The thread title is the question. Many extrasolar Rocky planets are being discovered, but few, if any, are the size of Earth, most seem to be twice to several times the size of our home planet. Under what conditions would it be possible to have a super-Earth with 1g?
All it’d need to have would be the same density as Earth, would it not?
You need an earth that is less dense.
I don’t have time to crunch any numbers, but one simple example would be to envision an Earth that is entirely water, which is about 1/7th density of iron. That water-planet would have to be much larger to have the same weight as ours, but that size means the surface is farther away from the center and therefore gravity would be lower at the surface. Therefore, to get 1 g with water, you’d need a planet that is not only larger, but with higher total mass.
For a spherical planet of uniform density, gravitational acceleration at the surface is proportional to both the density and to the radius; so if we want the gravitational acceleration at the surface to be some particular fixed value, then density is inversely proportional to the radius. The density of Earth is about 5.5 g/cm[sup]3[/sup], so if you wanted a super-Earth with twice the radius of Earth to have 1 g gravity, it’d have to have an average density of about 2.75 g/cm[sup]3[/sup] — which isn’t too far from the density of aluminum or of most sedimentary rocks.
So it’s not prima facie unreasonable, at least. The problem, I suspect, is that if you built a super-Earth out of such materials, the core temperatures and pressures would be far too high to the material at the center to maintain enough strength to support its own weight. The planet would then compress itself into a denser configuration, with higher surface gravity.
What about a planet with a really fast rotation? We could live near the equator.
Nope. Gravity is directly proportional to its mass and inversely proportional to the square of the radius. Since mass increases by the cube of the radius, we would have gravity proportional to r[sup]3/2[/sup].
Because of this, the equation would be (r[sub]1[/sub])[sup]3/2[/sup] x (d[sub]1[/sub]) = (r[sub]2[/sub])[sup]3/2[/sup] x (d[sub]2[/sub])
or
d[sub]2[/sub] = (r[sub]1[/sub]/r[sub]2[/sub])[sup]3/2[/sup] x d[sub]1[/sub]
ETA: So a planet with twice the diameter would have a density just over 0.35X that of Earth to have the same gravity.
I think Mike S is right = gravity= GM/r[sup]2[/sup] = G4pi/3densityr[sup]3[/sup]/r[sup]2[/sup] = G4pi/3densityr (where G is the gravitational constant)
r[sup]3[/sup] / r[sup]2[/sup] = r, not r[sup]3/2[/sup]
Doh! :smack:
Now I feel like an idiot.
The effect for metal and rocky planets is not that significant. Earth’s inner core is only about 50% denser that iron/nickel at normal pressure.
[never mind, MikeS covered my point. Must teach myself to read before posting.]
Hal Clement thought of it, in “Mission of Gravity”:
By the way, the reason the planets being discovered isn’t necessarily that that there are more large planets, but because smaller (Earth-sized) ones are more difficult to detect. The planets are almost always identified by the “wobble” they exert on the star they orbit or the amount of light they obstruct when they pass between their star and the Earth. Planets the size/mass of Earth don’t make enough of an impact to be detected.
So if you’re asking to determine if there are “~1g” planets out there, the answer is probably, but we can’t really detect them yet. The fact that we’re only finding larger planets in no way limits the possibility of smaller ones - it’s just that we can only see the big ones.
I’m not sure precisely what the question being asked is, but our own Neptune has a surface gravity of about 1.14 g, along with a mass 17 times Earth’s and a diameter 3.8 times Earth’s. From Gravity on Neptune - Universe Today
Unfortunately, Neptune doesn’t really have a surface.
Good point. And I suspect the same will be true of any planet whose density is low enough to be supersized yet only 1 G.
Depends on how you define “supersized”, now doesn’t it? There are surely plausible planet materials less dense than the Earth’s, and any 1g planet made out of such materials would necessarily be larger (both in radius and in mass) than the Earth. As a thought experiment, suppose you had a big ball of ice. Make the ball bigger and bigger, and it’ll eventually reach 1g. Now, the density of such a world would almost certainly be higher than that of terrestrial ice, due to the extreme core pressure, but I’d be very surprised if it were as dense as iron. And the core of such a world might end up being liquid or who-knows-what state of matter, but the surface, which is under low pressure, should remain nice and solid.
More plausible would be a planet that was 100% rock instead of of iron.. Replace iron with silica .. it exists because the material hasn’t been through so many super nova ..
Along the same lines, is it possible to have a planet that is 100% (or reasonably close to 100%) liquid water? I’m imagining an Earth-sized glob of water floating in space.
I think the more interesting question is what sort of lifeforms are still possible under 3G / 5G / 10G assuming that the planet lies within the Goldilocks zone allowing liquid water and has all the other necessary ingredients for life.
Could invertebrates eventually evolve on a 10G planet or is there some physical limit that would prevent skeletons and muscles being sufficiently strong?