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I'm thinking a planet orbiting a nearby star colonized by human settlers sometime in the not near, but not too distant future. How small could a planet be while still standing in as a relatively close substitute to Earth? Let's suppose the atmosphere, the climate, and the gravity would be very similar to Earth's. Is it realistically possible for a planet half the size of Earth to have these qualities, or even smaller?

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  • $\begingroup$ Related question in progress, though it doesn't yet cover this. I'll add in some information tomorrow, if I can. On a side note, are you interested in mass, too, or just size? $\endgroup$ – HDE 226868 Feb 9 '15 at 3:09
  • $\begingroup$ Thanks. And yeah, just size. As long as the planet's mass is believable, it's not an issue at all. $\endgroup$ – akaddoura Feb 9 '15 at 3:13
  • $\begingroup$ So, the planet is like the planets from The Little Prince? $\endgroup$ – grimmsdottir Feb 11 '15 at 1:15
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Size and Gravity

Here's a handy equation if you want to find the radius of a planet with the same surface gravity as Earth (or near it), but with a different density. If you want to change the size but keep the same gravity, you need to mess with the density.

$$ r = {{g}\over{{{4\pi}\over{3}} * G * \rho}} $$

Where $ r $ is the radius in meters, g is Earth gravity (9.8 m/s), $G$ is the gravitational constant (6.67384E-11), and $\rho$ is the density of your planet in kilograms per cubic meter. I derived this equation from the surface gravity equation.

You can check this by entering earth's density in kg per cubic meter: 5510 kg/m^3.

$$ r = {{9.8}\over{{{4\pi}\over{3}} * 6.67384 * 10^{-11} * 5510 }} = 6362240 m = 6,362km $$

Check.

So, you can start looking up densities for various materials or mixtures and finding out how large your planet would be with a surface gravity the same as Earth.

For instance I'll check the radius for a planet made of platinum. The density of platinum is 21.09 grams per cubic centimeter. Convert that to kilograms per cubic meter: 21,090 kg/m^3.

Now, plug it into the equation and you'll get a radius of 1,662 km for a planet of solid platinum. That's a little smaller than our moon.

It's possible to get a planet this small with Earth gravity but, intuitively, this is not at all likely.

Atmosphere and Climate

As I'm sure someone would point out if I didn't mention it, these are a lot more things than gravity needed to get an Earth like planet.

The planet can't rotate too quickly. It also needs a magnetic field to protect from solar wind. So your planet can't be made of solid platinum. But you can mix in some different materials and include them in the density measurement by ratios of their mass in your planet.

Assuming you start with an atmosphere and the various requirements to hang on to it. You're well on your way to a habitable planet.

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  • $\begingroup$ Your rotation link says nothing about rotation, but about gravity being able to hold onto lightweight gases. $\endgroup$ – user3082 Feb 9 '15 at 7:49
  • $\begingroup$ @user3082 You stopped reading after the first paragraph. Try again. $\endgroup$ – Samuel Feb 9 '15 at 15:06
  • $\begingroup$ It also depends upon how long you need it inhabitable. Mars should have been capable of supporting some types of terrestrial life during its youth but can't now. Is millions of year enough, a billion, two? $\endgroup$ – Jim2B Mar 24 '15 at 2:48
  • $\begingroup$ What would be the escape velocity of such a small dense world? The planet would need a thin silicate mantle to support life, the planet would be pretty unfavorable to life if the ground was just solid platinum $\endgroup$ – Stephanie Mar 18 '16 at 5:50
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The planet will need sufficient gravity to retain oxygen and water. Technically less than Earth normal would be sufficient, but the size of the planet also has an effect. Annoyngly smaller planets are worse at retaining atmosphere, so we can start by assuming 1G will be needed. The actual physics is naturally more complex, but the sad fact is that it is too complex to model. My understanding is that due to only having one habitable planet to study much of what you read about this topic is unproven.

The ratio the planet diameter can be decrease while retaining the same gravity is the inverse of the ratio density can be increased.

Unfortunately, the Earth is already pretty dense. No natural process creating significantly denser planets is known. I think 10% increase of density would be plausible, but that gives nowhere near the level of decrease in size you want.

So you'll need to forget having the same gravity and find a loop hole ...

The obvious one is that since the colonists have only been on the planet for a short time, the atmosphere only needs to be stable for a short time. The planet would be losing volatiles rapidly, but a high level of volcanism would be replenishing them just as fast. Some of the volatiles could have been gained relatively recently from comet and asteroid impacts. Such heavy bombardment would also have heated and fractured the planets crust enough, to trigger release of other volatiles from there.

Mars used to have such an atmosphere and Mars has roughly half the Earth diameter and 30% surface area. So it should be possible for the halfling planet to be habitable for a few million years. Additionally, heavier elements do not naturally concentrate near the surface. This means that valuable minerals are brought by asteroid impacts. The halfling planet would probably be rich in valuable minerals due to the bombardment being relatively recent and no process having yet allowed them to sink deeper. (The planet would probably be too small for plate tectonics.)

