Inertial vs Gravitational Mass

What you're seeing: Test particles in a Kepler field \(\ddot{\boldsymbol{x}} = -\eta\, GM\, \boldsymbol{x}/r^3\), all launched from the same point with the same tangential velocity. The parameter \(\eta = m_g/m_I\) is the ratio of gravitational to inertial mass.

If the universality of free fall (UFF) holds, then \(\eta = 1\) for all matter and all particles follow the same orbit — regardless of their composition. Drag the slider to see what would happen if \(\eta \neq 1\): the orbits immediately diverge.

Experimental precision: No deviation has ever been observed.

Experiment	Year	Precision \(|\Delta\eta|\)
Newton (pendulum)	1687	< 10−3
Eötvös torsion balance	1922	< 10−9
Lunar laser ranging	1969–	< 10−13
MICROSCOPE satellite	2022	< 10−15