One option when traveling to Mars from the Earth is to use a Hohmann transfer orbit like t...

One option when traveling to Mars from the Earth is to use a Hohmann transfer orbit like that described in Probs. 5.105–5.109. Assuming that the Sun is the primary gravitational influence and ignoring the gravitational influence of Earth and Mars (since the Sun accounts for 99.8% of the mass of the solar system), determine the change in speed required at the Earth Δve (perihelion in the transfer orbit) and the required change in speed at Mars Δvm (aphelion in the transfer orbit) to accomplish the mission to Mars using a Hohmann transfer. In addition, determine the amount of time τ it would take for orbital transfer. Use 1.989×1030 kg for the mass of the Sun, assume that the orbits of Earth and Mars are circular, and assume that the changes in speed are impulsive, that is, they occur instantaneously. In addition, use 150 × 106 km for the radius of Earth’s orbit and 228 × 106 km for the radius of Mars’ orbit.

Figure P5.111