Category Archives: seismology

Measuring the Speed of Gravity (Waves)

Newton’s equations give the speed of gravity as infinite. For example, in Cartesian coordinates, suppose a gravitating mass 2M is at the origin up until time t=0.  At that time, the mass splits into two masses of mass M, one going in the +x direction at speed v the other in the -x direction at speed v. For times greater than 0, the gravitational potential is given by the sum of the two gravitational potentials:

(1) \;\Phi(x,y,z,t) = \frac{GM}{\sqrt{x^2+y^2+(z-vt)^2}} + \frac{GM}{\sqrt{x^2+y^2+(z+vt)^2}}.

At any distance, the above depends on t so the gravitational potential (and it is easy to show the gravitational force) is instantaneously changed at all distances from the origin. The speed of gravity is therefore infinite in Newton’s theory.
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