How Does Mining Affect the Gravity of a Hollowed-Out Planet?

[Khatti]

I'm working on a planet that is earth-sized, but has been essentially a dead stone for millions of years: no volcanic activity, the core has completely cooled down, the atmosphere has long since drifted off. In turn it has been mined for so long that a sixth of its mass has been dug up and shipped off. Much of that mass has actually come from the core. Does anyone have any thoughts how hollowing out an earth-sized planet would effect its gravity?

 

[jfizzix]

Thanks to Gauss's law...

Assuming these tunnels are more or less evenly dispersed throughout the planet, and assuming that the planet is more or less uniformly dense, then the force due to gravity is proportional to the radial distance from the core.

If the core is hollowed out, but the the rest of the planet is more or less still radially symmetric, then throughout the hollow core, the net gravitational force will be zero, and you'll be able to float throughout the hollowed core (assuming the mass of air in the core is negligible).

 

[greswd]

I'm working on a planet that is earth-sized, but has been essentially a dead stone for millions of years: no volcanic activity, the core has completely cooled down, the atmosphere has long since drifted off. In turn it has been mined for so long that a sixth of its mass has been dug up and shipped off. Much of that mass has actually come from the core. Does anyone have any thoughts how hollowing out an earth-sized planet would effect its gravity?

simple, since a sixth of the mass has been removed, and from the core, the gravity at the surface will be reduced by a sixth.

 

[member 656954]

It is highly unlikely that the cored planet would remain structurally intact, unless the coring is perfectly distributed as @jfizzix notes. But more likely, slight mass unbalances would cause it to collapse in parts, with obvious devastation to the surface as thousands of kms of depth subside. This is going to take some time, and will likely be in parts, not all at once. It will eventually be pretty much spherical, with some massive craters that remain because there is no continental shift to recycle the mantle and no air to erode the surface features.

It's gravity would decrease, obviously, but because the radius would as well, it might not be as straightforward as being exactly one sixth less as @greswd notes, but that's probably close enough.

 

[greswd]

It is highly unlikely that the cored planet would remain structurally intact, unless the coring is perfectly distributed as @jfizzix notes. But more likely, slight mass unbalances would cause it to collapse in parts, with obvious devastation to the surface as thousands of kms of depth subside. This is going to take some time, and will likely be in parts, not all at once. It will eventually be pretty much spherical, with some massive craters that remain because there is no continental shift to recycle the mantle and no air to erode the surface features.

It's gravity would decrease, obviously, but because the radius would as well, it might not be as straightforward as being exactly one sixth less as @greswd notes, but that's probably close enough.

yeah, it would actually shrink a lot, and the size would depend on the density profile, which itself is dependent on the internal pressure, which is dependent on the internal gravitational field, and which is dependent on the density profile!

it'll also depend on the strength of the planet's composition. Realistically a swiss-cheese planet would be super unlikely to be possible.