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From spherical triangle SAE, we have coti{/sini]=cot4>sinA+cosi]CosA (11-42)

which yields

From Eq. (11-54) to be derived later, we have

Substituting Eqs. (11-42) and (11-43) into Eq. (11-41), we obtain

IsinfrlVcos^ + cot2^

Because of the Sun/Earth symmetry in Fig. 11-15, d^ also can be expressed in terms of i) and A as

Note that 0 when 2 = /3=90° or when A = i)=90°, i.e., when the attitude is at the null. If we define { as the arc-length separation between the attitude and the null (Sun-Earth cross product), then Eqs. (11-44) and (11-45) can be reformulated as

0 0

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