. Elements of theoretical and descriptive astronomy, for the use of colleges and academies. period is longer than the sidereal period, as maybe seen in Fig. 55. Let S be the sun, E theearth, and MANB the or-bit of the moon. Let themoon be at M, in conjunc-tion with the sun. As themoon moves about E inthe curve MANB, thuearth also moves about thesun in the direction next conjunction willtherefore not occur until themoon reaches M. Now,rig. 55. if through Ef we draw the line MN parallel to MN, the sidereal period of the moon iscompleted when the moon reaches M. The synodical period isthe?
. Elements of theoretical and descriptive astronomy, for the use of colleges and academies. period is longer than the sidereal period, as maybe seen in Fig. 55. Let S be the sun, E theearth, and MANB the or-bit of the moon. Let themoon be at M, in conjunc-tion with the sun. As themoon moves about E inthe curve MANB, thuearth also moves about thesun in the direction next conjunction willtherefore not occur until themoon reaches M. Now,rig. 55. if through Ef we draw the line MN parallel to MN, the sidereal period of the moon iscompleted when the moon reaches M. The synodical period isthe?efore greater than the sidereal period by the time requiredby the moon to pass through the angle MEM. This angle isevidently equal to the angle ESE, which is the angular advanceof the earth in its orbit in the period of one synodical revo-lution of the moon. In one lunar month, then, the angular ad-vance of the moon in its orbit is greater by 360° than the angu-lar advance of the earth in its orbit. If, therefore, we denotethe moons sidereal period in days by P, its synodical period by. SIDEREAL AND SYNODICAL PERIODS. 129 S, and the earths sidereal period, or one sidereal year, by T, weshall have, ~L = the earths daily angular velocity,360° —p- = the moons daily angular velocity,360° —^- = the moons daily angular gain on the earth. Hence we shall have, 360° _ 360° _ 360^.P T 8 9 . p- ST S+T The sidereal peiiod of the moon is therefore obtained by mul-tiplying the sidereal year by the mocks synodical period, anddividing the product by the sum of the sidereal year and thesynodical period. 142. Values of the Synodical and Sidereal Periods.—The valueof the synodical period is not constant, but varies from monthto month. A mean value may, however, be obtained by divid-ing the interval of time between two oppositions, not consec-utive, by the number of synodical revolutions in that , the day, the hour, and even the probable minute, at whichan opposition to the
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