Paul Ledoux developed a variational form of this statement to predict the pulsation period of a star. When this statement  was used to estimate the mass of the Coma cluster, it yielded a mass-to-light ratio that differed by over an order of  magnitude from that of our Sun and led Zwicky to propose the existence of dark matter. This statement is used to derive  the approximate relation between the size of a cluster and its velocity dispersion. One of Lagrange's identities reduces to it  when the time average of the second time derivative of the moment of inertia is zero. It can be derived by taking the (*)  spatial mom
Paul Ledoux developed a variational form of this statement to predict the pulsation period of a star. When this statement  was used to estimate the mass of the Coma cluster, it yielded a mass-to-light ratio that differed by over an order of  magnitude from that of our Sun and led Zwicky to propose the existence of dark matter. This statement is used to derive  the approximate relation between the size of a cluster and its velocity dispersion. One of Lagrange's identities reduces to it  when the time average of the second time derivative of the moment of inertia is zero. It can be derived by taking the (*)  spatial moments of the equations of motion; other derivations use a quantity defined as the sum, over all point particles, of the dot  product between momentum and position vectors of the point particles. For 10 points, name this theorem stating that twice the  time average of the total kinetic energy plus the time average of the total potential energy is zero.
Paul Ledoux developed a variational form of this statement to predict the pulsation period of a star.