Could a Giant Earth planet have lower gravity than Earth?

Question

I'm writing a neo-pulp adventure and one of the planets that appears needs to have the following characteristics:

• Is populated by giant non-sentient non-humanoid insect-like aliens, some from the sizes of cattle but some from the size of a Boeing 747. Some of the bigger creatures should be able to fly.
• The atmosphere is very thick and most of the planet is very jungle-like like a rain forest.
• The flora is not so Earth-like, there are no trees, but plants with flowers can grow taller than redwoods.
• There will be one type of spider-like creature that creates something similar to a spider web but strong enough to capture a small flying vehicle. Thus this creature should be able climb plants.

Now I was thinking that for many of these characteristics it should have lower gravity however I'm not sure if is physically possible for a rocky planet some N times Earth's size to have lower gravity. I know that a planet's gravity has to do also with density and not only size, but again, not sure if a rocky planet can not be dense enough to have lower gravity than Earth. Another possibility is to make the opposite, a planet with high gravity with its fauna adapted to it, however in that case I doubt flight will be possible.

Keep in mind that:

• Earthlings (as I'm not using the term human) are not going to stay there for much longer, just a couple of days, weeks at most.
• If Gravity is higher than Earth it should not crushed humans and human-size aliens that arrive there, but can cause some discomfort.
• Technically is not necessary for it to be a super Earth, even an Earth-size planet is still huge but if possible to keep this will be more fun.
• Is preferable that the atmosphere is human-breathable.

Thanks in advance.

PD: Is a neo-Pulp novel so is certainly not hard sci-fi, science doesn't have to be rigorous (although some scientific accuracy doesn't hurt anyone) but the point is it's soft sci-fi as long as avoids magic or fantasy explanations will be enough.

Answer 1

I think it depends on the definition of "giant".

Let's consider a planet 2 times Earth's size, identical density. Gravitation gets multiplier 8 due to volume => mass increase and 0.25 due to increased radius. So, it is 2g on the surface.

Planet density can compensate for it to some extent, e.g. Moon density is ~0.6 of Earth's. So, if the planet's density is 40% of Earth you get 0.8g on the planet surface.

It gets worse as N grows, there certainly is a lower limit for density.

A planet twice larger than Earth has 4 times greater surface and if you get rid of oceans you can increase it ~4 times more.

Your planet can rotate really fast. Earth's gravity on the equator is 0.3% lower due to centrifugal force. Planets can rotate much faster, Earth's rotation was slowed down by tidal locking with the Moon. If the planet rotates fast enough it will not be a sphere which would reduce gravitation near the equator even more.

Answer 2

Make it a mini Dyson sphere

Inside, we're going to put a garden variety white dwarf, about the mass of the Sun (332950 Earth masses). We're going to put the life, oh, 1000 times the radius of the Earth away, so the inverse square law gives this gravity a little over a quarter of Earth's. Now 1000 x 6370 km is a little over 6 million km, which is about 4% of Earth's orbital radius, so the light from a Sun would be 625 times brighter, but this is a white dwarf, so it's dimmer. We can fine-tune the brightness if we'd like a different gravity, by either dumping on a little accretion material from some orbit inside the structure, or letting the white dwarf sit around and lose some of its heat before using it. (You can mostly work out the tuning you need from a Hertzsprung-Russell diagram which has +5 to maybe +10 difference in absolute magnitude depending on the white dwarf mass, but without nailing down the scenario I might as well steer clear of the math errors)

Now we just have to keep the mass of the planet hovering suspended above a star that is pulling it in at a significant fraction of Earth gee force. Well, that's not so trouble is it? We'll just make the lower surface of this Dyson sphere super reflective, so that the photons emitted from the white dwarf make the rounds internally many, many times before they come up through the ground. The result is enough light pressure to suspend a statite that weighs thousands of tons at each square meter of terrain. Hopefully this doesn't rile up the superheated white dwarf to the point where it comes into contact with the sphere - I know there's a way to calculate that also...

But provided the planet doesn't burst into a brief mini type Ia supernova, you've got yourself an Earth 1000 times bigger than any you've seen before, with comfortable heating from below. (Make sure to warn the greedy dwarves not to mine too deeply, or they'll release an explosive amount of light, tear open the sphere, release the light pressure, and soon dump the entire planet into the gullet of a white dwarf) Perhaps you can add an ornamental star for aesthetics. Otherwise you can power your plants with anti-solar cells (NOT making this up!).

Answer 3

There are many characteristics that astronimicalobjects have, and changes in one ae likely to results in changes to another.

