Question

For a space telescope, such as Hubble or the forthcoming JWST, the desired pointing direction to a new star or planet is specified as a three dimensional "line of sight" vector. To rotate the telescope to the new target, three spinning wheels on the spacecraft, with mutually orthogonal rotation axes, have their rotation rates increased or decreased. Conservation of momentum turns the spacecraft as the wheel speeds are changed. To accomplish the reorientation, two things must be computed: 1) the angle 0 through which the telescope must be rotated to point at the new target, and a three-dimensional vector r which specifies the required braking or acceleration of the individual wheel speeds. Given the current and desired line of sight vectors, c and d respectively, we can compute theta = cos^1 (c d) t = (c times d)/sin (theta) where c = c/||c|| and d = d/||d|| are unit vectors along the current and desired line of sight direction respectively. Note the equation for 0 uses the dot product of these two unit vectors, while the equation for r uses their cross product. Write a script called Hubble. m which will compute and display the required values for theta (in degrees) and r based upon vectors c and d that have been defined in the workspace. Reference values: if c has components 1. -1, and 1. while d has components 2, 0. 0, then theta - 54.74 degrees and t has components 0, Squareroot 2/2, Squareroot 2/2. Use column vectors for c and d.

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