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Derivation of the "absolute" earth movement from observed lengths of Jupiter’s satellites

-      Leopold Courvoisier -

Sternwarte Berlin-Babelsberg, 1930, April 27.

    From my previous studies on the movement of the earth relative to the light aether (s. AN5416, etc.) it can be seen that the target point of the general translation movement found is not far from the ecliptic (A = 80 deg., D = +40 deg.) and the speed (v = 500km / s) is a very substantial one. Accordingly, the maximum difference in light time (t = v / c) for appearances on the Jupiter satellites (e.g. eclipses) would be, like K.F. Bottlinger noted years ago (AN 5051), principally to determine the "absolute" solar and Earth movement, respectively, approximately = 7s (= 2r  x v / c) depending on Jupiter during the observation geocentrically near the apex or anti-apex of translation; in the first case the light time was shortened by about 3.5s, in the second case by just as much. The question now is whether the accuracy of the existing satellite observations is sufficient for such a determination. After the in-depth discussions that D. Brouwer (1) and W. de Sitter (2) had on older and newer observation material, at least an attempt had to be made from the outset to evaluate the most homogeneous, modern observation series, some (A) of those carried out in Johannesburg Eclipse observations from 1908 to 1926 (and only the entries and exits, arranged by Brouwer and (B) the photographic records (arranged by: de Sitter) obtained at the Cape, in Greenwich and Leiden from 1913 to 1924, appear to be worthwhile in the aforementioned respects and was therefore undertaken by me as follows.

    A brief overview of the series of annual averages of the residual values ​​of the observed satellite lengths given in the two sources, which remain in comparison with the latest orbital theory, has at least consistently identified a pronounced wave in the three inner satellites, which is of approximately twelve-year period and which, in terms of phase and amplitude, also corresponds sufficiently close to the expected fluctuation in light time. Since such a phenomenon cannot be satisfactorily explained by any of the previously known inequalities in the length of the Jupiter satellites, since (according to de Sitter) on the one hand the period of the vibration is only about 6 years, but that of the secular inequalities on the other hand exceeds 12 years, there is nothing in the way of actually viewing it as a periodic change in the time of light caused by the "absolute" movement of the earth and the solar system, respectively, the period of which is Jupiter's orbit.


    If one calls aJupiter the respective opposition right ascension of Jupiter, A the right ascension of the apex of the "absolute" movement, y the amplitude of the long light-time fluctuation, expressed in time seconds, respectively, then the latter in our case can be reasonably approximated by a sine wave representation, which results in the following form of the condition equations:


                        Rest(s) = x + y cos (aJupiter - A +180 deg)

   The adjustments of the individual remaining series then give values for A and y respectively, the speed component in the Jupiter orbit, which can be compared with my numbers found elsewhere.

    In the tables below, the residual values of longitude that I have summarized for each observed satellite in annual mean, as they emerge from the two observation groups mentioned above, are expressed both in longitude degrees and in time, together with their quadrasums (n, n).

    The tables also contain, in addition to the years of opposition, the approximate opposition right ascension of Jupiter, the number of individual observations in the annual averages, and the residues B-R of the individual sine waves remaining after my adjustments and their sums of squares (dd).



   In the figure, these series of numbers have been shown graphically one after the other for a more convenient overview and, experimentally, have also been compensated graphically by simple lines. The next tables of the random errors of the observations derived from Brouwer and de Sitter provide sufficient information about the expected average accuracy of an individual annual or curve point, respectively. For comparison purposes, the mean errors of the weight unit resulting from my adjustments are also included in these.

    When carrying out the adjustments of the above remaining series for each satellite, the individual annual means were given the same weight, since the situation at the moment can only be a rough calculation. Furthermore, the adjustment of the relatively inaccurate observations of the IV satellite under B., as expected to be useless or delivering values that are too uncertain, has been completely omitted. The adjustments of the six observation series of the three inner satellites then give the numerical values compiled below for the unknowns A and y or v and their approximated mean errors.

    The internal agreement of these values generally corresponds to the calculated random errors. With regard to the error limits, the agreement with the above-mentioned average results ( A=80 deg., D=+40 deg. V = 500 km/s) that I have received so far is for the darkening observations of the I and II and the photographic images of the II and III. To call satellites a complete one, for the final mean at least as good as can be expected given the circumstances, given the possible systematic errors of satellite observations. It must be borne in mind that systematic errors occur all the more easily because the observations on average comprise little more than one Jupiter orbit. In this regard, it would be very desirable for the task dealt with here if these important observations, as well as those of the eclipses (Johannesburg) as well as the photographic images of the satellites, were to be as homogeneous as possible for at least a second, or at least over a second orbit of Jupiter Way could be continued.

L. Couvousier   Sternwarte Berlin-Babelsberg, 1930, April 27.