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spacecraft nutation

Fig. 16-11. Body-Fixed Celestial Sphere Showing Change in Measured Spin Period From the Observation of Sun Sighting limes for a Symmetrical Nutating Spacecraft See text for explanation.

¿2. We wish to examine the rotation of the body coordinate system relative to the inertial coordinate system defined by L and S. At time /,, the x axis is in the L—S plane. At time t2, it is past the L-S plane by the angle a. Thus, because of the change in the orientation of the body coordinate system relative to the inertial coordinate system, it has rotated through more than 360 deg to pick up the Sun again and the measured spin period is greater than the true spin period. Similarly, when L is to the left of center in Fig. 16-11, the measured spin period will be less than the true spin period. (Gearly, over a long term the average measured spin period must be close to the true spin period.) The spin period oscillation has the same period as L in the spacecraft frame.

For a symmetric spacecraft and small nutation angles, we can express 9 as a function of J, j8, and the variation in the spin period, bP, defined by

where Pmax is the maximum measured period, and P^ is the minimum measured period. As shown below, the desired relation is

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