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I'm designing a low gravity world, and when taking into account a variety of factors from plate tectonics to escape velocity, I've figured that 75% gravity is about as low as I can go and still maintain a long-lived atmosphere. Do you think reducing gravity by a quarter would have dramatic effects on the life of this planet? Would they grow substantially larger? Would they be significantly lankier? I want the effects of lower gravity on morphology to be obvious but I guess I'm wondering to what degree we would see the effects of a 25% reduction in gravity.

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  • $\begingroup$ @DKNguyen "I've figured that 75% gravity is about as low as I can go and still maintain a long-lived atmosphere." $\endgroup$ May 19 at 18:08
  • $\begingroup$ @LoganR.Kearsley Yeah I just looked up Venus and was about to delete my comment. $\endgroup$
    – DKNguyen
    May 19 at 18:09
  • $\begingroup$ (1) When making a comparison you need two terms to be compared. Grow substantially larger than what? Be significantly lankier than what? (2) Consider aquatic organisms on our own very Earth. They live essentially in zero gravity. A few of them are large. Some are medium sized. Most of them are small, even tiny or microscopic. Some are lanky. Some are bulky. Some are long and thin. Some are flat. (3) Consider land animals here on Earth. Nowadays elephants the largest, but in the Mesozoic there lived truly gigantic dinosaurs, four or five times heavier than an African elephant. $\endgroup$
    – AlexP
    May 19 at 18:15
  • $\begingroup$ @AlexP - We obviously have a lot of biological diversity here on Earth and a range of possible sizes/shapes, but my question is asking - would a 25% decrease in gravity produce land animals outside of that range that we have here on earth. Would the effects be noticeable with an only 25% reduction. You brought up ocean animals - and the oceans do support the largest animals that have ever existed. But they are, like you said, living in essentially zero gravity. So I'm trying to envision the possibilities on a 75% gravity planet. $\endgroup$
    – Elhammo
    May 19 at 18:33
  • $\begingroup$ One would expect to see many more flying and gliding species on this planet, and those that jump would be able to jump higher. $\endgroup$ May 20 at 6:07

2 Answers 2

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Everything weight only 3/4 as much as the same mass would on Earth.

Thus, for a given mass that must be supported, and constant material strength, compressive structures can be about 87% small in linear dimensions--3/4 of the cross-sectional area.

Alternately, for fixed support structures, the mass to be supported can be 1/3 larger--or about 10% larger in linear dimensions. This also applies to flying creatures--wings could be about 13% smaller (for equal atmospheric conditions), or the creatures could be about 10% bigger. That's much smaller than the range between the largest current flying creature on Earth, and the largest flying creatures that ever lived, so probably not really noticeably significant.

Of course, support structures (legs, trunks, etc.) themselves have mass, so there's some compounding of effects here, but for most creatures, that won't matter too much. You'd see the biggest effects for things like trees, which are pretty much all support structure, and so could be much thinner for a given height... except things like bending forces from winds won't change, and they'll still need to be thick enough to resist that. Additionally, for a fixed atmospheric pressure, trees could be about 33% taller.

Also keep in mind that for many creatures, gravity has never been a limiting factor in size; e.g., aquatic vertebrates are limited by their food supply, and terrestrial arthropods are limited by their respiratory systems.

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  • $\begingroup$ Thank you! But what do you mean by "compressive structures" and "fixed support structures"? $\endgroup$
    – Elhammo
    May 19 at 18:38
  • $\begingroup$ @Elhammo "compressive structures" = structures that support weight under compression. Legs, vertical spines, stems, trunks, etc. "Fixed support structures" = structures that you choose to keep the same (fixed) between Earth and your new planet. If you fix the mass, support structures can be smaller; if you fix the support structures, mass can be larger. $\endgroup$ May 19 at 18:54
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Here is a frame challenge to the idea that 75 percent of Earth's surface gravity is the minimum possible for a planet that can keep a dense atmosphere for geological eras of time.

Part One: the minium mass of a planet habitable for humans?

The gravitational aspect of a world which is important for retaining atmosphere is escape velocity, not surface gravity. As a general rule a world with higher surface gravity will have higher escape velocity, and vice versa. But there are different formulas for calculateing surface gravity and escape velocity, and they do not increase or decrease at the same rate.

