(a) A particle is dropped (from radius a with zero velocity)into the gravitational potential corresponding to a statichomogeneous sphere of radius a and density Ï. Calculate how longthe particle takes to reach the other side of the sphere. [Hint:the equation of motion is d2r/dt2 =−GM(r)/r2 .]
(b) Calculate the time required for a homogeneous sphere ofradius a and density Ï with no internal pressure support tocollapse to zero radius under its own gravity. [Apply the previousequation of motion to a particle on the surface.]
