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Newton's shell theorem
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A spherically symmetric body attracts as if its mass were at its centre.
A spherically symmetric shell attracts external bodies as if its mass were at the centre and exerts no force inside. This allows planets to be treated as point masses.
Inside a hollow sphere you float freely.
The theorem needs spherical symmetry.
In more detail
Newton's shell theorem states that a uniform spherical shell attracts external masses as if all its mass were at the centre, and exerts no net force on masses inside it.
Real-world uses
- Planetary and stellar models use the shell theorem to simplify gravity calculations.
- Understanding why Earth's gravity acts as if its mass were at the centre.
- Engineers simplify planetary gravity models by treating a spherical planet as a point mass at its centre.
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Frequently asked questions
Does it apply to non-uniform shells?
No, the shells must be spherically symmetric.
Does it hold for atoms?
The same mathematics applies to electrostatic shells.
Does the shell theorem apply to a non-spherical body?
Not exactly. It needs spherical symmetry, so for irregular bodies such as asteroids a different model is needed.
Related topics in Gravitation & Orbits
Schwarzschild radius · Neutron stars and white dwarfs · Dark matter evidence · Gravitational self-energy · Inertial vs gravitational mass · Equivalence principle