Center of Gravity in Non-Uniform Gravitational Field

Theorem

Let $B$ be a body in a gravitational field $\mathbf G$ which is non-uniform.

The forces on $B$ are reducible to:

$(1): \quad$ a single force $\mathbf F$

$(2): \quad$ a couple $C$ whose plane is perpendicular to the line of action of $\mathbf F$.

The line of action of $\mathbf F$ does not pass through some fixed point as $B$ rotates in $\mathbf G$ unless $C$ is zero.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): centre of gravity
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): centre of gravity