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We learn and teach classical mechanics essentially as it was developed by Newton. The theory is more than 300 years old, but still useful for many purposes. However, even in contexts where it produces correct results, it has a flaw: it uses actions at a distance. In addition, it is not able to describe the transport and storage of energy in the gravitational field locally.

The general theory of relativity not only eliminated the actions at a distance of Newtonian mechanics, but also predicted phenomena which the Newtonian theory of gravitation could not explain. However, for solving many problems and for an introduction of gravitation in a standard lecture, general relativity is too complicated, mainly because of the tensor calculus.

To bridge the gap between these two theories we propose to use Heaviside’s theory of gravitoelectromagnetism. This theory has the same structure as Maxwell’s electromagnetism. It has the advantage that it does not describe forces as actions at a distance and that it allows to establish a local energy balance.

We discuss the limits of applicability of Heaviside’s theory. It turns out that besides the well-known condition low field/slow motion, another condition must be satisfied. The theory is only applicable to quasi-stationary processes. In particular, it cannot describe gravitational waves. Nevertheless, it is useful for teaching, because some major shortcomings of the Newtonian theory are avoided.

Mass is usually introduced as a measure of the inertia of a body. But what do we mean by inertia anyway? We introduce a measure of inertia. It turns out that for high, relativistic velocities neither the rest mass nor the relativistic mass fulfills the requirements for a meaningfully defined measure of inertia. But how are we going to talk about inertia in the physics lesson? How can we use students' everyday language and still arrive at a clear conceptualization? We will try to give an answer to these questions.