Could there be a planet bigger than Earth, but with less gravity?

Bigger planets don't always have greater masses. Remember, mass and volume are related by $$M=\rho \frac{4}{3} \pi R^3$$ where $\rho$ is density. Make $\rho$ small enough and the gravity and be as weak as you like. So the answer to the title question is a firm "yes." I did some playing around with this based on mass-radius relations by Seager et al. 2008 and created a modified plot of mass and radius based on several different compositions:

The blue shaded region is the allowed subset of parameter space with planets satisfying $R>R_{\oplus}$ that have surface gravities less than Earth's - the properties you want. Very few terrestrial planets occupy this area, and few are primarily silicates, like Earth. Your planet is likely to have significant quantities of water and may be an ocean world.

with weaker gravity, and a magnetic field strong enough so that people don't need extra protection from sun radiation?

This is trickier. According to the dynamo theory, the magnetic field is governed by the induction equation $$\frac{\partial \mathbf{B}}{\partial t}=\eta\nabla^2\mathbf{B}+\nabla \times (\mathbf{u} \times \mathbf{B})$$ where $\mathbf{B}$ is the magnetic field, $\mathbf{u}$ is velocity, $t$ is time and $\eta=1/\sigma\mu$, where $\sigma$ is the electrical conductivity and $\mu$ is the permeability. Note that nowhere in there is a term involving the radius of the core. In the nonlinear theory, density does come into it. But that's the density of the material in the core. The planet could have a large mantle that contributes significantly to its radius. So the magnetic field can be any (reasonable) strength you want; it might not be impacted by planetary radius.

The tricky thing is that while the magnetic field protects us from the solar wind, we also have to worry about UV radiation. That's why the ozone layer is our saving grace, so to speak, and why its depletion by chlorofluorocarbons is such a big deal. I bring this up because a planet with certain characteristics (i.e. much bigger and yet less massive) will have a weaker gravitational pull on its atmosphere (with the strength depending on radius and mass).

Lighter gases escape easier from a given planet than do heavy gases. That's why the Earth lost any primordial hydrogen and helium envelope it might have had. Make this planet too big and you risk losing ozone. Sure, the planet would have to be pretty big (while staying at the same mass), but it could happen. A stronger magnetic field might solve this, but its contributions might not be too great.

posted almost 10 years ago

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