# Could a planet about 30% larger than earth but only 80% as dense still support a strong magnetosphere?

I've been trying to work out a few calculations for a planet I am working on and hit a bit of a roadblock. The planet in it's current state is 1.35x the size of Earth, but in order to get a density similar to that of Earth's so that it could support a stable magnetic field I made the density 20% more dense than that of Earth's and 3x as massive. This has come with a side effect of 60% higher gravity which isn't idea for the world I am trying to create, specifically the size of life. I am aiming to make gigantism more common, although more in line with Earth's prehistoric periods or the planet Pandora's megafauna, but 60% more gravity seems to prevent that from happening.

The other solution would be to make the planet 80% as dense as Earth, making it 2x as massive and only 8% more gravity than Earth's. The issue I am worrying about is the potential for a magnetic field strong enough to hold in the atmosphere and protect the planet from potential solar radiation. Would this be possible? A planet 30% larger and twice as massive as Earth to be 80% as dense and still have a dense core like Earths?

Yes, this wouldn't be a problem. The magnetic field at the outside of a planet's core very roughly scales like $$B_{\text{core}}\sim\sqrt{\frac{\rho\Omega}{\sigma}}$$ with $$\rho$$ the core density, $$\Omega$$ the rotational speed and $$\sigma$$ the core's electrical conductivity. The field should be a dipole, and a dipolar magnetic field falls off cubically, i.e. as $$B(r)\propto r^{-3}$$. Putting all of this together, we can estimate the magnetic field at a distance $$r$$ as $$B(r)\approx\sqrt{\frac{\rho\Omega}{\sigma}}\left(\frac{r}{R_c}\right)^{-3}$$ with $$R_c$$ the radius of the core. If the planet's radius is $$R$$, then the field at the surface is $$B_{\text{surf}}\approx\sqrt{\frac{\rho\Omega}{\sigma}}\left(\frac{R_c}{R}\right)^3$$ If we set $$\rho$$ to be 80% of Earth's core density and the radius of the planet to be 130% that of Earth while keeping everything else the same, I find that the surface magnetic field of the planet should be roughly 41% that of Earth's - not bad!
I think that counts as fairly strong, and if we want to bring it back up to Earth's strength, we could, say, simply increase $$\Omega$$ by a factor of about 6. That's quite a lot, but to be honest, we don't necessarily need the magnetic field to be as strong as Earth's is; we retain atmospheric gases fine enough as it is, and a decrease by a factor of 2 isn't awful. We could also make up for the drop in magnetic field in other ways:
• @PcMan Would you mind explaining your reasoning a bit more? A planet of $1.75M_{\oplus}$ and $1.3R_{\oplus}$ fits well with models of predominantly silicate or silicate planets with iron cores (Seager et al. 2007), assuming some water ice on the surface. – HDE 226868 May 31 at 13:56