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 s speed of ?vA . 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 B ?v . Finally, as the probe reaches point C, it is inserted in the desired circular orbit by reducing its speed by C ?v . Knowing that the mass of Venus is 0.82 times the mass of the earth, that rA = 15 × 103 km 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 be reduced(a) at A,(b) at B,(c) at C.

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Approach trajectory Second transfer orbit 9000 km Circular orbit- First transfer orbit