[ADDENDUM 11/26/12: It has been pointed out to me that two planets that have the same surface gravity won't necessarily have the same escape velocity, which appears to undermine my argument that it could be as easy to get off of a super-Earth as Earth itself. I've posted an expanded version of this blog entry accounting for that; you should read it instead of this posting.]
Earth-sized exoplanets have been very much in the news lately. Two days ago Space.com reported the discovery of HD 40307g, a rocky planet orbiting in its star’s habitable zone. It joins a list of six other planets thought to be in the same situation.
But it’s way bigger than Earth. The Habitable Exoplanet Catalog estimates its mass as 8.2 times that of Earth. Doesn’t that mean it would have a crushing gravity? Wouldn’t a petite 100-pound woman find herself weighing 820 pounds? Not very comfortable! It would make landings and launches on such planets all but impossible. And think of the buildings we’d have to build, squat and massive, never daring to go higher than a story or two.
That’s what I thought until Abel Méndez, who runs the Habitable Exoplanet Catalog, told me the formula for calculating a planet’s surface gravity: mass divided by the radius squared. That is, SG=M/R^2. If you express mass and radius in Earth units, you get surface gravity as multiples of Earth's.
Really!? Let’s try it with HD 40307g, using data from the Habitable Exoplanet Catalog. Mass, 8.2 Earths. Radius, 2.4 times Earth's. That gets you a surface gravity of 1.42 times Earth.
It seems counterintuitive, doesn’t it? How can a planet be so much more massive than Earth yet have only 1.42 times the gravity at the surface? The answer lies in the radius. The further you are from the planet’s center, the less its gravity pulls at you. Another way of putting it is that the greater the planet’s radius is for its mass, the less dense it is.
Let’s test that. Jupiter has 317.8 times the mass of Earth. That’s a lot. Yet its radius is also 11.2 times larger. Do the math and you get a surface gravity of “only” 2.53 times that of Earth. What that tells you is that Jupiter is much less dense than Earth, which makes sense given that it’s mostly hydrogen and helium. Its mass is neutered, so to speak, by its large radius.
So it’s all about the radius. Oddly enough, all of the seven known potentially habitable exoplanets have nearly the same surface gravity, if the estimates of their mass and radius are correct. Take a look:
Name: Mass, Radius, Surface Gravity
Gliese 581g: 2.6, 1.4, 1.33
Gliese 581d: 6.9, 2.2, 1.43
Gliese 667Cc: 4.9, 1.9, 1.36
Kepler 22b: 6.4, 2.1, 1.45
HD40307g: 8.2, 2.4, 1.42
HD85512b: 4.0, 1.7, 1.38
Gliese 163c: 8.0, 2.4, 1.39
Fictional Planet: 8.0, 2.83, 1.00
(All figures are expressed as multiples of Earth units. For example, Gliese 581g has 2.6 times Earth’s mass and 1.4 times its radius, for a gravity 1.33 times that of ours. Source: Habitable Exoplanet Encyclopedia. Most of the masses and radii are marked as estimates.)
You can see that except for Fictional Planet, which I’ll get to in a moment, they all have pretty much the same surface gravity despite huge differences in mass. Gliese 581g, with a mass 2.6 times that of Earth’s, has a surface gravity essentially the same as Gliese 667Cc’s, which has 4.9 times the mass of Earth. In fact, if you round the figures off to one decimal, they all have about 1.4 Earth gravities.
It seems very curious that they all have such similar surface gravities. I have no idea why. Perhaps it’s an artifact of what our instruments can detect with current technology.
It’s cheering that these planets aren’t absolutely crushing, but still, they wouldn’t be easy for Earth visitors. On Earth I weigh 122 pounds (yes, I’m always looking up at things.) On HD 40307g, I’d weigh 174 pounds. That would be just terrible for my back. Can you imagine trying to sleep comfortably with that much extra weight? I can’t.
But it’s amazingly easy to imagine a super-Earth with a comfortable gravity. If a planet had eight Earth masses and 2.83 times the radius, its surface gravity would be exactly 1g. This is the “Fictional Planet” at the bottom of the table.
Fictional Planet would be huge by Earth standards, with a circumference of 70,400 miles and an area eight times larger. Yet the surface gravity would be the same as Earth's. We could land and take off with exactly the same technology we use here, assuming the atmosphere is similar.
Think about that. On a planet eight times the area of ours, a single continent could have the entire surface area of Earth. Imagine how much more room and resources an emerging civilization would have. More land, more water, more vegetation, more fossil fuels.
In fact, if Fictional Planet’s radius was a bit larger, 3 times that of earth, its surface gravity would be only .89g, making space travel that much easier. Such a planet might have a civilization that would prosper and escape into space much more easily than ours has.
That would seem to sharpen the Fermi paradox. If the galaxy has plenty of light super-Earths in habitable zones, then you really have to wonder where everyone is.
Perhaps there’s geological reasons why such planets are unlikely. Maybe 1-gravity super-Earths would have too few heavy metals to sustain a civilization. Or maybe they couldn’t have the plate tectonics to stabilize an atmosphere and biosphere for long enough for complex life to arise.
But still, I feel cheered. We have only found seven super-Earths so far. It may not be long before we find one that has a gravity like ours. And it might be a super super-Earth.