A science fiction writer may want to consider where they want their story to be on the sliding scale of science fiction hardness.

https://tvtropes.org/pmwiki/pmwiki.php/SlidingScale/MohsScaleOfScienceFictionHardness

The higher the score they want for their story, the more thought theyshould put into designing their planet.

So I will suggest some alternatives to the desired giant planet with low gravity and a thick atmosphere, since the story might be able to do without every one of those properties of the world. And then I wull point out some some of he problems of trying to design a natural planet with the desired surface area, gravity, and atmosphere.

Part One: Maybe Gravity Doesn't have to be Low.

The surface gravity of Earth doesn't stop some sea cratures from evolving into giant forms, their maximum sizes are determned by other factors. The surface gravity of Earth didn't stop some mammal species from growing bigger thant he largest prent day elephants, and it didn't stop some dinsaur species becoming gigantic. The surface gravity of Earth does keep the sizes of flying animals rather small.

But the largest flying animals on Earth were a lot larger than the largest present flying animals.

Floating animals, supported by giant gasbags of gas lighter than the atmosphere, culd get much larger than flying animals. And the denser the atmosphere becomes, the closer to an ocean, the easier it would be for those animals to move like swimming animals, or like squit using eets of water.

Also the higher the surface gravity of the planet, the easier it might be for desnity differences to enable anmals to flat in the air.

Part Two: Maybe the Planet Doesn't Have to be Big to Have Giant Animals.

As I remember, the planet Earth is about 71 percent ocean, and about 29 percent continents and islands. But if a planet had about half the surface area of Earth, and the proportion of land and sea was reversed, it would have a land surface equal to 0.359 of Earth's totalsurface, greater than Earth's land surface.

And the sizes of continents were about the same when the largest mammals lived. The age of dinosaurs lasted anout 180 million eyars and the contnents moved around a lot during that time. Atthe beginning of the age of dinasaurs all the continents weretogether in thesupercontinent called Pangaea which broke apart and some of the moving fragments eventually met and joined other fragments.

And whenever there were giant dinosaurs on a continent the same size as it is now, that was proof that giant land masses are not necessary for giant animals.

The prehistoric breakup of the supercontinent Gondwana resulted in the separation of East Gondwana (comprising Madagascar, Antarctica, Australia and the Indian subcontinent) and West Gondwana (Africa–South America) during the Jurassic period, around 185 million years ago. The Indo-Madagascar landmass separated from Antarctica and Australia around 125 million years ago[25] and Madagascar separated from the Indian landmass about 88 million years ago during the Late Cretaceous.[26] This long history of separation from other continents has allowed plants and animals on the island to evolve in relative isolation.

So any dinosaurs found in Madagascar or India after about 125 milion years ago would have been living on a small continent. And after Indiaa nd Madagascar separated about 88 milion years the land availabe in eachplace was evern less.

And it turns out that the legendary lost fossil of Bruhathkayosaurus, possibly the largest dinosaur ever, dates to the late Cretaceous, about 70 million years ago, in India. Weight estimates for Bruhathkayosaurus go from 30-55 tonnes, 95 metric tons, up to 126 metric tons, to 175-220 tonnes. Some of the larger estimates make it as massive as a blue whale - on land. So the comparatively small size of India didn't inhibit the giantism of Bruhathkayosaurus much.

There were sauropod dinosaurs in Madagascar after it separated from India, Rapetosaurus. They were small for sauropods, but much longer than even the largest prehistoric mammals, and weighed as much as the largest elephants.

Adn of course a small planet could have low surface gravity, helping land animals and flying aniamls grow larger.

Of course there is a limit to how small a planet with life can be, and to how low its surface gravity can be, because the planet has to have a high enough escape velocity to retain its atmosphere for geological eras of time.

Part Three: Maybe the Planet Doesn't to Have a High Escape Velocity (or even be a planet).

According to my calculations Mars has about 0.283 the surface area of Earth,larger than the entire land surface of Earth. Mercury has a surface area of 0.1466 that of Earth, Io has 0.0812 Earth's surface area, The Moon has 0.0739 Earth's surface area, Europa has 0.0576 Earth's surface area, and Ceres has 0.0053 Earth's surface area.

So even Ceres has nearly as much surface area as the Republic of India, which was large enough to support a species of supergiant dinosaurs like Bruhathkayosaurus.

The surface gravities of those worlds go from 0.378 g, down to 0.029 g, Ceres. So a small enough astronomical body can have a surface gravity a lot smaller than Earth's, while still having the surface area of a large country on Earth and room for large animals.