Unfortunately, this atmosphere would not have free oxygen. So your colonists will either need some simple terraforming (introduce photosynthetic life and wait) or somebody or something else will have already introduced such life to the planet. This would mean either another life bearing planet in the same system or a visit from aliens a long time ago.

Alternately, you could simply have an Earth sized planet that has less habitable land area available in the form of a single, small continent. This would emulate all the effects of "smaller, but same gravity" planet, but without any speculative science. Really depends on why you want a smaller planet.

An ocean world with a single continent with habitable coastal areas and a central desert would have restricted space for the colony to grow, but not to the point people would be pushed to building floating arcologies or vast scale desert irrigation projects. Alternately, a planet without plate tectonics might not have real continents at all. All land would be from large igneous provinces. Why would this be a good thing? A quote from the linked article might tell the answer:

The study of LIPs has economic implications. Some workers associate them with trapped hydrocarbons. They are associated with economic concentrations of copper–nickel and iron. They are also associated with formation of major mineral provinces including Platinum-Group Element (PGE) Deposits, and in the Silicic LIPs, silver and gold deposits. Titanium and vanadium deposits are also found in association with LIPs.

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  • $\begingroup$ A big part of the question is, how long do you need the planet to retain human life? Really small planets may hold their atmosphere for some hundred thousand years, which si usually too short for life to evolve. But if you just bring plants/animals and everything with you at just the right time, it might work! $\endgroup$ – Falco Feb 9 '15 at 10:21
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    $\begingroup$ @Falco Yes, this is actually kind of interesting idea that is skipped in SciFi. In realistic interstellar civilization with terraforming, most planets might not really be habitable in the long term. Just for a few dozens of millennia. Such planets might be interesting settings for those lost technology stories set millennia after initial terraforming. Precursors might have left the galaxy full of such planets. $\endgroup$ – Ville Niemi Feb 9 '15 at 10:27
  • $\begingroup$ "Alternately, you could simply have an Earth sized planet that has less habitable land area available in the form of a single, small continent." <= this is a good point. I wanted to build a world with only one really major city on it, but a well-established one. The problem is that if we were to colonize a world I imagine we'd start to spread out pretty quickly. Thus some constraints on space are needed. I like the idea of a mostly ocean world with maybe an Australia-sized landmass on it, maybe a few other island groups, and ocean otherwise. $\endgroup$ – akaddoura Feb 9 '15 at 23:31
  • $\begingroup$ @akaddoura Added more on that to the answer. $\endgroup$ – Ville Niemi Feb 10 '15 at 6:35
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This question was looked at in a nice, very simple and readable paper by Williams, Kasting & Wade in 1997 (see here). That paper focuses on moons of gas giant planets but the idea is the same, and they address the question of what exactly is needed in terms of planet mass for life.

The trick is, we don't know exactly what is on the checklist for life. Williams et al considered 2 key things: 1) the planet must have enough gravity to hold onto an atmosphere, and 2) the planet must have enough long-lived radionuclides in its interior to provide a heat source capable of maintaining plate tectonics.

They came up with a lower limit for habitability of about Mars mass (0.1 Earth masses). The key limiting factor is the internal heat source, and there is some uncertainty there. I re-did their calculation a few years later with slightly more conservative assumptions and ended up with about 1/3 of an Earth mass as a lower limit.

Here is a summary of the different factors: https://planetplanet.net/2014/05/20/building-the-ultimate-solar-system-part-2-choosing-the-right-planets/

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One trick is getting the right atmospheric density. Too thin, and it's tough to breath. Too thick, and you don't have enough light at the bottom of the atmosphere to energize an ecology.

Planets lose atmosphere. There is an energy distribution among gas molecules at any given temperature. At the top of the atmosphere a few of them are faster than escape velocity from that point.

Average molecular speed is temperature dependent. A hotter sun, or being closer to the sun means faster escape.

Escape velocity is dependent on both mass and distance from the centre of the planet. Heavier planet = slower escape. Larger planet = slower escape.

This last one may be counter intuitive: If you have a larger planet that is less dense, but that still has a 1g surface gravity, the escape velocity is considerably higher.

A strong magnetic field helps keep an atmosphere. Many of the molecules in the upper atmosphere are ionized. An ion can't travel in a straight line in a magnetic field, but instead will spiral around the magnetic field lines. Since the field is embedded in the earth at either end the ion eventually hits the atmosphere again. (Ok, it's messier than that. There's a convergence of field lines at the poles. This acts as a mirror for slow ions. So they bounce back and forth between north and south poles.)

So why does Venus with essentially the same mass and diameter as Earth have so much atmosphere. It's hotter. It doesn't have much of a magnetic field. It should lose atmosphere. Good question. My suspicion is that it's the lack of oceans. No oceans = no processes that turn CO2 into carbonate rocks.

Mars with a strong magnetic field might hold an atmosphere for a long time.

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