Consider Iron asteroid (density 7900 kg/m^3) shaped like a cylinder 5.0 km long and 3.0 km in diameter. Imagine that we hollow it out so that what remains is a canlinke shell 100 m thick. The spin rate required to give an effective gravitational force of at least one-half of what one experience on earth turns out to be about 1 revolution per 100 s for an asteroid of this size. We are going to spin up the asteroid using two rocket engines attached on opposite sides of the asteroid's equator(considering the asteroid's flat ends to be its poles). These advacned nuclear rocket engines deliver an impulse per unit mass of 20,000 m/s.
1. How much fuel is required to spin up the asteroid?
2. How large is the mass of this fuel compared to the mass of the hollowed-out asteroid?