IV-D:      In homework I-D, we considered the problem of a rocket which left the earth by accelerating straight up (antiparallel to g) until it reached earth escape velocity. A more energy-efficient approach to interplanetary travel is to coast from one orbit to another. Suppose that a space vehicle is already in orbit around the sun in the same orbit as the earth, semimajor axis a_E = 150 million km, and is far enough from the earth that the Sun's gravity dominates. Using the approximation that the eccentricity of both Earth and Mars is roughly zero, calculate the minimum increase in velocity needed to enter an elliptic orbit which intersects the orbit of Mars, a_M = 228 million km. Also calculate the duration of the journey. Express answers in terms of periods and a values, and also give numerical values.