There is a discussion of atmospheric retention in 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 Dole discusses a formula to roughly calculate how long it will take for a planet to lose enough of its original atmosphere for its atmosphere to go down to 1/e, which is equal to 0.368 of the original amount.

The ability of a planet to retain a specific gas depends strongly on the ration between the eplanet's escape velocity divided by the root-mean-square velocity of atoms and molecules of that gas at the temperatures in the exosphere of the planet's atmosphere, the zone where gases escape into interplanetary space.

According to table 5 on page 35:

When the ratio is 1 or 2, the time for the atmosphere to go down to 0.368 is is zero.

When the ratio is 3, the time for the atmosphere to go down to 0.368 is a few weeks.

When the ratio is 4, the time for the atmosphere to go down to 0.368 is several thousand years.

When the ratio is 5, the time for the atmosphere to go down to 0.368 is about 100 million years.

When the ratio is 6, the time for the atmosphere to go down to 0.368 is infinite.

So in some cases merely doubling the escape velocity of a world can increase the time it takes for its atmosphere to go down to 0.368 of its original amount by a factor of millions of times.

The temperatures in the exospheres of habitable planets are likely to be much higher than the surface temperatures. The average surface temperature on Earth is about 287 degreess Kelvin, but temperatures in Earth's exosphere are in the range of 1000 to 2000 K. On page 54 Dole calculates the minimum mass of a planet that can retain oxygen in its atmosphere for long times.

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

0.63 Earth radius would be about 4,013.73 kilometers or 2,494.016 miles. And this world would have a surface gravity of 0.49 g, considerably less than 0.75 g.

however, Dole doesn't believe w world that small would produce an oxygen rich atmosphere. Dole calculated two different minimum masses to produce an oxygen rich atmosphere, 0.25 Earth mass and 0.57 Earth mass, and on pages 56-57 more or less arbitarily selects 0.4 Earth mass as the minimum mass to produce an oxygen rich atmosphere. According to Dole's planetary density calculations a planet with 0.4 Earth mass would have a radius of 0.78 Earth radius (4,969.38 kilometers or 3,087.829 miles) and a surface gravity of 0.68 g, which is still considerably less than 0.75 g.

Part Two: A somewhat smaller minimum mass of a habitable world

There are other calculations of the minimum mass necessary for a world to retain a significant atmosphere for long periods. The mass range of habitable worlds is briefly discussed by Heller and Barnes in "Exomoon habitability constrained by illuminaitn and tidal heating", 2013.

On pages 3 to 4 at: https://arxiv.org/vc/arxiv/papers/1209/1209.5323v2.pdf

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).

The articles on the minimum mass to retain a substantial atmosphere are:

https://pennstate.pure.elsevier.com/en/publications/habitable-moons-around-extrasolar-giant-planets

And: Kaltenegger, L. 2000, ESA Special Publication, 462, 199

Apparently a mass of 0.12 Earth mass would be enough to retain substantial atmosphere, which is somewhat less than Dole's 0.195 Earth mass.

Part Three: Some calculations of surface gravities and escape velocities

So I suggest that you consider designing worlds which have various masses, radii, diameters, volumes, densities, surface gravities and escape velocities. What you want is a planet with a high enough escape velocity to retain an atmosphere for hundreds of millions or billions of years, and with a surface gravity as low as possible so animals can be as different as possible from Earth life.

Remember that the surface area of a planet changes with the square of its radius, and that the volume of a planet changes with the cube of its radius. A planet with 1/2 the radius of Earth would have 1/8 the volume. The radius of Earth is 1 Earth radius or about 6,371 kilometers or about 3,958.755 miles.

The mass of a planet depends on its volume and its average density. The average density of Earth is 1 Earth density or 5.514 grams per cubic centimeter. If a planet has the average density of earth and twice the radius of Earth it will have 8 times the volume of Earth and 8 times the mass of Earth. If a planet has half the average density of Earth and the same volume as Earth it will have 1 half Earth mass.

There is a considerable but far from infinite possible variation in the densities, volumes, and masses of possibly habitable planets, and thus variation in their possible surface gravities and escape velocities.

Here is a link to an online surface gravity calculator:

https://philip-p-ide.uk/doku.php/blog/articles/software/surface_gravity_calc

Here is a link to an online escape velocity calculator:

https://www.calctool.org/CALC/phys/astronomy/escape_velocity

Heller and Barnes suggested that the minimum mass of a potentially habitable world would be about 0.25 Earth mass.

