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A spherical object with a radius rrr = 4.2×10−7 mm  and mass m is in...

A spherical object with a radius rrr = 4.2×10−7 mm  and mass m is in equilibrium at a distance ddd = 9.1×1012 mm  from a star due to the cancellation of gravitational and radiation forces. Let MsMsM = 2.1×1032 kgkg be the mass of the star, and PsPsP = 5.9×1028 WW be the total average power radiated by it uniformly in all directions. You will also need the gravitational constant GGG = 6.7×10−11 Nm2/kg2Nm2/kg2  and the speed of light ccc = 3×108 m/sm/s  in the following questions.

a)What is the intensity of the star's electromagnetic radiation at the position of the object? Express your answer in units of W/m22.

b) What is the average radiation force FradFradF on the object if all the incoming light is absorbed by it? Express your answer in units of Newtons. Pay attention to the fact that the radiation pressure acts effectively on the cross-sectional area of the object facing the star.

c)What is the magnitude of the gravitational acceleration agaga of the object due to the star? (Recall Phys.101) Express your answer in units of m/s22.

d)Find the mass density (mass/volume) of the object if it is in equilibrium under radiation and gravitational forces. Express your answer in units of g/cm33.

e)Another spherical object with the same density is located at a distance 2d2d from the star. If it is also in a similar equilibrium, what is its mass in terms of mm?

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genius_generous answered 2 years ago
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