Page:Das Relativitätsprinzip und seine Anwendung.djvu/8

 sign, it is much too great to be explained by those supplementary terms. It is rather explained by as due to a disturbance of the carrier of the zodiacal light, whose mass one can conveniently determine in a plausible way. From that, no decision can be gained as long as the precision of astronomical measurements is not essentially increased. At absolute precision, also the difference between the "proper time" of earth and the time of the solar system has to be considered.

Another method to test the correctness of the modified law of gravitation, can be based upon a procedure proposed by for the decision, as to whether the solar system is moving through the aether. If this is the case, then the eclipses of the satellites of Jupiter, depending on the location of these planets with respect to Earth, must suffer earlinesses or delays.

If the distance Jupiter-Earth is $$a$$ and the velocity component of the solar system in the aether in the direction of the connecting line Jupiter-Earth is $$v$$, then the time $$\frac{a}{c}$$ which would be required by light (in the case of rest) to traverse distance $$a$$, is transformed into $$\frac{a}{c\pm v}$$; thus an earliness or a delay occurs due to motion, which amounts to $$\frac{av}{c^{2}}$$ up to terms of second order, and which attains different values, depending on the value of velocity component $$v$$, which indeed depends on the location of both planets. Now it is clear, that such a dependency of the phenomena from the motion through the aether contradicts the relativity principle.

To solve this contradiction, we want to simplify the state of facts in a schematic way. We imagine, that sun $$S$$ shall have a mass which is infinitely great in relation to that of the planets. Let the velocity of the solar system coincide with the $$z$$-axis, which we let go through the sun. The intersections of the orbit of the planets with the $$z$$-axis, is denoted by us as the upper and lower transit $$A$$ and $$B$$.

We place the observer upon the sun. At every transit of the planet through the $$z$$-axis, a light signal shall be traveling to the sun. Let $$T$$ be the orbital period. When the sun is at rest, the time between the upper and lower transit will amount to $$\frac{1}{2}T$$ (at a motion being presupposed as circular); the same is true for the time between the arrival of