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The expression recapitulates the iterative procedure to a given order. 6 Uses and Limitations of Two and Three-Body Solutions First we illustrate a use for the two-body system, one that has generated billions of dollars of profit for communications satellite corporations. 1 Use of two-body system celestial mechanics The two-body equations of motion suffice for approximate solutions in the presence of a dominating mass and in the absence of major sources of perturbations. For example, consider the case of a synchronous satellite.

31) ζ =z+Z where X, Y , and Z are the rectangular coordinates of the Sun in geocentric equatorial coordinates, tabulated annually in the Astronomical Almanac as quantities labeled “x,” “y,” and “z,” respectively. 34) More detailed treatment can be found in Moulton (1914, pp. , Brouwer and Clemence (1961), Danby (1962/1964; 1988), Neutsch and Scherer (1992), Smart (1953), or Szebehely (1989)], and, in somewhat more abridged but focused discussions, in Montenbruck (1989) or Schlosser et al. (1991/4).

From the horizon to the equatorial system. 753◦ /(15◦ /h) ∼ = −02h 15m = 02h 15m East. 3 What is the angular distance across the sky from Deneb (α Cygni) at α = 20h 40m 24s , δ = +45◦ 10 to Sirius (α Canis Majoris) at α = 6h 43m 48s , δ = −16◦ 41 ? 9 illustrates the (α,δ) equatorial coordinate system, the relevant spherical triangle, and the angles involved. Subscripts D and S signify Deneb and Sirius, respectively. We want to find the arc length of side a. 83◦ There are several ways of expressing the angle A, all of which are equivalent by the fact that cos θ = cos (−θ) = cos (360◦ −θ).

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