If such a world had twice the density of Earth, it would have 0.125 the volume of Earth. The cube root of 0.125 is 0.5, so a world with twice Earth density and 0.25 the mass should have a radius of 0.5 Earth radius or 3,185.5 kilometers. It would have a surface gravity of 1 g and an escape velocity of 7.91073 kilometers per second, 0.7071991 of Earth's escape velocity of 11.186 kilometers per second.

If such a world had the same density as Earth, it would have 0.25 the volume of Earth. The cube root of 0.2500112 is 0.62997, so a world with the same density as Earth and 0.25 the mass should have a radius of 0.62997 Earth radius or 4,013.5388 kilometers. It would have a surface gravity of 0.63 g and an escape velocity of 7.04760 kilometers per second, 0.6300518 of Earth's escape velocity.

If that world has an average density of 2.757 grams per cubic centimeter, half that of the Earth, it would need to have 0.50 the volume of Earth to have 0.25 the mass of Earth. 0.7937 is the cube root of 0.4999989 so the planet would have a radius of 0.7937 Earth radius or 5,056.6627 kilometers. It would have a surface gravity of 0.4 g and an escape velocity of 6.27875 kilometers per second, 0.5613 that of Earth, and a tiny bit more than what Dole considered the minimum to retain an oxygen rich atmosphere.

Heller and Barnes mentioned calculations that a mass of 0.12 Earth might be the minimum to retain a substantial atmosphere.

If such a planet had a density of 11.028 grams per cubic centimeter, twice that of Earth, it would need 0.06 the volume of Earth to have 0.12 the mass of Earth. 0.3915 is he cube root of 0.060006, so it would have 0.3915 Earth radius or 2,494.2465 kilometers or 1,549.85 miles. It would have a surface gravity of 0.79 g and an escape velocity of 6.19379 kilometers per second, 0.5537091 that of Earth.

If a planet with 0.12 Earth mass had the density of Earth< it would need 0.12 the volume of Earth to have 0.12 the mass of Earth. 0.49325 is the cube root of 0.1200055, so it would have 0.49325 Earth radius or 3,142.4957 kilometers or 1,952.656 miles. It would have a surface gravity of 0.49 g and an escape velocity of 5.51809 kilometers per second, 0.4933032 that of Earth.

If a planet with 0.12 Earth mass had half the density of Earth< it would need 0.24 the volume of Earth to have 0.12 the mass of Earth. 0.62145 is the cube root of 0.240004 so it would have 0.62145 Earth radius or 3,959.2579 kilometers or 2,640.1688 miles. It would have a surface gravity of 0.32 g and an escape velocity of 4.91608 kilometers per second, 0.439485 that of Earth.

So to make a low mass planet have as low a surface gravity and as high an escape velocity as powwible, it shoudl have a lower over all density than Earth.

Part Four: small cold worlds like Titan

You should also consider Titan, the largest moon of Saturn. Titan has a radius of 2,574 kilometers, 0.4040 of earth's radus, and thus 0.659392 of Earth's volume. I thas mass of 0.0225 Earth mass and a density of 1.8798 grams per cubic centimeter, 0.340914 of Earth's density. It has a surface gravity of 0.138 g, and an escape velocity of 2.639 kilometers per second, 0.2359 that of Earth.

With such a low escape velocity Titan shouldn't have much atmosphere, but its mostly nitrogen atmosphere is quite significant.

Observations from the Voyager space probes have shown that Titan's atmosphere is denser than Earth's, with a surface pressure about 1.45 atm. It is also about 1.19 times as massive as Earth's overall,[44] or about 7.3 times more massive on a per surface area basis.

https://en.wikipedia.org/wiki/Titan_(moon)#Atmosphere

One reason why Titan has so much atmosphere is that it is very cold. Saturn orbits about 9.5388 times as far from the Sun as Earth does, and so receives only about 0.01099 times as much heat from the Sun as Earth does. The temperature of Titan is 93.7 K or minus 179.5 c, or minus 291.01 F.

It is a mystery why the atmosphere of Titan is billions of times denser than the extremely thin "atmospheres" of Ganymede and Callisto, the similarly sized moons of Jupiter. They are half as far from the Sun and thus get four times as much heat from it as Titan does, but that should not be enough to deplete their atmospheres so much. It is speculted that because Jupiter is much more massive than Saturn, it attracts more asteroids and comets, and large asteroid or comet impacts on Ganymede and Callisto may have destroyed their atmospheres.

