A hydraulic energy flow within the moving Earth

We consider the Earth moving through empty space at 30 km s$^{−1}$ (in the Sun's frame of reference). Associated with this motion is a convective flow of kinetic and internal energy. Since there is high pressure inside the Earth, and since the Earth is moving, there is yet another 'hydraulic' energy flow. This latter is what this article is about. Although this energy flow is huge, it is not addressed in the textbooks. The reason is that for the explanation one needs a concept which is not introduced in traditional presentations of classical gravitation: the gravitomagnetic field. The corresponding theory, gravitoelectromagnetism, was formulated in 1893 by Heaviside in analogy to Maxwell's theory of electromagnetism. We discuss the question of what are the sources and sinks of this hydraulic, non-convective energy flow. To answer the question, we need to study the energy flow density distribution within the gravitational field. In doing so, we will make some interesting observations. The energy flow within the field is twice as large as it should be to transfer the field energy from one side of the Earth to the other. The excess flow goes back through the matter of the Earth. ... mehrSince our readers may not be familiar with Heaviside's theory, we first treat the electromagnetic analogue of our problem and then translate the results to the gravitational situation.