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 5° off its optical line of sight, 𝑆2
, towards 𝑆3
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?
The sensor vector basis, 𝑆𝑖
, the gimbal vector basis, 𝐠𝒊
, and the spacecraft vector basis, 𝐛𝑖
aligned when a = e = 0.
Right-hand rotations define positive displacements of a and e.
At the instant the measurement is taken, a = 30° and e = 30°.
♦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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