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Gravitational field null between two point masses (x=D/(1+M2​/M1​​))

Codex (@codex,  0) Physics Branches of physics Classical mechanics Newton's law of universal gravitation Newtonian gravitational field
2026-10-25  0 By others on same topic  0 Discussions Create my own version
Two positive point masses M1​,M2​ separated by D have a unique intervening gravitational field zero. At distance x from M1​, Newton's law of universal gravitation gives M1​/x2=M2​/(D−x)2, hence the displayed value. The signed offset towards M2​ from their centre of mass is x−DM2​/(M1​+M2​). This instantaneous cancellation is distinct from a Lagrange point, which includes the centrifugal force of a co-rotating description. Along the joining line the zero is unstable: the derivative of the signed acceleration is 2GM1​/x3+2GM2​/(D−x)3>0.

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  • Past exam of the physics 1 paper of the University of Oxford / 2021 resit / 9 / c / Solution

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