4. A solar system is modelled by 1R3, with a sun at the origin. Let D be R3 with the origin removed. The gravitational force eld exerted by the sun on an object of mass 1 at the point (any, 3) in D is given by 1 :13 FWa=-f y r 2 ' (I+f+) 3 IV (a) [1 mark] Show that F is conservative on R3 (0,0,0). (b) [1 mark] A meteor of mass 1 is travelling in the solar system. At any time time t, the position of the meteor is given by R(t) = (t, t, t2 3). Calculate the work done by the sun on the meteor when 0 S t S 2. (c) [2 marks] This solar system is covered in dust particles, which causes the same meteor as in (b) to gain mass as it travels through the solar system. If m is the mass of the meteor and s is the distance travelled by the meteor, then the rate at which or changes with respect to s at the point (:r, y, z) is given by (on. ;r;,jr,z =:r.. rt.s'( } ) Calculate the total change in the mass of the meteor between t = U and t = 2