The Sun's Motion with respect to the ther

Abstract

Nothwithstanding the well-known principle of relativity, it is theoretically possible to determine the motion of the solar system with respect to the aether from observations of the eclipses of Jupiter's satellites; and the possibility was indicated by Maxwell some 30 years ago. For convenience, the motion of the aether with respect to the sun may be called a wind, and the method proposed is based on the consideration that the tidings of an eclipse will travel towards us more rapidly when the Jovian system is to windward of us than when it is to leeward. The residual discrepancies between the observed and calculated times of eclipses have to be analysed for systematic differences depending on the direction in space of the straight line drawn from the earth to Jupiter, and formulae are given for finding by the method of least squares the most values of a, b1, c1, the components of the Sun's velocity with respect to the aether. The material available is to be found in Prof. R. A. Sampson's discussion of the Harvard photometric eclipse-observations; about 330 eclipses of Jupiter's satellite I being included. In order to obtain a preliminary notion of the accuracy to be expected, a simplified system has been considered in which (for one thing) the eccentricity of the orbits was virtually neglected; and it appears that some advantage is to be gained by taking the plane of Jupiter's orbit, rather than the ecliptic, as one of the coordinate planes. The axis of x is drawn from the Sun's centre through the node of Jupiter's orbit, the axis of y lying also in that orbit, and the axis of z being perpendicular thereto. Taking 4.5 seconds as the probable discrepancy between theory and observation for a single eclipse, the following preliminary estimates are obtained:- Probable error in a = 43.6 km. per second. Probable error in b1 = 45.6 km. per second. Probable error in c1 = 10,000 km. per second. The determination of the component perpendicular to Jupiter's orbit is perhaps too badly conditioned to be worth considering; the two components in the plane of Jupiter's orbit can be much better computed, and even if the velocities found do not exceed the limits of error, an upper limit to the numerical values of those components can be assigned.