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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?

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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:

  • Increasing the distance from the star to decrease the impact of the stellar wind - or simply reduce the strength of the stellar wind, period.
  • Keep the surface gravity a bit higher, as you mentioned. That should make atmospheric escape just a bit harder.
  • Lowering the temperature might also work - it reduces the mean kinetic energy of air molecules, which also makes it harder for them to be lost to space.
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  • $\begingroup$ Is there room to move with electrical conductivity or is Earth already maximally conductive? $\endgroup$
    – Willk
    May 31, 2021 at 1:15
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    $\begingroup$ @Willk There likely is, but I don't know enough to say for sure. But given that we don't have to change the other key parameters much to keep the field in the range we need, and that changing conductivity dramatically might require some serious compositional changes, I'm inclined to stay away from that option. $\endgroup$
    – HDE 226868 ♦
    May 31, 2021 at 1:16
  • $\begingroup$ 30% larger and 0.8 density, means a severe shortage of iron and nickel in the core. The core would need to be something like Earth's mantle (mostly silicon, oxygen and magnesium), except even a bit less dense than that. Maybe a bit more magnesium and less silicon? Problem is, the resultant molten mess is not very magnetic. $\endgroup$
    – PcMan
    May 31, 2021 at 13:45
  • $\begingroup$ @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. $\endgroup$
    – HDE 226868 ♦
    May 31, 2021 at 13:56
  • $\begingroup$ @HDE226868 um, no it doesn't? It puts it between the "5% water ice, a 52.5% silicate shell and a 22.5% ironcore" and the "45% water ice, a 48.5% silicate shell and a 6.5% iron core" datasets. Which is a lot of ice, enough to make a planet an uninhabitable iceworld. One without significant magnetic field, due to the emasculated little core. 6.5% iron core vs. Earth's 32.5%. That is one huge difference.(actually Earth is a good bit past that 32.5% line, into heavier territory) $\endgroup$
    – PcMan
    May 31, 2021 at 14:30

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