The Virial Theorem University of Sheffield（维里定理谢菲尔德大学）.pdf

The Virial Theorem The (gravitational) Virial Theorem relates the gravitational potential energy of a system to the kinetic energy and provides an insight into the stability of the system. Its derivation is simple, if somewhat tedious. For a collection of N point masses the scalar moment of inertia about the origin is given by n n I = m r2 = m r2 k k k k k=1 k=1 where mk and rk are the mass and position of the kth particle. We can define a the scalar virial G as the time derivative of I n n dI drk 2G = = 2 m · r = 2 p · r k k k k dt dt k=1 k=1 and we can write the time derivative of the virial as n n dG = p · drk + dpk · r k k dt dt dt k=1 k=1 so n n dG drk drk = m · + F · r k k k dt