Can a planet have 10x Earth mass, 4x Earth gravity and support intelligent life?

In the Mass Effect series there's a terrestrial planet called Dekuuna with 10 times the mass of Earth, a surface gravity of 4G and a native intelligent race. I was just wondering if it was possible for a planet like that to exist in reality, and if yes, what are some factors that might lead to its formation assuming it formed around a Sun like star?

• To a first order approximation: Volume grows by 8x when the radius grows by 2x, and (for large differences in mass in objects) gravitational attraction grows linearly with the larger mass. So it sounds like it could very well be plausible, if the planet is composed of slightly lighter materials than Earth. – a CVn Jun 20 '16 at 20:26
• He said the planet is not at G, but at 4G. – knowads Jun 20 '16 at 21:59
• How dense would the atmosphere be on a 4G planet? – DrBob Jun 21 '16 at 9:21

If $R$ is the planet's radius and $\rho$ is the planet's average density, then its surface gravity is $\propto \rho R$ and its mass is $\propto \rho R^3$.

Let's measure in units where the Earth's radius and average density are both 1. Then for Dekuuna we have $\rho R=4$ and $\rho R^3=10$. Therefore we get \begin{align} R &= \sqrt{\frac{\rho R^3}{\rho R}} = \sqrt{\frac{10}{4}} \approx 1.6\\ \rho &= \sqrt{\frac{(\rho R)^3}{\rho R^3}} = \sqrt{\frac{64}{10}} \approx 2.5 \end{align} So that planet would have a radius of about 1.6 times the Earth's radius and an average density of about 2.5 times the Earth's average density. The radius is definitely possible, and I think the density should be, too. To begin with, the higher radius and mass would already cause an increased density, although that alone will not get a factor 2.5. But then, the planet could have a relatively bigger core, and it might have more heavy elements in its core.

I also think 4 times earth gravity should not preclude the evolution of intelligent life.

I'm going to work off of celtschk's excellent answer, which correctly comes up with a radius of $\sim1.6 R_{\oplus}$ and a density of $\sim2.5\rho_{\oplus}$, where $_{\oplus}$ denotes Earth. If we look at the mass-radius curves of Mocquet et al. (2014), we see that the planet lies very close to the line for pure iron planets:

Some fun facts about iron planets:

• They're essentially just cores of terrestrial planets.
• They likely cannot hold water.
• They have no tectonic activity or magnetic field.
• They may be close to their parent star, meaning surface temperatures will be extremely high.

This doesn't seem like a very pleasant place for life.

The earlier answers have done this better, but I found a mass/gravity/distance-from-center calculator at http://www.ajdesigner.com/phpgravity/gravity_acceleration_equation_planet_mass.php#ajscroll and ran some rough numbers through it. After a little trial and error, it looks as though a planet 10x as massive as Earth would have as surface gravity of 4G if its radius was approximately 10,106 km. That would make it about 2.55 (again, rough math) times as dense as Earth, at about 13.85 grams per cubic centimeter. That falls between the elements Americium (13.67 g/cc) and Berkelium (14.78 g/cc). Both of those are radioactive with relatively short half-lives - not sure if they degrade into something just as dense? My guess is that such a planet couldn't exist in reality, unless it was created and maintained by some highly tech-advanced race. Even so, I would think that the probable radioactivity of the thing would preclude the existence of intelligent life as we know it.