# Could a planet half the radius of Earth with the same surface gravity exist? [duplicate]

I've worked out that I require double the density in order to achieve the same surface gravity as Earth, so what kind of composition would be required for this sort of planet to exist?

I'm planning to make it very wet and warm, with rainforests extending between latitudes of 45 to -45, and of course this planet will be inhabited by humans.

## marked as duplicate by a CVn, bilbo_pingouin, Aify, Frostfyre, VincentJun 22 '16 at 12:48

• I'll be the first to admit that the proposed duplicate is not an exact duplicate, but the calculations are the same and the answers already given to that question should be helpful. – a CVn Jun 22 '16 at 7:55
• If this isn't a duplicate, then you should edit this question to specify exactly which measure you want to halve. Radius, volume, surface area? (You already ruled out mass by mentioning it specifically.) – a CVn Jun 22 '16 at 7:56

So looking at an old physics textbook you can work out the gravitational acceleration on the surface of the Earth as g = GM/R^2, where the mass of the earth is M, radius R and G is your gravitational constant. The density of a sphere (I'll call this D as I can't get greek stuff to work here) (ignoring the oblate spheroid/geoid shape of a real planet) D = M/V and V = 4/3 Pi R^3.

If you combine those two equations you get g = G * D * 4/3 * Pi * R, So yeah, you do have to double the density since g is nicely linear in R and D, meaning if you halve R you'll have to double D to get the same g.

That's the average density over the whole planet, to get this kind of extra mass you could have a metal rich structure, maybe a little like Mercury See here. You'd need a very large metallic core relative to mantle size, maybe 150-180% the size of the one on earth, and an exceptionally thin crust.

The planets core, given it's small size will likely be solid as it will have cooled quite quickly after formation, so there won't be much of a magnetic field, so you'd get a lot of nasty solar radiation on it's surface if it's close enough to it's parent body to be tropical.

If you REALLY wanted it shielded by radiation you'd need more fissile material in it's core, which would mean it would have to form in an environment rich in supernova remnants, as that's likely the only place elements larger than iron can form. So the sky might be quite colourful at night.

You'd also have an interesting birth for this sort of planet, Mercury is thought to be the remnant of a larger planet whose surface and most if it's mantle was removed in a catastrophic collision early in it's history (see this post).

• I know these comments apparently aren't allowed, but I really have to say thankyou; this is the best answer I could've asked for. Would there be any consequence of having an exceptionally thin crust? Perhaps shallow oceans? – Andrew Recard Jun 22 '16 at 11:49
• :D Glad you liked it! I'm not really sure about the thin crust, I guess it would depend on how how and mobile the mantle was, I'm not a geologist so this is all conjecture based on a general understanding of physics, so take this with a big pinch of salt: If the mantle is hot you'd likely have quite a lot of geological activity, volcanoes, earthquakes, and supervolcanoes as a result of very active plate tectonics, which would actually cool the planet to the second scenario; A cool/cold mantle (so no magnetic field), there would be larger but much deeper quakes that happen rarely, like Mars. – David Blackman Jun 22 '16 at 12:32
• Would it be possible to shield such a planet by having a larger planet or moon perennially eclipse the sun, yet provide enough coronal illumunation /atmospheric lensing that the shielded body remained relatively warm? – Adam Wykes Jul 14 '16 at 19:34

You do not need to increase the mass of all. If we decrease radius 2 times with the same mass - 3.185·10^6 (6.37·10^6 - Earth radius), it's be (6.67 * 10^-11) * (5.98·10^24)/(3.185·10^6)^2 =~40 m/s^2 (~ 4g!!!)

So, if you want 1g, mass of your planet must be around 1.5 * 10^24 kg

• I just did some calculations and my planet still requires double the density (10.95g/cm^3 compared to Earth's 5.51) to achieve this mass in the new volume. (1.355*10^26cm^3 compared to Earth's 1.083*10^27cm^3). My question is how can I achieve this through the composition of the planet. – Andrew Recard Jun 22 '16 at 10:38
• Then, obviously, need more the heavy elements in the mantle and the core. For example, as if to replace the ice layers of Ganymede (~ 1/3 of the Earth's radius) to similar in composition to Earth's mantle. But this is more of chemistry or geology than space, if you need a more accurate calculation. Try to add a tag. – arnotrench Jun 22 '16 at 11:02
• Please look up how to use mathjax formatting. – JDługosz Jun 22 '16 at 11:28
• @arnotrench , welcome to the site, Great first answer (Hope to see more of you either here or on other SE sites) as JDlugosz said look how to do mathjax formatting, found here, meta.math.stackexchange.com/questions/5020/… – Mr.Burns Jun 23 '16 at 13:49