Problem 1 A spacecraft of constant mass m is in orbit about the Sun. It deploys...

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Problem 1 A spacecraft of constant mass m is in orbit about the Sun. It deploys a perfectly reflecting flat solar sail and controls it so that it is always normal to the radius vector from the Sun (see Figure 1). The acceleration due to solar radiation pressure is then a = 2SA r 3 where S is the solar intensity at 1 AU from the Sun, A is the sail area, and c is the speed of light in vacuum. a) Show that the equation of motion of the spacecraft is 2SA r + = 0. Problem 1 A spacecraft of constant mass m is in orbit about the Sun. It deploys a perfectly reflecting flat solar sail and controls it so that it is always normal to the radius vector from the Sun (see Figure 1). The acceleration due to solar radiation pressure is then a = 2SA r 3 where S is the solar intensity at 1 AU from the Sun, A is the sail area, and c is the speed of light in vacuum. a) Show that the equation of motion of the spacecraft is 2SA r + = 0.