So possibly soem adanced civilization could take a small planetary mass object and terrform it, giving it water and an atmosphere, and building a shell around it to keep the atmosphere from escaping into space.
Thus it would have a surface area much smaller thna Earth's but still large enough to support giant animals, and very low surface gravity to make giant land and flying animals more plausible, and could also keep its atmosphere.

Shellworlds are hypothetical megastructures. One type of a shell world would be:

An inflated canopy holding high pressure air around an otherwise airless world to create a breathable atmosphere.2 The pressure of the contained air supports the weight of the shell.

https://en.wikipedia.org/wiki/Shellworld

Many other types of megastructures have been imagined, many being larger than any habitable plant could be. And many of those megastructures would be impossible to build without the ability to manufacture materials strnger than any known at the present.

https://en.wikipedia.org/wiki/Megastructure

https://en.wikipedia.org/wiki/Bigger_Than_Worlds#:~:text=%22Bigger%20Than%20Worlds%22%20is%20an,of%20the%20Mind%20(1991).

But studying all the proposed types of mega structures could find a design for a structure with more surface area than any habitabitable planet could have, and very low gravity, and a higher enough escape velocity to keep its atmosphere or else a shell to hold the atmosphere in.

Part Four: Planetary Surface Area.

The OP asks for a giant planet for their giant creatures to live on, apparently believing - incorrectly - that the size of animals scales with the size of planets. The vast variatiion in the sizes of Earth animals should prove that the sizes of animals are not proportional to the sizes of their planets.

The surface area of a planet is proportional to the square of the radius, so for a planet to have X times the surface area of Earth, it has to have the square root of x times the radius of Earth.

If a fictional planet has 2 times the surface area of Earth, the planet will have a radius and diameter 1.414 times that of the Earth. For 3 times the Earth's surface area, the planet should have 1.732 the radius. For 4 times the surface area, the planet should have 2 times the radius, for 10times the surface area, the planet has to have 3.162 times the radius,for 100 times the surface area the planet has to have 10 times the radius, and so on.

https://www.calculator.net/root-calculator.html?cvar1=100&ctype=1&x=35&y=17

Part Four: Planetary Volume.

The volume of a planet is proportional to the cube of the radius, so for a planet to have X times the volume of Earth it has have the cube root of X times the radius of Earth.

For a planet to have 2 times the volume of Earth, it has to have 1.259 times the radius of Earth. To have 3 times the volume it has to have 1.442 times the radius, to have 4 times the volume it has to have 1.587 times the radius, to have 10 times the volumeithas to have 2.154 times the radius, to have 100 times the volume it has to have 4.641 times the radius, and so on.

https://www.calculator.net/root-calculator.html?cvar2=100&ctype=2&x=17&y=8#cubic

Part Five: Mass and Average Density.

The mass of a planet is its volume multiplied by its average density. The average density of a planet is it's mass divided by its volume.

The average density of a planet is calculated from the densitiies and relative abundances of all its elements. Undfortunately, the deeper within a planet some of its matter is, the more dense it will be, compressed to greater density by the weight of all the matter above it, pressing down on it.

So if two planets are formed out of materials with the same density, the larger and more massive planet will have the greater density. If two planets have the same density, the planet with the greater volume will have the greater mass.

The least dense element,and the most common in theU universe,is hydrgen, with an average density of 0.089 grams per cubic centimeter. The most dense naturally occurring element osmium, at 22.59 grams per cubic centimeter. Irridium is much less toxic and almost as dense, at 55.56 grams per cubic centimeter. Both are very rare; the densest common element is iron, at 7.847 grams per cubic centimeter.

In our solar system the giant planets have average densities less than 1.76 grams per cubic centimeter, because they are massive enough to have retained very large atmospheres of the lightest elements, hydrogen and helium.

There are many objects in the outer solar system which seem to be mixtures of rocks and frozen liquids and gases. They all have densities less than 2.43 gams per cubic centimeters (Eris). If those objects were heated up to Earthlike temperatures all their ice would melt into water and they would be covered by oceans tens of kilometers deep.

So a science fiction story on a planet with some solid surface and Earthlike temperatures must be set on a planet with a high enough density to be made out of rocks, with only a small amount of liquids and gases.

Part Six: Examples of Density Range.

There are about seven large objects in our solar system that seem to be mostly rocks. Earth is the densest, at 5.52 grams percubic centimeter, while the three least dense are the Moon at 3.3464g grams per cubic centimeter, Europa at 3.01 grams per cubic centimeters, and Ceres at 2.16 grams per cubic centimeter.

https://en.wikipedia.org/wiki/List_of_gravitationally_rounded_objects_of_the_Solar_System

So the dividing line between rocky and largely icey worlds seems to be at about 2.00 to 3.00 grams per cubic centimeters.

