B How Would a Hollow Earth Structure Impact Gravity?

[Tris Fray Potter]

This is a question that has been bothering me, but I can't find an answer anywhere:
If I were to hollow out Earth so that the crust was the only mass, and Earth was to keep it's shape, how would this affect the outside gravity?

 

[Vanadium 50]

You'd be a lot lighter. Like 99% lighter.

 

[Student100]

This is a question that has been bothering me, but I can't find an answer anywhere:
If I were to hollow out Earth so that the crust was the only mass, and Earth was to keep it's shape, how would this affect the outside gravity?

If you turned Earth into a thin uniform spherical shell,
$$\vec {F}=-G\frac {M_sm_p} {r^2}\hat {r} $$
Still holds assuming your r is greater than the radius of the shell. You would still treat the shell as though all the mass is concentrated in the center. So what changes is the mass of the shell, and as a result your force of attraction becomes much smaller assuming the only difference is you've simply gutted the Earth.

If you were to take all of Earth's mass and compress it into a thin uniform shell, so that the masses remain equal, you wouldn't see much of a difference from this stand point. Although, you probably wouldn't want to live there anymore.

 

[Tris Fray Potter]

Thank-you!