#####MATLAB##########

1. (Satellite Orbit, 25 pts) The initial value problem (IVP) below simulates the trajectory of a small satellite in the Earth-moon system, where all orbits lie in a plane C 2 22(0) 0, x (0) 2.0015851063790825. where. 0Stb- 17.06521656015796. = 0.012277471. *-1-. 213/2 12.213/2 The mass of the satellite is neglected. The coordinate system moves so that the origin is the center of mass of the Earth and moon, and it rotates so that the Earth and moon lie on the 1 axis a distance 1 apart (the Earth is just left of the origin, and the moon is just left of (1,0) The constants are chosen so that x(b) = x(0) (a) Use the ode45 function to calculate one period of the orbit for each of the relative error tol- erances of 10-2 . 10. 10-6. Create a phase port rait of x2 vs. x 1 for each case. Try setting the OutputFcn of the options structure toodephas2 (i.e. options = odeset('OutputFCn,,@odephas2)) and then passing this into the ode45 function to "animate" the orbit 1. (Satellite Orbit, 25 pts) The initial value problem (IVP) below simulates the trajectory of a small satellite in the Earth-moon system, where all orbits lie in a plane C 2 22(0) 0, x (0) 2.0015851063790825. where. 0Stb- 17.06521656015796. = 0.012277471. *-1-. 213/2 12.213/2 The mass of the satellite is neglected. The coordinate system moves so that the origin is the center of mass of the Earth and moon, and it rotates so that the Earth and moon lie on the 1 axis a distance 1 apart (the Earth is just left of the origin, and the moon is just left of (1,0) The constants are chosen so that x(b) = x(0) (a) Use the ode45 function to calculate one period of the orbit for each of the relative error tol- erances of 10-2 . 10. 10-6. Create a phase port rait of x2 vs. x 1 for each case. Try setting the OutputFcn of the options structure toodephas2 (i.e. options = odeset('OutputFCn,,@odephas2)) and then passing this into the ode45 function to "animate" the orbit