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Field of a spherical shell
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Zero inside, like a point mass outside.
Outside a uniform shell the field is as if all mass were at the centre; inside it is exactly zero. Newton proved this by integration.
There's no net gravity inside a hollow planet of uniform shell.
Applies to spherically symmetric shells.
In more detail
Newton showed that a uniform spherical shell attracts external objects as if all its mass were at its centre. Inside the shell, the net gravitational field is zero.
Real-world uses
- Models of planets and stars use shell theorems to simplify calculations.
- Electrostatics has the same result for charged shells.
- Physicists use the shell theorem to show that the Earth's gravity outside its surface is the same as if all its mass were at the centre.
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Frequently asked questions
What is the field inside a shell?
Zero, because the forces from all parts of the shell cancel.
Does it hold for non-spherical shells?
No. The result requires spherical symmetry.
Why is gravity zero inside a hollow shell?
The pull from each part of the shell cancels out, so no net force acts on a mass inside the shell.
Related topics in Gravitation & Orbits
Gravitational field · Gravitational potential energy · Gravitational potential · Field inside a uniform sphere · Escape velocity · Escape velocity of Earth