There are several previous questions concerning concentric shells. I won't reference them here because this is different.
I understand that there is no gravitational effect inside a concentric shell*. But what about a non-concentric one?
I've looked online and found nothing. Maybe I'm just using the wrong search terms?
I'd like to have a cavity inside a small planet. Assuming perfect spheres and uniform density, is there a general equation for the gravitational field inside the cavity, taking into account:
- The radius of the solid sphere
- The radius of the hollow spherical cavity
- The offset between centres.
If no exact solution exists, is there an approximate formula that will let me play with the variables to get a rough idea of the effects?
In classical mechanics, the shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetrical body. This theorem has particular application to astronomy ... A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its centre. If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell.