A particle P of mass m moves under the simple harmonic field F = -(mΩ2r)r^, where is a positive constant. Obtain the radial motion equation and show that all orbits of P are bounded. Initially P is at a point C, a distance c from O, when it is projected with speed c in a direction making an acute angle α with OC.
Find the equation satisfied by the apsidal distances. Given that the orbit of P is an ellipse with centre O, find the semi-major and semiminor axes of this ellipse.