And the more massive a planet is, the more its gravity will compress its core materials to be much more dense than their natural density, and so the higher its average density will be compared to less massive planets made out of the same materials.

Since the average density of Earth is 5.52 grams per cubic centimeter, an average density of 2.000 grams per cubic centimeter would be 0.3623 that of Earth, 3.000 grams percubic centimeter would be 0.543 tha tof Earth, 4.000 grams per cubic centimer would be 0.724 that of Earth, 5.00 grams per cubic centimeter would be 0.905 that of Earth, 6.000 grams per cubic centimeter would be 1.086 that of Earth, 7.000 grams per cubic centimeter would be 1.268 that of Earth, 8.000 grams per cubic centimeter would be 1.449 that of Earth, 9.000 grams per cubic centimeter would be 1.630 that of Earth, and 10.000 grams per cubic centimeter would be 1.811 that of Earth.

So if you decide a planet will have X times the mass and Y times the density of Earth, you can multiply the volume of Earth by X and divide by Y to get the volume of that planet. With the volume of that planet you can calculate the radius of the planet relative to Earth, which will be Earth's radius times the square root of its volume compared ot Earth.

Part Seven: Habitable For Earth Humans.

If you want Earth humans to explore your planet without space suits, and if you want them to colonize the planet or spend much time there, the planet will have to be habitable for humans. And Earth animals or alien animals and people with similar requirments will be restricted to planets habitable for humans or only slighly different.

There is a scientific study of what would make a world habitable for humans, Habitable planets for Man, sTephen H. Dole, 1964.

https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf

Dole dicussed tehsurface gravity requirements for humans on pages 11 to 13, and decided that humasn wouldn't want to live on a planet with a surface gravity higher than 1.25 or 1.50 g, the surface gravity of Earth. Since 1 g is 9.807 meters per second per second,the limit would be 12.258 to 14.710 meters per second per second.

Dole discussed the atmospheric requirments for humans on pages 13 to 19.

Dole discussed the ability of a planet to retain its atmosphere for geological eras of time without the atmosphere escaping into space from the exosphere, the outermost layer of the atmosphere where gasese scape. On pages 34 to 35Dole discussed a rule of thumb formula for calculating the the amount of time a planet or other world could retain 1/e, or 0.368, of the original amount of a gas to ration between the planets escape velocity and the root-mean-square velocity of gas particles of that gas in the exopshere. I note that the root-mean-square velocity of those particles would depend on their weight and temperature in the exosphere, which is often much higher than the temperature onthe surface of the planet.

Table 5 on page 35 gives the time for the amount of a gas to fall to 1/e of its original amount compared to the ratio of the world's escape velocity divided by the root-mean-square of that gas's velocity in the exosphere of that planet.

The table shows that a comparitively minor difference in that ratio makes the difference between the time period being seconds and being billions of years.

On page 53, Dole calculated that a planet with a surface gravity of 1.5 g, would have 2.35 the mass of Earth, a radius of 1.25 Earth radius, and an escape velocity of 15.3 kilometers per second, 1.367 times Earth's escape velocity of 11.186 kilometers per second. With 1.25 times he radius of EArht, it would have 1.5625 teh surface area of Earth, and 1.953125 time the volume. With 2.35 times the mass and 1.953125 times the volume, it would have 1.2032 times the average density of Earth, or 6.632 grams per cubic centimeter.

Dole calculated a minimum mass of a planet capable of retaining an oxygen atmopshere long enough for mulitcelled land planets and animals to evolve on page 54.

Dole said that Earth, which has an Earthlike surface temperature by definition, has exosphere temperatures of 1000 k to 2000 K. The verage temperature on Earth 15 degees C or 288 degreess K, so the exosphere temperature is about 3.4 to 6.9 times the average temperature of Earth.

If the exosphere temperature is mainly due to solar radiation and not infrared heat waves raidiated outward by the Earth, the exosphere temperature could be lowered by simply moving Earth farther from the Sun to receive less radiation.

Anyway, Dole wrote that if the maximum exosphere temperature could be as low as 1000 K while the surface temperature was warm enough for liquid water, a planet could retain oxygen for a long time with an escape velocity of 6.25 kilometers per second (5 times the root-mean-square velocity of oxygen of 1.25 kilometers per second) According to table 5 on page 35 the amount of oxygen would fall to 1/e in about 100 million years, which should be slow enough for the oxygen to be replaced by various processes.

