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The well known general relativistic Lense-Thirring drag of the orbit of atest particle in the stationary field of a central slowly rotating body isgenerated, in the weak-field and slow-motion approximation of GeneralRelativity, by a gravitomagnetic Lorentz-like acceleration in the equations ofmotion of the test particle. In it the gravitomagnetic field is due to thecentral body's angular momentum supposed to be constant. In the context of thegravitational analogue of the Larmor theorem, such acceleration looks like aCoriolis inertial term in an accelerated frame. In this paper the effect of thevariation in time of the central body's angular momentum on the orbit of a testmass is considered. It can be shown that it is analogue to the inertialacceleration due to the time derivative of the angular velocity vector of anaccelerated frame. The possibility of detecting such effect in thegravitational field of the Earth with LAGEOS-like satellites is investigated.It turns out that the orbital effects are far too small to be measured.Comment: LaTex2e, 1 table, no figures, 7 page

A GRAVITOMAGNETIC EFFECT ON THE ORBIT OF A TEST BODY DUE TO THE EARTH'S VARIABLE ANGULAR MOMENTUM