use python to code this problem. This task requires physics and computer science knowledge.

F=Gr2Mmr^ between them. Here G=6.6741011Nm2/kg2 is the gravitational constant and r the distance between the two bodies. r^ is a unit vector connecting the two bodies. Here we are interested in simulating the motion of bodies due to the gravitational force in two dimensions. (a) (20 pts) Write a Python program using Numpy arrays and the velocity Verlet algorithm to simulate the motion of ten probes in the gravitational field of the sun with mass M=21030 kg. The sun is placed at position x=y=0 and we assume that the probes have such a small mass m that they do not affect the suns position, i.e., the position of the sun is stationary 1 during the simulation. The probes are initially all at the position x=150109m and y=0. We want to understand, how differences in the initial velocities of the probes affect their trajectories. We therefore consider a distribution of velocities around vx=0 and vy=30,000 m/s. To do so, we add to these velocities random components which can be obtained by using the numpy.random.rand() function. For example, the distribution of velocities in x and y direction could have a width of 20,000m/s centered around the velocities above, i.e., vx[10000,10000] and vy[20000,40000]. Plot the trajectories of the probes. [Hint: The distance is given by r=x2+y2 and the x-component of the force is therefore given by Fx=Gr3Mmx and similarly for the y-component.] (b) (10 pts) Run your program for different velocity distributions. What different types of trajectories can you identify