# What if Earth's core was bigger than now?

What would happen if Earth's core got bigger? Could this result in stronger magnetic field and as a result stronger Van Allen Belt? What would this mean for space travel?

• How bigger? Over which period of time would this growth happen? Would it be simply expanding or would new matter be somehow added to it? These are important to determine the effects of the growth, but particularly here, sounds like it'd cause an increase in internal pressure, resulting in many volcanic eruptions worldwide, with a risk of the crust being ripped open in certain weaker points. Jun 1 '20 at 14:13
• Note it is already extremely difficult to escape Earth's gravitational well as things stand. So difficult that it was only achieved in the late 50's. Any significant increase in gravitation would make it impossible to leave Earth with chemical rockets. Jun 1 '20 at 16:12
• "Got bigger" or "were bigger"? Jun 1 '20 at 18:24
• If Earth's core got bigger. Jun 1 '20 at 18:41
• Are we talking adding millions of tons of mass, or infusing energy somehow to liquify more of the inside of the Earth? If mass, then what form and temperature? Or are we smashing a moon or something and reliquifying the whole thing? Jun 1 '20 at 21:30

## Yes, it would increase the magnetic field.

The strength of Earth's magnetic field in the outer core can be roughly estimated by$$^{\dagger}$$

$$B_{\text{core}}\sim\sqrt{\frac{\rho\Omega}{\sigma}}$$

where $$\rho$$ is density, $$\Omega$$ is rotational velocity and $$\sigma$$ is electrical conductivity. These are all material properties of the core, which would not change if the size of the core increased. However, note that this is the magnetic field at the edge of the core. With a larger core, this same field strength is reached further out from the center than in the case of a smaller core. As the field falls off as $$B(r)\propto r^{-3}$$, we therefore see that a larger core indeed yields a stronger magnetic field. Why? We can write $$B(r)=B_{\text{core}}\left(\frac{r}{R_{\text{core}}}\right)^{-3}\propto R_{\text{core}}^3$$ where $$R_{\text{core}}$$ is the radius of the outer core.

I can't say much about the van Allen belts - I haven't been able to find derivations of their size from first principles - but we can say some things about the characteristics of a planet with a larger core-to-mass ratio. First, data indicates that terrestrial planets have decreasing core-to-mass ratios with increasing distance from the Sun (Solomon 1979). This appears to be due to the heat required for chemical differentiation and therefore the formation of a particular internal structure. (An alternative route to having a large core is to simply have a giant impact strip off much of the outer layers.) Therefore, for Earth to have a substantially larger core, we could simply have it form closer to the Sun.

You could also make an argument that the importance plate tectonics would be different. If the core is larger but Earth's total size is the same, then the mantle must logically be smaller. This in turn means less radiogenic heating - the generation of energy from radioactive decay - which primarily takes place in Earth's mantle and crust (Dye 2012). If tectonic activity is strongly linked to this type of heat production, we could indeed see less tectonic activity over a given timescale.

Finally, surface gravity on Earth would increase. The density of the inner core is $$\sim$$12.5-13 grams per cubic centimeter and the density of the outer core is $$\sim$$10-12 grams per cubic centimeter.. Compare that to the mean density of Earth (roughly 5.5 grams per cubic centimeter) and the density of the mantle (3.3 to 5.7 grams per cubic centimeter). If the core is a larger fraction of the planet, the Earth's mass will increase and so will its surface gravity, as $$g\propto\rho R$$, with $$R$$ the radius of Earth..

$$^{\dagger}$$ The Wikipedia derivation is simpler, but see Chapter 4 of these notes for a more detailed description to satisfy the hard-science tag. Considering the electric current density $$\mathbf{J}$$ and magnetic field $$\mathbf{B}$$, we have the following expressions for the electric current density and then Lorentz force on a parcel moving at velocity $$\mathbf{v}$$, assuming the latter is equal to the Coriolis force on that same parcel:

$$\mathbf{J}=\sigma\mathbf{u}\times\mathbf{B},\quad -2\rho\mathbf{\Omega}\times\mathbf{u}=\mathbf{F}=\mathbf{J}\times\mathbf{B}$$

and so

$$J\approx\sigma uB,\quad JB\approx\rho\Omega u$$

and finally we get our expression for $$B$$ from above.

• What would happen to the Van Allen's belt? Jun 1 '20 at 16:11
• @RoghanArun I'm still working on that. Jun 1 '20 at 17:50
• Also, would there be consequences? Can we assume a larger core means greater mass and therefore higher gravity? Would a larger core result in greater or less tectonic activity (aka, volcanoes)? Jun 1 '20 at 22:19
• @JBH I've made an edit - TL;DR tectonic processes (and mantle convection!) are complicated, but it seems like we could see less tectonic activity. Jun 1 '20 at 22:41
• @RoghanArun Indeed, the Earth would have a greater mean density and therefore would have a higher surface gravity. Jun 2 '20 at 1:00

nothing much of anything would change for spaceflight. SO long as the mass of the planet stays the same, and it retains the same atmospheric pressure, there will be no changed in the difficulty of reaching orbit.

Trappist 1E is said to have a bigger core than Earth, and in space engine, i had no trouble reaching orbit. Albeit a simulation, it clearly states my point that nothing would change for any spacecraft.