Dole calculated that a planet with an escape velocity of 6.25 kilometers per second (0.5587 that of Earth) would have a mass of 0.195 Earth, a radius of 0.63 Earth, and a surface gravity of 0.49 g. I add that with a radius of 0.63 Earth it would have 0.3969 the surface area and 0.250047 the volume. With 0.195 the mass in 0.250047 the volume it would have 0.7798 the density of Earth, or 4.2998 grams per cubic centimeter.

Dole didn't believe that such a small world form a dense oxygen rich atmopshere, and so try to calculated the minimum mass of a world capable of doing so. On pages 56-57 Dole more or less arbitarily decided the minimummas to form an oxygen rich atmosphere would be about 0.4 the mass of Earth.

Dole calculated that would be a planet with a radius of 0.78 Earth and a surface gravity of 0.68 g. It would have an escape velocity of 8.01 kilometers per second (0.716 that of Earth) according to this online calculator.

https://www.omnicalculator.com/physics/escape-velocity

If it has 0.78 times the radius of Earth it would have 0.6084 the surface area and 0.474 the volume. With 0.4 the mass of Earth in 0.474 the volume, it would have a density 0.8438 that of Earth, or 4.653 grams per cubic centimeter. Part Eight: Designing Giant Planets with Low Gravity.

I don't think that there is such a strict relationship between the mass and radius of a planet as Dole assumes. I believe that there can be a bit of variation in the average density of the materials that planet can be made of, so a human habitable planet can probably a n averge density a bit lower than 4.2998, or a bit higher than 6.632, grams per cubic centimeter.

The OP specifies a giant planet with a low surface gravity - tohelp the giant animals become giant. And I add it needs a high enough escape velocity for the planet to retain a dense atmosphere to keep water liquid, and to retain a lot of atmospheric oxygen for the animals.

So I will try a planet with the same average density as Earth, but twice the radius, four times the surface, area, and eight times the volume and mass. Earth's radius is about 6,371 kilometers, so twice that would be 12,742.

According to this calculator, it would a have a surface gravity of 2 g.

Trying a planet with 3 times the radius and the same density as Earth, it has a surface gravity of 3.01 g. So increasing the radius of a planet X times while keeping the density the same will increase the surface gravity proportionally to the radius.

So now try a planet with the twice the radius of Earth (4 times the surface area, 8 time the volume) but only half the average density (2.756 grams per cubic centimeter). It would have a surface gravity of 1 g (and an escape velocity of 15.82 kilometers per second). Apparently if you change the density inversely to the radius, the surface gravity will stay the same.

So a world with three times the radius of Earth (nine times the surface area, 27 times the volume) but one third the density (1.838 grams per cubic centimeter) would have a surface gavity of 1 g and an escape velocity of 19.375 kilometers pers second.

And I think that this might already be going too far, and it might not be possible to have a planet with a solid surface with that mass, radius and density. The density might be too low to achieve except by giving the world a lot of volatile materials, which would melt to cover the world with oceans many tens miles deep if teh world had Earth like temperatures. And the escape velocity might be high enough to give the world a dense and possibly unbreathable atmosphere of hydrogen and helium.

The escape velocities of the giant planets range from 60.20 kilometers per second on Jupiter down to 21.38 kilometers per second on Uranus. So that planet seems near the upper limit for escape velocity.

So try a planet with half the mass of Earth but with the radius and volume of Earth, and thus half the density (2.756 grams per cubic centimeters). It would have a surface gravity of 0.5 g and an escape velocity of 7.91 kilometers per second, 0.707 that of Earth.

So give the world 2 times the radius, 4 times the surface area, 8 times the volume, but half the density and thus only 4 times the mass of Earth. It would have a surface gravity of 1 g, and an escape velocity of 15.82 kilometers per second.

So give the world 2 times the radius, 4 times the surface area, 8 times the volume, but a density of only 2.00 grams per cubic centimeter (0.3628447 that of Earth) and thus only 2.9027 times the mass of Earth. It would have a surface gravity of 0.72 g and an escape velocity of 13.476 kilometers per second.

So give a world 2.1 times the radius, 4.41 times the surface area, and 9.261 times the volume of Earth, and a density of 2.1 grams per cubic centimeter, 0.3809 that of Earth. It will have 3.5283 times the mass of Earth. It will a surface gravity of 0.81 g, and an escape velocity of 13.5 kilometers per second.

And I think that the lastest calculations are close to the limits for a world larger than Earth, with a lower surface gravity, and a high enough escape velocity to retain an atmosphere. It sems that naturally formed and naturally developing palnets will not be able to go very far in the direction desired by the OP.