On the running down of the motion of the planets
Euler reiterates that if the aether, a subtle matter that fills all of space, has a resistance, then the period times of the planets and comets and the corresponding eccentricities must become smaller; hence, the resistance of the aether should be very small. He points out that as the speed of a planet or comet is decreased by the resistance of the aether, the planet or comet is drawn nearer to the sun by the sun's force while its speed increases. But these two effects of the sun's force should force the planet or comet's distance from the sun, as well as its periodic time, to decrease. Euler also points out that his findings about how the resistance of the aether should affect the planets and comets are consistent with observations. (Based on Eric Aiton's introduction to Opera Omnia Series II, Volume 31.)
Original Source Citation
Opuscula varii argumenti, Volume 1, pp. 285-276.
Opera Omnia Citation
Series 2, Volume 13, pp.195-220.