4. Dynamics of a Comet's Tail: Cometary nuclei are mountain sized giobs of dust and ice. As the nucleus approaches the sun1 the surface iws vaporize and tiny particles of dust and ice are blown off to form the brilliant cometary tail (g 5). @MTMIRAN '_:_" 0".\" if!" I 'I ' 3; .. -_ Figure 5: The Bayeux tapestry depicting the appearance of Halley's comet in 1066 before the Battle of Hastings. (a) Let L denote the total power radiated by the sun. Calculate I, the intensity of sunlight, at a distance R from the sun. [Hint L is the total energy per second radiated by the sun. The intensity is the energy per second per unit area. To calculate the intensity imagine that the sun is surrounded by a sphere of radius R. How much energy passes this sphere per second? How much energy passes the sphere per second per unit area?] (b) Model the tail particles as dark spheres of radius T which completely absorb all incident solar radiation (together with the field momentum it carries). Calculate the magnitude of the force exerted by solar radiation on the tail particles. Give your answer in terms of L, R, r and c = speed of light. [Hint- The force is the radiation pressure of sunlight multiplied by the cross section area of the tail particles] (c) Calculate the radius of a dust particle for which radiation pressure forces precisely balance the sun '3 gravitational attraction. Give your answer in terms of G = Newton's constant of gravitation. M = mass of the sun. p = density of silicate dust. c and L. (d) Particles of radius smaller than the critical value calculated in part (c) will be blown outward by radiation pressure. Calculate the critical radius in pm. Take ,0 = 2.5 x103 lcg/m3 and L =4 x 1026 W. Also M = 2 x 10'\" kg, C: 3.0 x103 m/s1 and G= 6.67 x 10'1| 5.1. units