If Titan was close enough to the Sun to have Earthlike temperatures, its exosphere temperatures would be much higher than they are and it would lose atmosphere much faster, and the solar wind would be almost 100 times stronger and strip away Titan's atmosphere much faster.

So Titan would not have its dense atmosphere if it was warm enough for liquid water using lifeforms. But maybe there can be lifeforms with exotic biology who use liquid methane instead of liquid water, that could live on Titan.

It is claimed that a human wearing breathing apparatus and very warm clothing could attach artificial wings to their arms and fly in the low gravity and dense atmosphere.

So if there can be multicelled plants and animals on Titan using an exotic biology, the low gravity on Titan could permit them to avoid many limitations faced by Earth life.

Part Five: small water worlds

In 2019, an article suggested that low gravity water worlds would retain atmospheres dense enough for wter to remain liquid even with masses as low as 2.7 percent of Earth. That is 0.027 Earth mass.

https://www.researchgate.net/publication/335150295_Atmospheric_Evolution_on_Low-gravity_Waterworlds

Ice covering an airless tiny world can sublimate directly into water vapor. If the ice produces water vapor faster than it escapes into space, the density of water vapor will increase until the atmopshere becomes dense enough for liquid water to be stable. Then water ice will tend to melt into liquid water as well as sublimating into water vapor. Water vapor is a greenhouse gas, so as water vapor accumulates in the atmosphere, it will warm up the icy planet until it is covered with a world wide ocean instead of by ice.

Such small planets would lose water vapor atmosphere into space quite rapidly, but if water was a major component of them they would have a lot of water sand so could maintain water vapor atmospheres for long times.

But of course any hypothetical sea life in those small worlds would be buoyed up the water anyway and wouldn't need the low gravity, so the gravity of those worlds wouldn't matter for the purpose of your question.

But if such a small water world has seasons, ice might form at its poles, especially if its sea water is less salty than Earth's. The planet might possibly have permanent floating icecaps which get larger in winter and smaller in summer.

If there are multicelled plants and animals in the ocean, they might eventually colonize the surfaces of the polar icecaps. And if the polar icecaps get thick and strong enough, they might be able to support giant trees and land animals more massive than sauropod dinosaurs, especially in such low gravity.

The trans-Siberian railway detours around Lake Baikal today. But they used to lay railroad tracks over the ice whenever the lake froze over. Ice thick enough to support a train could probably support a sauropod dinosaur, especially in a world with much lower surface gravity.

For example, suppose that such a hypothetical water world has the density of Titan, about 0.340914 of Earth's density. For it to have 0.028 of Earth's mass it would have to have 0.0821321 of Earth's volume. The square root of 0.0821313 is 0.43468. A planet with 0.43468 Earth's radius would have a radius of 2,769.3462 kilometers or 1,720.79195 miles. It would have a surface gravity of 0.15 g, and an escape velocity of 2.83939 kilometers per second, 0.2538 that of Earth.

Part six: shellworlds

As we all know, the gravity within the International Space Station is much lower than any surface gravity calculated so far, and yet there is a breathable atmosphere there for the astronauts. The atmopshere is retained by the airtight shells of modules of the ISS.

A shellworld13 is any of several types of hypothetical megastructures

The type of shellworld which might have noticeable but very low surface gravity would be:

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

Obvioulsy shells could be built around very small worlds with very low surface gravities and escape velocities, with their artificial atmospheres held in by the shells around them. Presumably the shells would have giant airlocks for spaceships to enter and leave.

And possibly plants and animals could grow enormously large in the very low gravity of such a world.

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  • $\begingroup$ Hey thanks for the detailed reply!! Originally I used 0.25M as the mass and then calculated the gravity for a planet with Earth-like density and came up with 0.63g. Earth-like density was important to me, because core composition and density affect the ability to generate an internal dynamo and I wanted a strong magnetic field. Then I plugged those numbers in to Artefexian's atmosphere calculator excel spreadsheet and it told me water vapor would not be stable on this planet :( So I had to increase the mass to increase the escape velocity. $\endgroup$
    – Elhammo
    May 23 at 20:23

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