A deep space probe mission is planned to explore the composition of interstellar space. Assuming the three most important objects in the solar system for this project are the Sun, the Earth, and Jupiter,
(a) what would be the distance of the Earth relative to Jupiter that would result in the lowest escape speed needed if the probe is to be launched from the Earth: (1) the Earth should be as close as possible to Jupiter, (2) the Earth should be as far as possible from Jupiter, or (3) the distance of the Earth relative to Jupiter doesn’t matter?
(b) Estimate the least escape speed for this probe, assuming planetary circular orbits, and only the Earth, Sun, and Jupiter are important. (See data in Appendix III.) Comment on which of the three objects, if any, determines most of the escape speed.