# Gravity Limits Organism Size

1. Dec 11, 2008

### Widdekind

According to the DK documentary Eyewitness -- Life (VHS), Galileo correctly calculated that the tallest Earthling lifeforms can get is ~300'. The tallest Sequoia's are almost exactly that tall.

I'm told this has to do with the limits of Capillary Action, which allows organisms to pump water up to that height.

PARALLEL: According to the National Geographic documentary Naked Science -- Earth's Crust (TV), the tallest possible mountain on Earth is only 45,000'. Any taller, and Earth's gravity creates such pressures beneath its base, that the crust melts, and the mountain sinks back down.

But, on Mars, whose gravity only around 1/3 that of Earth, Olympus Mons is 90,000' tall, 3x that of Mt. Everest.

CONCLUSION: Earth-like lifeforms, limited by gravity, could grow taller on smaller worlds, but would be shorter on larger worlds. On Mars, w/ ~1/3g, Seqoia's could grow to nearly 900'. But, on a 2.0g planet, the tallest "tree-forms" could only grow to ~150'.

2. Dec 11, 2008

Staff Emeritus
Why is this astrophysics?

3. Dec 11, 2008

### Andy Resnick

I disagree with some of the specifics of your post (water transport in trees is more complex than pure capillary action, for example), but it is definitely true that 'g' (or its otherworldly equivalent) is involved in setting certain length scales.

4. Dec 12, 2008

### Widdekind

Would you please be more (mathematically) specific, or point me in the right direction ?

-W

5. Dec 12, 2008

### franznietzsche

On gravity limiting length scales of certain phenomena? That's more difficult to hunt down, even I am but a google padawan.

6. Dec 12, 2008

### Crazy Tosser

So in outer space a living organism could get infinitely large?

7. Dec 12, 2008

### Captain Barbosa

No, the organism's own gravitational field would put limits on its growth then.

8. Dec 12, 2008

### Gnosis

Per http://en.wikipedia.org/wiki/Sequoia their max height is 379 feet, so 300 feet max clearly wasn't an accurate assessment.

9. Dec 12, 2008

### DaveC426913

Only if its mass increases too.

10. Dec 12, 2008

### DaveC426913

Perhaps, but Galileo also came up with the square-cube law. You might look into that too.

11. Dec 13, 2008

### Widdekind

That is technically true. However, the documentary I cited is at a rather basic level. I suspect they were rounding, in Galileo's favor, b/c he got the "essential physics" correct.

12. Dec 14, 2008

### Danger

Widdekind, don't overlook Dave's last post; it's critical. In the simplest terms, the structural integrity of an object increases as the square of its size, while the mass increases as the cube. "The Attack of the 50' Woman" could never happen because her leg bones would shatter if she tried to stand up.

13. Dec 15, 2008

### Widdekind

But doesn't the square-cube law restrict heights to well under ~300' ? You yourself said, "50' woman".

14. Dec 15, 2008

### DaveC426913

Yes it does, which is why it may be critical to the OP (though he may not realize it yet). The square-cube limit is more restrictive than the relatively more forgiving capillary action limit. If the OP were looking at the maximum size of a living thing, he would misoverestimate its likely size judging on capillary action alone.

As to why they predict different things, the answer lies in the application. Square-cube applies more to motile things, things that require flexible legs for movement. The larger a motile thing (i.e. animal) gets, the larger the cross-section of its legs must be (which is why a bird has skinny legs but and elephant has great stumps for legs), At some point in scaling up, your legs would not fit under the body; you could only have a giant, single pseudopod-that's-no-longer-a-leg. This is a direct, emergent consequence of the square-cube law.

A tree is an idealized form of creature: a single leg (i.e. trunk) that is as large (actually, larger) in cross-section than its body. All its mass is situated directly above its trunk, not in a spheroid shape as with animals. And, in reaching that height, it has lost its motility (or would have, if were an animal ... and had motility).

15. Dec 15, 2008

### Danger

Also, the structural properties of wood are far different from those of bone.

16. Dec 15, 2008

### Widdekind

My OP title may be imprecise.

GENERAL STATEMENT: Gravity limits organism size.

SPECIFIC STATEMENTS:
(A) Gravity limits animal sizes (~50' per g)
(B) Gravity limits plant sizes (~300' per g)

All organisms are linearly limited by surface gravity (g), yes ?

Even w/ the square-cube law, muscle strength (R2 in denom.) is independent of gravity, whereas weight (g x R3 in numerator) is linearly dependent on gravity.

I therefore suggest, that Galileo's square-cube law can be generalized to include the "g" term:
$$\frac{g \times R^{3}}{R^{2}} = g \times R \leq constant$$​
(I'm assuming that Alien muscles are about as strong as Terrans'.)

