【大地测量学基础】200602 Earth and Its Motions.ppt

School of Geodesy and Geomatics,WHU 2 Earth and Its Motions Since various kinds of extraterrestrial measurements—such as astronomical (both optical and radio), satellite, and lunar—play a major role in geodesy, it is necessary to develop some understanding of how the earth moves among other celestial bodies. /geog/webasp/vod/play1.asp?id=819 It is known that the earth undergoes the following kinds of motions simultaneously: (a) It moves with our galaxy in respect to other galaxies. (b) It circulates with the solar system within our galaxy. (c) It revolves around the sun, together with other planets. (d) It rotates (spins) around its instantaneous axis of rotation. 2.1 Earth’s annual motion In a description of the annual motion, the dimensions of the earth and other celestial bodies can be regarded as negligible, compared with the dimensions of the solar system. Under these conditions, Keplers three laws apply as follows: (a) The orbit of any planet is an ellipse and the sun (H) stands in one of its foci. (b) A planet moves along its orbit with a constant area velocity; i.e., the area swept by the radius vector of the planet (see FIG. 2.1) is constant for a given time interval. (c) The ratios of squares of orbital periods (m) of the planets and the cubes of lengths of major semi-axes (a0) of their orbits are constant. m2/a03 = const. (2.1) The plane of the earths orbit is called the ecliptic. Because of Keplers second law, the earth moves faster when it is closer to the sun and slower when it is farther away. It completes one revolution (with respect to the stars) in one sidereal year. In reality, the presence of other planets and the moon influence (perturb) the shape of the earths orbit, so it is not exactly elliptical and not even planar. 2.2 Earth’s spin, precession, and nutation In describing the earths spin, the earths dimensions can no longer be neglected. In the next dynamically simplest model, the earth is taken as