A space probe is to be placed in a circular orbit of 9000 km radius about the planet Venus...

A space probe is to be placed in a circular orbit of 9000 km radius about the planet Venus in a specified plane. As the probe reaches A, the point of its original trajectory closest to Venus, it is inserted in a first elliptic transfer orbit by reducing its speed of ΔυA .This orbit brings it to point B with a much reduced velocity. There the probe is inserted in a second transfer orbit located in the specified plane by changing the direction of its velocity and further reducing its speed by ΔυB. Finally as the probe reaches point C, it is inserted in the desired circular orbit by reducing its speed by Δυc. Knowing that the mass of Venus is 0.82 times the mass of the earth, that rA = 15 × 103km and rB = 300 × 103 km, and that the probe approaches A on a parabolic trajectory, determine by how much the velocity of the probe should he reduced (a) at A, (b)at B (c)at C.