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Field inside a uniform sphere
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Grows linearly with distance from the centre.
g ∝ rInside, only the mass within radius r counts: g(r) = GMr/R³, proportional to r. At the surface it matches GM/R².
Halfway to the centre: g is half.
This describes a uniform density; real planets differ.
In more detail
Inside a uniform solid sphere, the gravitational field grows linearly with distance from the centre, g = GMr/R³. Only the mass inside the radius contributes.
Real-world uses
- Estimating the field inside Earth as a simple model.
- Planetary interior models use this linear relation.
- Models of planetary interiors use the linear variation of gravity inside a uniform sphere to predict surface behaviour.
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Frequently asked questions
Why does the field decrease to zero at the centre?
Because the net pull from the surrounding mass cancels at the centre.
Is this consistent with the shell theorem?
Yes. The mass outside a given radius contributes nothing inside.
Is the Earth a uniform sphere?
No. Its density increases toward the core, so the real variation of gravity with depth differs from the uniform model.
Related topics in Gravitation & Orbits
Gravitational potential energy · Gravitational potential · Field of a spherical shell · Escape velocity · Escape velocity of Earth · Orbital velocity