Consider three gravitationally interacting particles in 2-D space, each with unit mass. To make the notation more compact, We'll represent their x and y posi- tions as the real and imaginary components of a complex number z. By Newton's law of gravitation, the equations describing their motion are 22 21 23 21 zi + |22 21|3" |23 z13 21 - 22 23 - 22 + |21 2213 |23 2213 23/3: 21 23 22 - 23 za + |21 23|3 122 Suppose that the initial conditions are 21(0) = 22(0) = 0.97000436 0.24308753i, 23(0) = 0, zz(0) = 221(0) = 22:0) = -0.93240737 - 0.86473146i. = Solve numerically for the trajectory of the particles from t=0 tot = 7. Plot the particle trajectories in the complex plane. You'll find that all three particles stay on a single oo-shaped curve. In general, integrating the motion of planetary or similar systems over many orbits is a challenging numerical ODE problem. Consider three gravitationally interacting particles in 2-D space, each with unit mass. To make the notation more compact, We'll represent their x and y posi- tions as the real and imaginary components of a complex number z. By Newton's law of gravitation, the equations describing their motion are 22 21 23 21 zi + |22 21|3" |23 z13 21 - 22 23 - 22 + |21 2213 |23 2213 23/3: 21 23 22 - 23 za + |21 23|3 122 Suppose that the initial conditions are 21(0) = 22(0) = 0.97000436 0.24308753i, 23(0) = 0, zz(0) = 221(0) = 22:0) = -0.93240737 - 0.86473146i. = Solve numerically for the trajectory of the particles from t=0 tot = 7. Plot the particle trajectories in the complex plane. You'll find that all three particles stay on a single oo-shaped curve. In general, integrating the motion of planetary or similar systems over many orbits is a challenging numerical ODE