17. Dec 17, 2008

Staff Emeritus
The square-cube relationship is far more important than just structurally. Organisms get air, sunlight and often nutrients in proportion to their surface area, but use them in proportion to their volume. This puts a limit on organism size independent of gravity - and if one looks at the very largest organisms (e.g. Pando), they tend to be very sparse as a strategy to get their surface areas up.

In fact, gravity only imposes a limit on an organism's height, not size. Furthermore, the "limit" is both a function of gravity and the organism's construction. The bug-people of the planet Mongo, where there are no vertebrates, might well calculate the the largest animal on earth can't be much larger than a giant scarab.

18. Dec 17, 2008

### DaveC426913

An excellent point.

I don't know why you say this. Size (volume) is proportional to mass. Whether an organism is tall or not, its volume is still limited because its mass is limited, and its mass is limited because its limbs can't take the weight.

The point though is that gravity is a limit imposed virtually independent of other factors (such as construction); while construction will also tend to limit things, the list of possible limits endemic to a particular organism-type is virtually without end (for example, availability of food, expulsion of waste heat, etc.).

I suppose I see your point though. The wavy-tendril people of Zaxxon IV have limbs that easily exceed a thousand feet, since their limbs are gossamer-light.

Gravity being a limit is really an Earth-biotope-centric view.

19. Dec 17, 2008

Staff Emeritus
I am thinking of organisms like Pango, which are broad but not very tall. Each stem/trunk has a height limit, but there is no gravitational limit to how many stems the root system can have.

20. Dec 17, 2008

### LURCH

Exactly what I was thinking; you could have a multi-ton millipede, so long as each leg only supports a thousandth of the weight. And of course, floating or semi-floating plants like kelp would not be limitted by gravity at all, so long as they retain near-nuetral bouyancy.

Cappilary action doesn't have to be a limit, either. As has been mentioned, the world's tallest tree is considerably taller than predictions would have indicated. What has not been mentioned is that, when researchers examined the top leaves of tha tree, they were suprised to find the leaves fat. That means they were filled with water, not "barely surviving" on just a trickle. As far as anyone can tell, there is no reason the tree will stop growing taller.

But this should not come as a suprise; early mining efforts proved that the so-called "limits" to pumping water to great heights can be worked around. I suspect this tree uses a strategy similar to that employed by mining engineers; pump the water as high as you can, then deposit it in a resevoir (microscopic, in the tree's case). Use the resevoir as your new "zero" level, and repeat the process.

-That's only my guess, of course; the experts are still doing some head-scratching as to how this is actually accomplished.

21. Dec 18, 2008

### Widdekind

It is a valid point, that Organisms are "Oxygen-limited" -- especially so for organisms w/ "passive respiration" (eg., Arthropods like arachnids & insects). For example, the dinosaurs were much bigger than present vertebrates, b/c O2 concentrations were ~30% higher at that time*.
* Discover Channel Life Before Dinosaurs (DVD) ; BBC Walking w/ Prehistoric Beasts ; BBC Prehistoric Park (DVD) ; BBC Prehistoric Planet (DVD)
Now, consider Habitable Planets, orbiting in the Habitable Zones, of bigger & brighter F-Class stars. Since said stars are hotter, their radiation is "harder" (more UV). Thus, they can generate more protective Ozone (O3) for the same amount of Molecular Oxygen (O2). Assuming that an Ozone Layer is a necessary pre-requisite for the evolution of Complex Life*, then advanced Lifeforms in F-Class star systems will tend to be smaller, since they'll evolve when O2 concentrations are still only ~70% of Earth's. Conversely, Complex Life in cooler, darker K-Class star systems will appear after O2 builds up to about ~200% of Earth's.
CONCLUSION: Bigger, brighter, & hotter stars probably develop smaller Complex Lifeforms (albeit more quickly), while cooler, dimmer, & darker stars probably develop bigger Complex Lifeforms (albeit more slowly).

Last edited: Dec 18, 2008
22. Dec 18, 2008

Staff Emeritus
False. (And besides, "I saw it on TV" is a pretty crappy reference.) Work on trapped cretaceous air in amber indicates that it is oxygen-rich, not oxygen poor. (c.f. Berner and Landis. Science 18 March 1988:Vol. 239. no. 4846, pp. 1406 - 1409)

It doesn't make any sense anyway that less oxygen would cause creatures to grow larger.

Evidence?

23. Dec 18, 2008

### Widdekind

Cretaceous Era air is oxygen rich. The extra 30% O2 allowed dinosaurs to grow larger than comparable animals could today.

24. Dec 18, 2008