# Gravity of a Super-Earth

So, I created a planet that has a civilization that is beyond advanced.

The planet's radius is 10x the radius of Earth, and is has the same density as Earth. What issues would I have with the gravity?

• – slobodan.blazeski Dec 2 '16 at 0:16
• For the record, $10R_{\oplus}$ is way too big for a super-Earth. Try maybe $2R_{\oplus}$. – HDE 226868 Dec 2 '16 at 0:18
• So, basically, yeah. i need it to be in the same atmospheric sense, but about... a few times more gravitational push. I want it to be so, that aliens that are accustomed to planets with lesser or somewhat equal gravity don't get accustomed so easy. if that's possible. – JakeRGlezII Dec 2 '16 at 0:23

The gravity would be 10 times larger than Earth's gravity. Since mass grows by the cube and gravity falls by the square your planet would have 1000 Earth masses and surface gravity of 10g, assuming they have same density. And since your planet is very large it's uncompressed density must be much lower than Earth density.

I hope that you didn't plan to have humans there.

If you want realism take a look at The Trouble with Terrestrials and Mass-Radius Relationships for solid exoplanets:

In general you can't have more than 1.6 Earth radius if you want Earth like planet. Planets larger than 1.6 tend to keep their Hydrogen and become gas giants, sort of Mini-Neptunes. Though Universe is large and there might be exceptions

If you want more handwavium you can use Chthonian Planet that somehow got it's atmosphere stripped and after due to some collision moved back into habitable zone.

Whatever you decide to use 10g is way too much gravity.

• No, I planned on having an alien race that created humans in their own image, taking an ideology of religion and pooping on it, so much. They're a semi-warrior/semi-passifist race, that literally advances by the day. So, yeah, I did not plan on having humans on the planet. – JakeRGlezII Dec 2 '16 at 0:19
• I really doubt any animal could survive under such gravity, you'll need extreme energy to expend for motion. Did you plan your aliens to look like a snakes or centipedes at best? – slobodan.blazeski Dec 2 '16 at 0:27
• (Before i respond, I'd like to say i wasn't trying to be sarcastic before) – JakeRGlezII Dec 2 '16 at 0:28
• No, they're meant to look human-like. with Humans having taken the same 'evolutionary' route as these beings. They are a Genesis Race. A race at the beginning of the universe. I have an expanded universe & it's like very... very large & whatnot, so... you know, a Centipede-like race woudn't be a bad idea. – JakeRGlezII Dec 2 '16 at 0:30
• It's your story you can make them anyway you like, but 10g is way too much. If you want something realistic I wouldn't go more then 1.6 Earth radii. No way that human like backbone could take anything like 10g, not even if it's made of carbon nanotubes. Check what kind of genetic engineering is needed for 3g worldbuilding.stackexchange.com/questions/55624/… anything more and your race should resemble something flat without legs. Assuming you want realism – slobodan.blazeski Dec 2 '16 at 0:33

# How to create a world with just the right surface gravity

Surface gravity $$\hat{g}$$ is a function of the mass $$M$$ and radius $$r$$ of the planet:

$$\hat{g} = \frac{G\cdot M}{r^2},$$

where $$G$$ is the universal gravitation constant $$6.67\times10^{-11}\,\frac{\text{N}\cdot\text{m}^2}{\text{kg}^2}$$. If you assume your planet is in hydrostatic equilibrium (a good assumption for any planet with noticeable surface gravity), then mass is in turn a function of radius and density $$\rho$$:

$$M = \rho\frac{4}{3}\pi r^3.$$

Put these together and you get:

$$\hat{g} = \frac{4}{3}\pi G\rho r.$$

Proof. The radius of earth is 6371 km; the density is 5515 kg/m$$^3$$.

$$\hat{g}_{earth} = \frac{4}{3}\pi \left(6.67\times10^{-11}\,\frac{\text{N}\cdot\text{m}^2}{\text{kg}^2}\right) \left(5515 \frac{\text{kg}}{\text{m}^3}\right) \left(6371000 \text{m}\right) = 9.81 \frac{\text{m}}{\text{s}^2}.$$

Surface gravity scales linearly with radius and density. If you double your radius, but want surface gravity to stay the same, you must halve the density of your planet.

Example. If Earth had the density of the moon (3348 kg/m$$^3$$), then its density would be 0.607 of earth's, so its radius would have to change by 1/0.607 = 1.65 to give the same surface gravity. The new radius of earth would be 10500 km.

Size and Density Reference. From Wikipedia, here is a chart with both size and density for many solar system objects. You can read about what these objects are made of (iron, rocks, ice, hydrogen, etc) to find out what a reasonable density would be. Use a spreadsheet, plug in the equation above, and you can calculate surface gravity for all sorts of fantastical worlds.