Chapter 6, Problem 32E

Jump to Jupiter The gravitational potential energy of a 1 kg object is plotted versus position from Earth’s surface to the surface of Jupiter. Mostly it is due to the Sun, but there are downturns at each end, due to the attractions to the two planets.

Make the crude approximation that this is a rectangular barrier of width $6\times {10}^{11}\text{m}$ and approximate height $4\times {10}^8\text{J/kg}$ . Your mass is 65 kg, and you launch yourself from Earth at an impressive 4 m/s. What is the probability that you can jump to Jupiter?