## Ith Disk At Time Of Outtriqqerino

Fig. 11-3. Earth-Width Corrections Caused by Orbital Motion of the Spacecraft Between Times of In-crossing Observation and Out-crossing Observation. (Motion is greatly exaggerated.)

fictitious value, 8'= 8 — AQ. Because the horizon vectors for each of the four crossing events in Fig. 11-3 may be calculated (given an a priori attitude and Earth model), utility routine PHASED (Section 20.3) may be used to compute AO. Q' is the width that would have been observed for a spherical Earth of radius p, fixed'at its position at time t, and may be used to obtain an accurate attitude solution. For a spin-stabilized spacecraft, the spin axis attitude is completely described by its right ascension and declination. However, for some spacecraft, a knowledge of the pointing direction of a particular body fixed vector, X, may be required. The azimuth angle measures the rotation of this body vector about the spin axis. For spinning spacecraft with Sun or Earth sensors, this azimuth angle is effectively measured with every sensor triggering. Thus, the calculation of an azimuth angle is trivial.

### 11.12 Specific Solution Methods

The attitude determination methods described below all use the procedures for case (a), case (b), or some multiple-step combination of these. The reference vectors are arbitrary, but for convenience, we will use the Sun vector and the nadir vector throughout. For a spacecraft equipped with one Sun sensor and two Earth sensors mounted at different angles from the spin axis and capable of simultaneous operation, six attitude determination methods may be used:

1. Earth-width/Sun angle method

2. Dual Earth-width/Sun angle method

3. Earth midscan rotation angle/Sun angle method

4. Earth-width/Earth midscan rotation angle method

5. Dual Earth-width/Earth midscan rotation angle method

6. Single horizon rotation angle/Sun angle method

Each of these is described below. Figure 11-4 summarizes the geometry and epm6meris sensor sensor quantities alignments 08ssrvablcs

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