Question 3 (25 marks) The orbit of a planet around another larger mass body is governed by the following equations in a polar coordinate system (r, 0) der(t) GM de (t) dt2 r2(t) + r(t) (Eq 3.1) dt and de r2 (t) dt = H (Eq 3.2) where H is a constant. a) Noting that dx dx dy dy d thus dz dz dy show that H d [2] b) Using the substitution Page 4 of 8 TURN OVER ENGS103P Faculty of Engineering Science u(0) = 1/r show that equation Eq 3.1 can be rewritten as d2 u GM doz + u = - H2 [10]