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The orientation of a sensor relative to its spacecraft base is given by two angles: azimuth angle, a, and elevation angle, e. The sensor locates a star that is 5Β° off its optical line of sight, 𝑆2 , towards 𝑆3 , as shown in the figure. On-board sensor software computes a unit vector, u, that points to the star. The sensor software outputs components of u in a sensor-tixed basis 𝑆𝑖 . The 𝑆𝑖 based components are sent to the main spacecraft processor along with a and e. a.) What are the components of u in 𝑆𝑖? b.) What is the transformation matrix needed to change from u with components in 𝑆𝑖 to u with components in 𝑏𝑖? c.) What are the components of u in the spacecraft vector basis, 𝑏𝑖? Assume that The sensor vector basis, 𝑆𝑖 , the gimbal vector basis, π π’Š , and the spacecraft vector basis, 𝐛𝑖 ,are all aligned when a = e = 0. Right-hand rotations define positive displacements of a and e. At the instant the measurement is taken, a = 30Β° and e = 30Β°. ♦The elevation axis of rotation is parallel to 𝐠1, and 𝐬1 ♦The azimuth axis of rotation is parallel to 𝐛3 and 𝐠3

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