The elements of astronomy; a textbook . wo angles OBMand OCM, each of which isthe supplement of the moonsgeocentric zenith distance atB and C respectively. Theangle BOC, at the centre ofthe earth, is the differenceof the geocentric latitudes ofthe two observatories (numeri-cally, their sum). Moreover, the sides BO and CO are known, being radii of the quadrilateral can, therefore, be solved by a simple trigonometricalprocess,1 and we can find the line MO. Knowing MO and OK, theradius of the earth, the horizontal parallax, OMK, follows at once. 1 The solution is effected as follows: (1
The elements of astronomy; a textbook . wo angles OBMand OCM, each of which isthe supplement of the moonsgeocentric zenith distance atB and C respectively. Theangle BOC, at the centre ofthe earth, is the differenceof the geocentric latitudes ofthe two observatories (numeri-cally, their sum). Moreover, the sides BO and CO are known, being radii of the quadrilateral can, therefore, be solved by a simple trigonometricalprocess,1 and we can find the line MO. Knowing MO and OK, theradius of the earth, the horizontal parallax, OMK, follows at once. 1 The solution is effected as follows: (1) In the triangle BOC, we havegiven BO, OC, and the included angle BOC. Hence we can find the sideBC, and the two angles OBC and OCB. (2) In the triangle BCM, BCis now known, and the two angles MBC and MCB are got by simply sub-tracting OBC from OBM, and OCB from OCM: hence we can find BMand CM. (3) In the triangle OBM, we know OB, BM, and the includedangle OBM, from which we can find OM, the moons distance from thecentre of the Fig. 30. — Determination of the Moons Parallax. 96 PARALLAX, DISTANCE, AND VELOCITY. [§150 150. Parallax, Distance, and Velocity of the Moon. — The moons equatorial horizontal parallax is found to (57 ), according to Neison, but varies consider-ably on account of the eccentricity of the orbit. With thisvalue of the parallax we find that the moons average distancefrom the earth is about times the earths equatorialradius, or 238,840 miles, with an uncertainty of perhaps 20miles. The maximum and minimum values of the moons distance aregiven by Neison as 252,972 and 221,614. It will be noted that theaverage distance is not the mean of the two extreme distances. Knowing the size and form of the moons orbit, the velocityof her motion is easily computed. It averages 2287 miles anhour, or about 3350 feet per second. Her apparent angularvelocity among the stars is about 33 an hour on the average,which is just a little greater t
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