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Figure 89 d tries to support our imagination a little. The various directions of the impulses are symbolised by the lattice. Enlargements or reductions of the field will change the direction of the lattice components to the outside or to the inside - as shown by the small diagonals. The paths of the impulse change correspond-ingly and can always only be passed through at c.
Who does not think of Einstein when he hears the word velocity of light? Who of the “insiders“ does not already suspect that this causal existence of “c“ in the phenomena impulse, conservation of impulse, conservation of angular impulse, inertia, and gravitation could have something to do with the General Theory of Relativity? He suspects correctly - but we are not yet at that stage by far! Because the next thing we will examine is what the whole business of angular impulses has to do with Kepler's laws.
Well, some facts have to be noted down in particular. The rotational velocity is proportional to changes of the radius. The ballet dancer extends his hands and his rotation slows down. But within one unit of time his arms are passing over the same area as before ... and when he retracts his hands he rotates faster, though, but the area covered per unit of time is again the same. When we follow one point of a rotating body and measure the area which the radius covers within a second this area will always remain the same even if we vary the size of the body – only the velocity will change accordingly. A stone tied to a string and spun in a circle is getting faster when we reduce the length of the string while doing so – but the area which the string passes over within one unit of time always remains the same! That has to be expected for we did not change anything in the energy-impulse content (“mass“) of the stone, of course. This connection of the velocity with the radius and with the area covered is called the “law of areas“. And we will learn on the following pages that we already described Kepler’s second law with that...
When we tie two spheres together and make them rotate, we see how they appear to revolve around a mutual centre of gravity in reverse motion. In fact, the movements of the two spheres “depend on” each other in the sense of the word - but in truth there is no centre of gravity. And now we will examine why the sun plays a very similar game with its planets. |