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 ofgravitational and radiation forces. Let MsMsM = 2.1×1032kgkg be the mass of the star, and PsPsP = 5.9×1028 WW bethe 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 oflight ccc = 3×108 m/sm/s  in the followingquestions.
a)What is the intensity of the star's electromagnetic radiationat the position of the object? Express your answer in unitsof W/m22.
b) What is the average radiation forceFradFradF on the object if all the incoming light is absorbed byit? Express your answer in units of Newtons. Payattention to the fact that the radiation pressure acts effectivelyon the cross-sectional area of the object facing thestar.
c)What is the magnitude of the gravitational acceleration agagaof the object due to the star? (Recall Phys.101) Expressyour answer in units of m/s22.
d)Find the mass density (mass/volume) of theobject if it is in equilibrium under radiation and gravitationalforces. Express your answer in units ofg/cm33.
e)Another spherical object with the samedensity is located at a distance 2d2d from the star. If it is alsoin a similar equilibrium, what is its mass in terms of mm?
