350
miles per hour, while those of the Satellites iu their respectiveorbits round Jupiter are,—for the outermost about 18,500 milesper hour;—for the 3rd about 24,500 miles;—for the 2ndabout 31,000 miles;—for the 1st about 39,000 miles. Thetwo innermost will therefore, when new, and in their nearestpositions to the Sun, he really moving backwards in comparisonwith the onward motion of Jupiter.* This may be seen bya comparison of the arrows which refer to Jupiter , and to theSatellites respectively, in Fig . LXXYIII.
It will be remembered that the velocity of the Earth ’s Moon in space varies so little that it only changes from about 64 to68 thousands of miles per hour, the orbital velocity of theEarth being about 66,000, and that of the Moon around itrather more than 2,000 miles per hour, which latter velocity(see Lecture III., p. 60) is alternately added to and subtractedfrom the former. But the onward velocity of the outermostof Jupiter’s Satellites, when in the position of full moon, willequal the sum of Jupiter ’s orbital velocity of 29,000 miles perhour, and its own velocity of 18,500 miles per'hour roundJupiter ; while as a new moon its onward speed will only beequal to the difference of the same two velocities. It willtherefore vary from about 47,500 miles to about 10,500 milesper hour. In like manner, that of the 3rd will vary from53,500 miles to about 4,500 miles per hour; while, as we havejust remarked, the 2nd will have an onward velocity of 60,000miles as a full moon, changed to a retrograde velocity of about2,000 miles per hour as a new moon ; and the 1st will changean onward velocity of 68,000 miles for a backward velocity ofabout 10,000 miles per hour, when similarly situated.
It results that the path iu space of the 4th Satelliteduring one of its months of about 16f days is as shown inFig . LXXX.; and that of the 1st, during its much shortermonth of about 42£ hours, as in Fig. LXXXI.; the formerpath having its convexity towards the Sun when the Satelliteis a new moon \ while the path of the latter, under similar
* The only other Satellites for which this is also the case are the fourinnermost of Saturn.