Why are Earth-size Planets candidate as habitable planets?

[ecastro]

I have read in a book that the reason Earth-size planets become candidates for habitable planets is because of their capability to hold an atmosphere; a planet smaller than Earth would have a thinner atmosphere and otherwise if it is larger. My question is, does this size matter because of its gravitational pull to maintain an atmosphere? Can't planets having the same gravitational pull as our Earth become habitable as well; like massive planets with a larger size, or less dense planets with a smaller radius?

 

[mfb]

Not every earth-sized planet is habitable, many are way too hot or to cold for example.
The capability to hold an atmosphere is mainly given by the escape velocity from the surface, the temperature and the interactions of the stellar wind with the magnetic field (if present).

If the mass of the planet is too small, gas molecules can get a velocity above the escape velocity randomly due to thermal motion, and escape.
Stellar winds can also "kick out" molecules if no magnetic field deflects them.

Mars is quite small, for example. It does not have a magnetic field and the escape velocity from the surface is lower, so gas molecules can escape easier. The result is the thin carbon dioxide atmosphere we observe today.
A planet with several times the mass of Earth can attract much more gas, and fewer molecules will escape its deeper gravity well. As a result, on average they should have a thicker atmosphere. And if they get too heavy, they can even become gas giants.

 

[ecastro]

If I have the mass and radius data of a planet and given that it is within the habitable zone of its star, and disregarding cosmic interactions, would it be more sensible that its habitability (atmosphere) depends on the planet's mass and radius, or depends on its escape velocity?

 

[Bandersnatch]

If I have the mass and radius data of a planet and given that it is within the habitable zone of its star, and disregarding cosmic interactions, would it be more sensible that its habitability (atmosphere) depends on the planet's mass and radius, or depends on its escape velocity?

Escape velocity at the surface is determined by mass and radius, so it's pretty much the same thing:
$V_e=\sqrt{\frac{2GM}{r}}$
See here:
http://en.wikipedia.org/wiki/Escape_velocity

That is, if you have a planet that is half as massive and half as large as Earth, it will have the same escape velocity and the same conditions for retaining an atmosphere.
Note that for a planet half as large to be only half as massive its density would have to be four times higher (because the volume of a sphere grows with the third power of the radius), and vice versa.
This means there's a limit on how small a planet can be for these purposes, as you can't just have planets with arbitrarily large densities. Similarly, if you make the planet too large, but retain the same escape velocity (so that it doesn't turn into a gas giant by holding onto too much volatiles), you're running a risk of lowering its density below what's feasible.

 

[mfb]

While we do not have enough data for a proper analysis, the more mass a rocky planet has the denser it should be on average (not including the atmosphere) as the core pressure will compress the material more for larger planets. It will be hard to find some planet significantly smaller than Earth with a density significantly higher - you would need a very large concentration of very heavy elements.

 

[ecastro]

Thank you! Another question came into mind. Could life arise from gaseous planets? Jupiter, for example, if it were to be in the habitable zone?

 

[mfb]

If you find an answer, publish it.
At least earth-like life looks unlikely, but with our single data point where life evolved it is hard to rule out anything.

 

[DaveC426913]

Thank you! Another question came into mind. Could life arise from gaseous planets? Jupiter, for example, if it were to be in the habitable zone?

'Could' is the operative word. We don't know. But we'd want to allow for possibility.

 

[ecastro]

Thank you very much for this discussion.

 

[marcus]

I have read in a book that the reason Earth-size planets become candidates for habitable planets is because of their capability to hold an atmosphere; ...

A planet or moon does not need atmosphere to be habitable. Plants, animals, humans could live in subsurface ice caverns with sealed-in breathable air and interconnecting ice tunnels. The key factor is a reliable electric power supply to supply light.

Surface habitation involves one-in-a-hundred lucky hits. Atmosphere can't be too hot or too cold, or be made of the wrong gases, or have too high a pressure, or too low. Surface gravity must be strong enough to hold atmosphere but not too strong, or you can't walk upright. Water has to be available (so many places are dry). Planets suitable for surface habitation are not common.

Ice balls with rock core and icy outer layers some hundred kilometers thick appear to be common. If humans want to establish settlements abroad they need to learn to live in subsurface ice habitats.

Some of these solar system iceballs are believed to have subsurface oceans.

The term "habitable zone" is potentially confusing. It really means SURFACE habitable zone, where there might exist a rare lucky planet that actually had surface water, and had an atmosphere the right temperature for the water to remain liquid on the surface, and a magnetic field to protect the atmosphere from erosion by solar wind etc. None of the ice-worlds shown here are in the solar system's "habitable zone" as conventionally defined even though some are believed to have sealed-in subsurface oceans.

 

[snorkack]

While we do not have enough data for a proper analysis, the more mass a rocky planet has the denser it should be on average (not including the atmosphere) as the core pressure will compress the material more for larger planets. It will be hard to find some planet significantly smaller than Earth with a density significantly higher - you would need a very large concentration of very heavy elements.

Not particularly hard. Mercury is almost as dense as Earth. And iron, like rock and any other substance, is compressible at the sizes of Earth.
How dense would a Mars-sized planet with composition of Mercury be?

 

[wabbit]

In addition to life on the surface or in subsurface caverns as mentionned above, (subsurface) oceans such as those on some of Jupiter's moons are speculated to provide a possible habitat for life. After all, life on Earth is thought to have appeared in its oceans, so the presence of liquid water might be more of a hint for the possibility of life than that of an atmosphere.

In fact my understanding is that liquid water, rather than an atmosphere, is one of the criteria (or even the primary one) used in defining the habitable zone.

 

[mfb]

Not particularly hard. Mercury is almost as dense as Earth. And iron, like rock and any other substance, is compressible at the sizes of Earth.
How dense would a Mars-sized planet with composition of Mercury be?

That's why I said "significantly higher". We see a compression effect for earth, but it is not so prominent yet. A different chemical composition like Mercury can give the same effect size.
How would a mercury-sized planet with twice its mass look like? Iron is not dense enough and elements with a density above 10g/cm^3 without pressure are rare.