A solar sail allows a spacecraft to use…

A solar sail allows a spacecraft to use radiation pressure, instead of rockets, for propulsion (similar to the way wind propels a sailboat). The sails of such spacecraft are usually made out of a large reflecting panel. The size of each panel is maximized to allow the largest possible flux of incident photons, leading to the largest possible total momentum transfer from the incident radiation. Because the surface is reflective, the momentum transferred by the photons is twice what they carry. For such spacecraft to work, the force from the radiation pressure exerted by the photons must be greater than the gravitational attraction from the star providing the photons. The critical parameter turns out to be the mass per unit area of the sail.To solve this problem you will need to know the following:* mass of the sun: M_sun = 2.0*10^30 kg* intensity of sunlight as a function of the distance R from the sun:I_sun(R) = 3.2*10^25(1/R^2) W/m^2and* gravitational constant: G = 6.67*10^-11 m^3(kg.s^2)Suppose that a perfectly reflecting circular mirror is initially at rest a distance R away from the sun and is oriented so that the solar radiation is incident upon, and perpendicular to, the plane of the mirror. What is the critical value of mass/area for which the radiation pressure exactly cancels out the force due to gravity?

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