Apoint mass- half the mass of the earth is initially located at an altitude - the radius of the earth. the gravitational interaction between the point mass and the earth pulls them toward each other. let the initial velocities of both bodies were zero given mass of earth-6 x1024kg, radius of the earth-6.4x106m, the universal gravitation constant g-6.67x10-11n-m/kg2. (a) locate the center of mass (cm) of this system, initially how far is the cm from the center of the earth? (b) what is the speed of each body immediately before impact? (c) how far did the point mass move and how far did the earth move from initial time to impact? (d) set up the newton's second law equation for the point mass and that for the earth using the cm as the origin of your coordinate system (e) the differential equation in (d) is not easy to solve analytically, but you can solve them numerically with a computer. method: you know initial position of both bodies => you can find force acting on the bodies=> you can find the initial accelerations of each body -> to find the position and velocity of each body at small increment of time later, you assume the acceleration is constant during that small time interval=> once you have the new positions, you can find the new values for the forces and accelerations and keep propagating the process. (i will show you the procedure for a similar problem in class) solve the equations numerically and find the time of impact. (you can check how accurate your computer code is by comparing the distance travel by the two bodies from this method with the exact result of part c.