Question: suppose that you are a spacecraft engineer and wish to...
Suppose that you are a spacecraft engineer and wish to send a spacecraft to Mercury's orbit (0.35 AU) from an orbit around the Sun at 1 AU, the same as Earth. Assume that the initial orbit around the Sun is circular and neglect all other gravitational forces aside from that of the Sun.
A. Draw a diagram sketching the orbits of Earth, Mercury, and the required elliptical Hohmann transfer orbit to achieve the goal. Indicate on this diagram the direction of the two burns (or delta v's) that are needed at the two end points of the transfer orbit. It might also be useful to indicate, with words, whether spacecraft must speed up or slow down at these two points.
B. Determine the magnitude of the change in velocity needed at the first of these burns, in going from an orbit at 1 AU to the required elliptical transfer orbit.
C. How long will it take to get to Mercury?
D. Suppose you wish to send another spacecraft to Jupiter (5.2 AU) using a Hohmann transfer orbit. Repeat part B for this case (i.e. what is the delta v for the first burn)? Compare your answer to that in part b, and comment on whether this agrees with your intuition.