Turgor_pressure

But the tallest Earth plants are only half the height of the turgor pressure. This means turgor pressure is not the sole limiting factor for maximum plant height on Earth.

Turgor pressure is more than enough to transport water to the top of the tallest redwood. The height of palm trees (as specified in the OP) is nowhere near this height, so their growth must be limited by other factors. These other factors may very well limit their height even if they were grown on a planet with lower gravity.

On a planet with 1/3 the gravity of Earth, turgor pressure could potentially transport water and nutrients three times as high. Of course, Earth plants cannot grow on Mars for a multitude of reasons. But if plant life evolved on a low-gravity planet, it could very well produce plants taller than Earth’s.

It is interesting that the tallest trees on Earth (Eucalyptus and Redwoods) are much shorter than the limit imposed by turgor pressure. Height imposes evolutionary costs, so that higher is not necessarily a selective advantage.

There is an analogy with building height. Tall buildings spend disproportionately on elevator shaft volume. Once a building is over about 50 stories, adding more floors does not add useful floor area. Skyscrapers are an exercise in vanity. https://www.economist.com/interactive/culture/2024/09/20/what-supertall-skyscrapers-reveal-about-countries-that-build-them

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    $\begingroup$ I think skyscrapers are pretty cool $\endgroup$
    – Dragongeek
    Commented Sep 29 at 10:56
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    $\begingroup$ "R2, activate elevator 31174." $\endgroup$
    – Wastrel
    Commented Sep 29 at 16:31
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    $\begingroup$ The issue with the space required for elevators is a solved problem that doesn’t make extra tall skyscrapers pointless. When you have long elevators, they are more like trains with their tracks turned 90 degrees. So in a really tall building, you would have your express t̶r̶a̶i̶n̶ elevator and the local ones. Each floor is like a train stop so local elevators can go to the side to allow the express elevators to stop at only every maybe tens floors or more. Having elevators like trains in tall buildings is a solution to the space problem and I think that there are others as well. $\endgroup$
    – The Rocket fan
    Commented Sep 29 at 20:55
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    $\begingroup$ @TheRocketfan Extra tall skyscrapers are usually not pointless because they deliberately add antenna or spires or other things for extra height - and those things have a physical point at the top. $\endgroup$
    – manassehkatz-Moving 2 Codidact
    Commented Sep 29 at 21:23
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    $\begingroup$ There's also the matter of competition. The tallest trees tend to be taller because they're in densely forested areas, where they are literally competing with other trees to get the most access to sunlight. A lone palm tree has no evolutionary drive to grow taller, and in fact has every reason not to, regardless of whether the lower gravity would make it easier. $\endgroup$
    – Darrel Hoffman
    Commented Sep 29 at 22:16
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No, the calculation is misguided. The height of water is not solely determined by gravity or by a conservation-of-energy argument like yours. Water does not go up trees because it's moving very fast in its roots (and, even if it was, why assume the velocity would be the same everywhere?). Water goes up trees because it evaporates out of the leaves and atmospheric pressure pushes the water up from the roots into this lower pressure environment created by this evaporation. The height water can go via this mechanism depends on the ratio of gravity to atmospheric pressure.

Surface gravity on Mars is about $3$ times weaker than on Earth, but atmospheric pressure is about $150$ times less. So the maximum height of a column of water maintained only by negative pressure is about $50$ times smaller. Hence trees for which this is the limiting factor (which is far from all of them, I don't know if palms falls into this category) would be about $50$ times smaller.

Not to mention that the much reduced sunlight, lack of air, low temperatures, and toxicity of the soil would kill any tree far before it could grow.

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    $\begingroup$ Do you have a source for "atmospheric pressure pushes the water up from the roots into this lower pressure environment"? Wouldn't that limit the tree height to like 10 meters? $\endgroup$
    – Organic Marble
    Commented Sep 29 at 1:26

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