Introduction to Geometry on the Celestial Sphere

The celestial sphere is an imaginary sphere of unit radius centered on the observer, used to represent directions in space. It comes from classical observational astronomy and is far older than almost any other modern astronomical concept The compelling image of the bowl of the sky at night makes it easy to think of stars and planets moving on a fixed, distant sphere. We now know, of course, that their distances from us are vastly different But the concept of watching and computing the position and motion of things on the unit celestial sphere remains a very valuable contribution of classical astronomy to modem spaceflight analysis. Unfortunately, relatively few modern references are available. By far, the most detailed treatment is provided by Wertz [2001]. Green [1985], and Smart [1977] provide information on spherical astronomy.

Figure 5-3 illustrates the use of the celestial sphere to represent directions to objects in space. These objects may be very close, such as other components of the spacecraft,

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