Problem 1: Describe the motion of a planet for each of the following sets of initial condition. The sun is assumed to be at the origin and its motion is not considered. The only force involved being the force of gravitation. Assuming G m_1 = 1, where G is gravitation constant & m_1 is the mass of sun, one can avoid dealing with astronomical magnitudes for positions
(i) x_0 = 0.5 ; y_0 = 0.0 ; v_ 0,x = 0.0 ; v_ 0,y = 1.63Problem 2.(ii) x_0 = 0.5 ; y_0 = 0.0 ; v_ 0,x = 0.0 ; v_ 0,y = 1.80
(iii) x_0 = 0.5 ; y_0 = 0.0 ; v_ 0,x = 0.0 ; v_ 0,y = 1.40
(iv) x_0 = 0.5 ; y_0 = 0.0 ; v_ 0,x = 0.50 ; v_ 0,y = 1.80
(v) x_0 = 0.5 ; y_0 = 0.0 ; v_ 0,x = -0.50 ; v_ 0,y = 1.40
(vi) x_0 = 0.5 ; y_0 = 0.50 ; v_ 0,x = -0.50 ; v_ 0,y = 0.50